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1 Data availability

The manuscript builds on three data sets, two of them are generated by the authors. These two data sets are integrated into this report. They can be extracted by clicking here (Pilot Study) and here (Main Study).

2 Hypotheses

We preregistered our hypotheses prior to data analyses and will repeat them in the following.

2.1 The preregistered Hypotheses

  • Concerning their reasons for trusting educational scientists, teachers will score

    • higher on expertise-related reasons compared to benevolence-related reasons
    • and integrity-related reasons (H1).
  • Concerning their reasons for mistrusting educational scientists, teachers will score

    • lower on expertise-related reasons compared to benevolence-related reasons
    • and integrity-related reasons (H2)
  • Concerning their reasons for trusting scientists in general, teachers will score

    • higher on expertise-related reasons compared to benevolence-related reasons
    • and integrity-related reasons (H3).
  • Concerning their reasons for mistrusting scientists in general, teachers will score

    • lower on expertise-related reasons compared to benevolence-related reasons
    • and integrity-related reasons (H4).
  • Concerning their reasons for trusting scientists in general, a general population sample matched for age and SES will score

    • higher on expertise-related reasons compared to benevolence-related reasons
    • and integrity-related reasons (H5).
  • Concerning their reasons for mistrusting scientists in general, a general population sample matched for age and SES will score

    • lower on expertise-related reasons compared to benevolence-related reasons
    • and integrity-related reasons (H6).

3 Importing the data

library(tidyverse)
library(haven)
data_wb <- read_spss("data/wiss_baro_fr.sav")

data_mtmm <- read_spss("data/data_mtmm_fr.sav")

data_ttest <- read_spss("data/data_ttest_fr.sav")

3.1 Mapping variables to variable names in data_ttest (Main Study)

knitr::kable(tibble(labels = sjlabelled::get_label(data_ttest),
                    names = names(data_ttest)))
labels names
Alter numerisch altq
Welchem Geschlecht ordnen Sie sich zu? d1
F1.1: Politik f1_1
F1.2: Sport f1_2
F1.3: Wissenschaft und Forschung f1_3
F3: Wie sehr vertrauen Sie in Wissenschaft und Forschung? f3
F4.1: Weil Wissenschaftler/innen Experten auf ihrem Feld sind. f4_1
F4.2: Weil Wissenschaftler/innen nach Regeln und Standards arbeiten. f4_2
F4.3: Weil Wissenschaftler/innen im Interesse der Öffentlichkeit forschen. f4_3
F5.1: Weil Wissenschaftler/innen häufig Fehler machen. f5_1
F5.2: Weil Wissenschaftler/innen oft Ergebnisse ihren eigenen Erwartungen anpassen. f5_2
F5.3: Weil Wissenschaftler/innen stark abhängig von ihren Geldgebern sind. f5_3
F8: Wie sehr vertrauen Sie in Bildungswissenschaften und Bildungsforschung? f8
F9.1: Weil Bildungswissenschaftler/innen Experten auf ihrem Feld sind. f9_1
F9.2: Weil Bildungswissenschaftler/innen nach Regeln und Standards arbeiten. f9_2
F9.3: Weil Bildungswissenschaftler/innen im Interesse der Öffentlichkeit forschen. f9_3
F10.1: Weil Bildungswissenschaftler/innen häufig Fehler machen. f10_1
F10.2: Weil Bildungswissenschaftler/innen oft Ergebnisse ihren eigenen Erwartungen anpassen. f10_2
F10.3: Weil Bildungswissenschaftler/innen stark abhängig von ihren Geldgebern sind. f10_3
Berufsjahre berj

4 Descriptive overview Pilot Study

# Define misc skimming functions
library(skimr)
skewn <- function(x) DescTools::Skew(x, na.rm = T)
kurto <- function(x) DescTools::Kurt(x, na.rm = T)
maxabszvalue <- function(x) max(abs(scale(na.omit(x))))
my_skim <- skim_with(numeric = sfl(skewn, kurto, maxabszvalue))

data_mtmm%>%
  skim()
Data summary
Name Piped data
Number of rows 504
Number of columns 29
_______________________
Column type frequency:
numeric 29
________________________
Group variables None

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
reas_exp 18 0.96 4.06 0.86 1 4 4.0 5 5 ▁▁▃▇▇
reas_int 19 0.96 4.04 0.87 1 4 4.0 5 5 ▁▁▃▇▇
reas_ben 17 0.97 3.77 0.92 1 3 4.0 4 5 ▁▂▆▇▅
reas_exp_r 31 0.94 2.78 0.95 1 2 3.0 3 5 ▂▇▇▃▁
reas_int_r 33 0.93 3.15 1.04 1 2 3.0 4 5 ▁▆▇▇▂
reas_ben_r 31 0.94 3.77 0.94 1 3 4.0 4 5 ▁▂▅▇▅
reas_alt_exp 20 0.96 4.13 0.78 1 4 4.0 5 5 ▁▁▃▇▆
reas_alt_int 24 0.95 4.06 0.82 1 4 4.0 5 5 ▁▁▃▇▆
reas_alt_ben 22 0.96 3.74 0.85 1 3 4.0 4 5 ▁▁▆▇▃
reas_alt_exp_r 45 0.91 2.96 0.86 1 2 3.0 3 5 ▁▅▇▂▁
reas_alt_int_r 48 0.90 2.95 0.98 1 2 3.0 4 5 ▁▆▇▅▁
reas_alt_ben_r 32 0.94 3.87 0.93 1 3 4.0 5 5 ▁▁▅▇▅
meti_exp_01 0 1.00 3.93 0.91 1 3 4.0 5 5 ▁▁▅▇▅
meti_exp_02 0 1.00 4.10 0.89 1 4 4.0 5 5 ▁▁▃▇▇
meti_exp_03 0 1.00 4.04 0.90 1 4 4.0 5 5 ▁▁▃▇▇
meti_exp_04 0 1.00 3.97 0.94 0 3 4.0 5 5 ▁▁▃▇▆
meti_exp_05 0 1.00 3.87 0.86 1 3 4.0 4 5 ▁▁▅▇▃
meti_exp_06 0 1.00 4.00 0.88 1 3 4.0 5 5 ▁▁▃▇▆
meti_int_01 0 1.00 3.61 0.83 1 3 4.0 4 5 ▁▁▆▇▂
meti_int_02 0 1.00 3.60 0.84 1 3 4.0 4 5 ▁▁▇▇▂
meti_int_03 0 1.00 3.57 0.82 1 3 4.0 4 5 ▁▁▇▇▂
meti_int_04 0 1.00 3.58 0.83 1 3 4.0 4 5 ▁▁▇▇▂
meti_ben_01 0 1.00 3.45 0.85 1 3 3.0 4 5 ▁▁▇▆▂
meti_ben_02 0 1.00 3.53 0.88 1 3 3.0 4 5 ▁▁▇▆▂
meti_ben_03 0 1.00 3.76 0.90 1 3 4.0 4 5 ▁▁▆▇▃
meti_ben_04 0 1.00 3.40 0.87 1 3 3.0 4 5 ▁▁▇▅▂
education 0 1.00 2.48 0.73 1 2 3.0 3 5 ▂▅▇▁▁
sex 0 1.00 1.50 0.50 1 1 1.5 2 2 ▇▁▁▁▇
age 0 1.00 5.16 1.96 2 3 5.0 7 8 ▆▃▃▃▇
sjlabelled::get_labels(data_mtmm$meti_exp_01)
## NULL

4.1 Correlations (Kendall’s \(\tau\))

4.1.1 Plot

library(corrplot)
## corrplot 0.84 loaded
corrplot(cor(data_mtmm%>%
               na.omit(.),
             method = "kendall"))

4.1.2 Table

reactable::reactable(round(
cor(data_mtmm%>%
      na.omit(.),
    method = "kendall"),
2))

5 Descriptive overview Main Study

5.1 Central tendency, dispersion and distribution shape

data_ttest%>%
  mutate_all(as.numeric)%>%
  my_skim(.)
Data summary
Name Piped data
Number of rows 414
Number of columns 20
_______________________
Column type frequency:
numeric 20
________________________
Group variables None

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist skewn kurto maxabszvalue
altq 0 1.00 47.70 10.82 27 38.25 48.5 57 65 ▅▇▆▇▇ -0.11 -1.15 1.91
d1 0 1.00 1.67 0.47 1 1.00 2.0 2 2 ▃▁▁▁▇ -0.72 -1.49 1.42
f1_1 0 1.00 4.01 0.89 1 3.00 4.0 5 5 ▁▁▅▇▆ -0.69 0.18 3.38
f1_2 0 1.00 2.98 1.27 1 2.00 3.0 4 5 ▅▇▇▆▅ 0.09 -1.03 1.59
f1_3 0 1.00 3.81 0.84 2 3.00 4.0 4 5 ▁▅▁▇▃ -0.25 -0.56 2.16
f3 2 1.00 3.89 0.57 1 4.00 4.0 4 5 ▁▁▂▇▁ -0.40 1.56 5.06
f4_1 1 1.00 4.20 0.64 1 4.00 4.0 5 5 ▁▁▁▇▅ -0.64 1.65 5.01
f4_2 6 0.99 4.06 0.78 1 4.00 4.0 5 5 ▁▁▂▇▃ -0.91 1.48 3.93
f4_3 1 1.00 3.10 0.96 1 2.00 3.0 4 5 ▁▅▇▇▁ -0.15 -0.53 2.18
f5_1 7 0.98 2.44 0.80 1 2.00 2.0 3 5 ▂▇▆▁▁ 0.41 0.22 3.21
f5_2 8 0.98 3.20 0.97 1 3.00 3.0 4 5 ▁▅▇▇▂ -0.24 -0.56 2.28
f5_3 1 1.00 4.07 0.82 1 4.00 4.0 5 5 ▁▁▂▇▅ -0.86 0.76 3.73
f8 2 1.00 3.38 0.78 1 3.00 4.0 4 5 ▁▂▆▇▁ -0.89 0.69 3.04
f9_1 6 0.99 3.63 0.89 1 3.00 4.0 4 5 ▁▂▃▇▂ -0.80 0.53 2.97
f9_2 7 0.98 3.66 0.90 1 3.00 4.0 4 5 ▁▁▃▇▂ -0.93 0.97 2.96
f9_3 3 0.99 3.38 0.98 1 3.00 4.0 4 5 ▁▂▅▇▁ -0.60 -0.24 2.42
f10_1 11 0.97 2.82 0.94 1 2.00 3.0 3 5 ▁▇▇▅▁ 0.28 -0.39 2.31
f10_2 10 0.98 3.51 1.00 1 3.00 4.0 4 5 ▁▃▃▇▂ -0.48 -0.46 2.51
f10_3 8 0.98 3.32 1.14 1 2.00 3.0 4 5 ▁▆▆▇▅ -0.18 -0.93 2.03
berj 0 1.00 17.37 11.13 0 8.00 15.0 26 45 ▇▇▆▅▂ 0.38 -0.87 2.48

5.2 Correlations (Kendall’s \(\tau\))

5.2.1 Plot

corrplot(cor(data_ttest%>%
               select(f3:f5_3, f8:f10_3)%>%
               na.omit(.),
             method = "kendall"))

5.2.2 Table

reactable::reactable(round(
cor(data_ttest%>%
               select(f3:f5_3, f8:f10_3)%>%
               na.omit(.),
             method = "kendall"),
2))

6 Investigating construct validity Pilot Study

6.1 Psychometric properties METI

6.1.1 CFA METI

library(lavaan)
## This is lavaan 0.6-8
## lavaan is FREE software! Please report any bugs.
library(semTools)
## 
## ###############################################################################
## This is semTools 0.5-4
## All users of R (or SEM) are invited to submit functions or ideas for functions.
## ###############################################################################
## 
## Attaching package: 'semTools'
## The following object is masked from 'package:readr':
## 
##     clipboard
meti_mod1 <- 
  "trust =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06 +
            meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04 +
            meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04"
meti_fit1 <- cfa(meti_mod1, 
                data = data_mtmm)
fit1 <- 
  fitmeasures(meti_fit1)[c("chisq", "df", "tli", "cfi", "rmsea", "srmr")]

meti_mod2 <- 
  "exp    =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06
   intben =~ meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04 +
             meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04"

meti_fit2 <- cfa(meti_mod2, 
                data = data_mtmm)
fit2 <- 
  fitmeasures(meti_fit2)[c("chisq", "df", "tli", "cfi", "rmsea", "srmr")]

meti_mod <- 
  "exp =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06
   int =~ meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04
   ben =~ meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04"

meti_fit <- cfa(meti_mod, 
                data = data_mtmm)
fit3 <- 
  fitmeasures(meti_fit)[c("chisq", "df", "tli", "cfi", "rmsea", "srmr")]
Fit-idices of CFA models
Model \(\chi^2\) df p-value TLI CFI RMSEA SRMR \(\chi^2\)-difference Test
one-dim 643.4882662 77 NA 0.8837476 0.9016326 0.1208189 0.0519676
two-dim 276.7440084 74 NA 0.9586698 0.9663909 0.072039 0.0328895
three-dim 267.5517437 76 NA 0.9582621 0.965142 0.0723934 0.0329938

6.1.2 Model comparison

anova(meti_fit1, meti_fit2, meti_fit)
## Chi-Squared Difference Test
## 
##           Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## meti_fit  74 12538 12668 267.55                                  
## meti_fit2 76 12543 12665 276.74       9.19       2    0.01009 *  
## meti_fit1 77 12907 13026 643.49     366.74       1    < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

6.1.3 Reliability METI

semTools::reliability(meti_fit)
##              exp       int       ben
## alpha  0.9222729 0.9013068 0.8781069
## omega  0.9236665 0.9016438 0.8782946
## omega2 0.9236665 0.9016438 0.8782946
## omega3 0.9250794 0.9015949 0.8777437
## avevar 0.6696746 0.6964667 0.6437551

6.2 Convergent validity: Single items trust

6.2.1 Convergent Validity with method factors (UTUM-Model)

utum_trus_mod <- 
  "exp =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06 + reas_exp + reas_alt_exp
   int =~ meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04 + reas_int + reas_alt_int
   ben =~ meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04 + reas_ben + reas_alt_ben
   
   meti =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06 + 
           meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04 +
           meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04

   si =~ reas_exp + reas_alt_exp + reas_int + reas_alt_int + reas_ben + reas_alt_ben

   exp ~~ 0*int + 0*ben
   ben  ~~  0*int
   
   si ~~ 0*meti + 0*exp + 0*int + 0*ben
   meti ~~ 0*exp + 0*int + 0*ben"

utum_trus_fit <- sem(utum_trus_mod, 
                data = data_mtmm,
                missing = "fiml", 
                std.lv = T)
## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negative
fitmeasures(utum_trus_fit)[c("chisq", "df", "tli", "cfi", "rmsea", "srmr")]
##       chisq          df         tli         cfi       rmsea        srmr 
## 647.5301909 150.0000000   0.9144309   0.9324454   0.0811239   0.2283480
semPlot::semPaths(utum_trus_fit)

parameterEstimates(utum_trus_fit, standardized = T) %>% 
  mutate_if(is.numeric, function(x) round(x, 3))
##              lhs op          rhs      est      se       z pvalue ci.lower
## 1            exp =~  meti_exp_01    0.362   0.030  12.228  0.000    0.304
## 2            exp =~  meti_exp_02    0.369   0.033  11.040  0.000    0.303
## 3            exp =~  meti_exp_03    0.355   0.031  11.303  0.000    0.294
## 4            exp =~  meti_exp_04    0.381   0.033  11.546  0.000    0.317
## 5            exp =~  meti_exp_05    0.249   0.033   7.428  0.000    0.183
## 6            exp =~  meti_exp_06    0.480   0.031  15.622  0.000    0.420
## 7            exp =~     reas_exp    0.115   0.034   3.369  0.001    0.048
## 8            exp =~ reas_alt_exp    0.164   0.032   5.062  0.000    0.100
## 9            int =~  meti_int_01   15.361   5.945   2.584  0.010    3.710
## 10           int =~  meti_int_02    0.002   0.001   1.942  0.052    0.000
## 11           int =~  meti_int_03   -0.001   0.001  -0.942  0.346   -0.002
## 12           int =~  meti_int_04    0.001   0.001   1.303  0.192   -0.001
## 13           int =~     reas_int   -0.001   0.001  -1.027  0.305   -0.003
## 14           int =~ reas_alt_int   -0.001   0.001  -1.046  0.296   -0.003
## 15           ben =~  meti_ben_01    0.162   0.040   4.056  0.000    0.084
## 16           ben =~  meti_ben_02    0.172   0.042   4.049  0.000    0.089
## 17           ben =~  meti_ben_03   -0.050   0.040  -1.261  0.207   -0.128
## 18           ben =~  meti_ben_04    0.147   0.043   3.449  0.001    0.063
## 19           ben =~     reas_ben    0.303   0.051   5.958  0.000    0.203
## 20           ben =~ reas_alt_ben    0.416   0.061   6.827  0.000    0.296
## 21          meti =~  meti_exp_01    0.673   0.035  19.479  0.000    0.605
## 22          meti =~  meti_exp_02    0.594   0.036  16.697  0.000    0.524
## 23          meti =~  meti_exp_03    0.624   0.035  17.822  0.000    0.555
## 24          meti =~  meti_exp_04    0.648   0.037  17.663  0.000    0.576
## 25          meti =~  meti_exp_05    0.559   0.034  16.260  0.000    0.492
## 26          meti =~  meti_exp_06    0.583   0.035  16.750  0.000    0.514
## 27          meti =~  meti_int_01    0.710   0.031  23.055  0.000    0.650
## 28          meti =~  meti_int_02    0.704   0.031  22.918  0.000    0.644
## 29          meti =~  meti_int_03    0.669   0.031  21.823  0.000    0.609
## 30          meti =~  meti_int_04    0.671   0.031  21.680  0.000    0.610
## 31          meti =~  meti_ben_01    0.685   0.031  21.930  0.000    0.624
## 32          meti =~  meti_ben_02    0.663   0.033  19.863  0.000    0.598
## 33          meti =~  meti_ben_03    0.749   0.034  22.070  0.000    0.683
## 34          meti =~  meti_ben_04    0.633   0.034  18.765  0.000    0.567
## 35            si =~     reas_exp    0.663   0.035  19.024  0.000    0.595
## 36            si =~ reas_alt_exp    0.559   0.032  17.369  0.000    0.496
## 37            si =~     reas_int    0.691   0.035  19.481  0.000    0.622
## 38            si =~ reas_alt_int    0.600   0.035  17.216  0.000    0.532
## 39            si =~     reas_ben    0.576   0.040  14.488  0.000    0.498
## 40            si =~ reas_alt_ben    0.525   0.038  13.952  0.000    0.451
## 41           exp ~~          int    0.000   0.000      NA     NA    0.000
## 42           exp ~~          ben    0.000   0.000      NA     NA    0.000
## 43           int ~~          ben    0.000   0.000      NA     NA    0.000
## 44          meti ~~           si    0.000   0.000      NA     NA    0.000
## 45           exp ~~           si    0.000   0.000      NA     NA    0.000
## 46           int ~~           si    0.000   0.000      NA     NA    0.000
## 47           ben ~~           si    0.000   0.000      NA     NA    0.000
## 48           exp ~~         meti    0.000   0.000      NA     NA    0.000
## 49           int ~~         meti    0.000   0.000      NA     NA    0.000
## 50           ben ~~         meti    0.000   0.000      NA     NA    0.000
## 51   meti_exp_01 ~~  meti_exp_01    0.212   0.016  13.022  0.000    0.180
## 52   meti_exp_02 ~~  meti_exp_02    0.286   0.021  13.564  0.000    0.245
## 53   meti_exp_03 ~~  meti_exp_03    0.262   0.019  13.724  0.000    0.225
## 54   meti_exp_04 ~~  meti_exp_04    0.283   0.021  13.579  0.000    0.243
## 55   meti_exp_05 ~~  meti_exp_05    0.343   0.023  14.983  0.000    0.298
## 56   meti_exp_06 ~~  meti_exp_06    0.175   0.018   9.651  0.000    0.139
## 57      reas_exp ~~     reas_exp    0.270   0.023  11.483  0.000    0.224
## 58  reas_alt_exp ~~ reas_alt_exp    0.249   0.021  12.050  0.000    0.209
## 59   meti_int_01 ~~  meti_int_01 -235.777 182.634  -1.291  0.197 -593.733
## 60   meti_int_02 ~~  meti_int_02    0.209   0.016  13.312  0.000    0.178
## 61   meti_int_03 ~~  meti_int_03    0.230   0.017  13.731  0.000    0.197
## 62   meti_int_04 ~~  meti_int_04    0.237   0.017  13.797  0.000    0.204
## 63      reas_int ~~     reas_int    0.287   0.026  11.190  0.000    0.237
## 64  reas_alt_int ~~ reas_alt_int    0.321   0.026  12.584  0.000    0.271
## 65   meti_ben_01 ~~  meti_ben_01    0.208   0.017  12.223  0.000    0.175
## 66   meti_ben_02 ~~  meti_ben_02    0.279   0.021  13.258  0.000    0.238
## 67   meti_ben_03 ~~  meti_ben_03    0.261   0.020  12.884  0.000    0.221
## 68   meti_ben_04 ~~  meti_ben_04    0.317   0.023  14.067  0.000    0.273
## 69      reas_ben ~~     reas_ben    0.415   0.036  11.669  0.000    0.345
## 70  reas_alt_ben ~~ reas_alt_ben    0.278   0.046   6.057  0.000    0.188
## 71           exp ~~          exp    1.000   0.000      NA     NA    1.000
## 72           int ~~          int    1.000   0.000      NA     NA    1.000
## 73           ben ~~          ben    1.000   0.000      NA     NA    1.000
## 74          meti ~~         meti    1.000   0.000      NA     NA    1.000
## 75            si ~~           si    1.000   0.000      NA     NA    1.000
## 76   meti_exp_01 ~1                 3.929   0.040  98.915  0.000    3.851
## 77   meti_exp_02 ~1                 4.101   0.039 104.617  0.000    4.024
## 78   meti_exp_03 ~1                 4.036   0.039 102.764  0.000    3.959
## 79   meti_exp_04 ~1                 3.966   0.041  96.682  0.000    3.886
## 80   meti_exp_05 ~1                 3.871   0.038 102.635  0.000    3.797
## 81   meti_exp_06 ~1                 4.000   0.038 104.056  0.000    3.925
## 82      reas_exp ~1                 4.052   0.038 105.516  0.000    3.977
## 83  reas_alt_exp ~1                 4.115   0.035 118.558  0.000    4.047
## 84   meti_int_01 ~1                 3.605   0.037  96.896  0.000    3.532
## 85   meti_int_02 ~1                 3.595   0.037  96.113  0.000    3.522
## 86   meti_int_03 ~1                 3.573   0.037  97.489  0.000    3.502
## 87   meti_int_04 ~1                 3.581   0.037  96.944  0.000    3.509
## 88      reas_int ~1                 4.029   0.040 101.905  0.000    3.951
## 89  reas_alt_int ~1                 4.051   0.037 108.171  0.000    3.977
## 90   meti_ben_01 ~1                 3.450   0.037  92.358  0.000    3.377
## 91   meti_ben_02 ~1                 3.528   0.039  91.560  0.000    3.452
## 92   meti_ben_03 ~1                 3.760   0.040  92.976  0.000    3.681
## 93   meti_ben_04 ~1                 3.401   0.038  88.811  0.000    3.326
## 94      reas_ben ~1                 3.765   0.041  91.043  0.000    3.684
## 95  reas_alt_ben ~1                 3.740   0.039  96.862  0.000    3.664
## 96           exp ~1                 0.000   0.000      NA     NA    0.000
## 97           int ~1                 0.000   0.000      NA     NA    0.000
## 98           ben ~1                 0.000   0.000      NA     NA    0.000
## 99          meti ~1                 0.000   0.000      NA     NA    0.000
## 100           si ~1                 0.000   0.000      NA     NA    0.000
##     ci.upper   std.lv  std.all  std.nox
## 1      0.420    0.362    0.405    0.405
## 2      0.434    0.369    0.419    0.419
## 3      0.417    0.355    0.403    0.403
## 4      0.446    0.381    0.414    0.414
## 5      0.314    0.249    0.294    0.294
## 6      0.540    0.480    0.556    0.556
## 7      0.182    0.115    0.135    0.135
## 8      0.227    0.164    0.213    0.213
## 9     27.013   15.361   18.390   18.390
## 10     0.005    0.002    0.003    0.003
## 11     0.001   -0.001   -0.001   -0.001
## 12     0.003    0.001    0.001    0.001
## 13     0.001   -0.001   -0.001   -0.001
## 14     0.001   -0.001   -0.001   -0.001
## 15     0.240    0.162    0.193    0.193
## 16     0.255    0.172    0.199    0.199
## 17     0.028   -0.050   -0.055   -0.055
## 18     0.230    0.147    0.171    0.171
## 19     0.402    0.303    0.330    0.330
## 20     0.535    0.416    0.488    0.488
## 21     0.741    0.673    0.755    0.755
## 22     0.664    0.594    0.675    0.675
## 23     0.692    0.624    0.707    0.707
## 24     0.719    0.648    0.703    0.703
## 25     0.626    0.559    0.660    0.660
## 26     0.651    0.583    0.675    0.675
## 27     0.771    0.710    0.851    0.851
## 28     0.764    0.704    0.839    0.839
## 29     0.729    0.669    0.813    0.813
## 30     0.732    0.671    0.809    0.809
## 31     0.746    0.685    0.817    0.817
## 32     0.728    0.663    0.766    0.766
## 33     0.816    0.749    0.825    0.825
## 34     0.699    0.633    0.736    0.736
## 35     0.731    0.663    0.780    0.780
## 36     0.622    0.559    0.729    0.729
## 37     0.761    0.691    0.790    0.790
## 38     0.669    0.600    0.727    0.727
## 39     0.654    0.576    0.629    0.629
## 40     0.598    0.525    0.616    0.616
## 41     0.000    0.000    0.000    0.000
## 42     0.000    0.000    0.000    0.000
## 43     0.000    0.000    0.000    0.000
## 44     0.000    0.000    0.000    0.000
## 45     0.000    0.000    0.000    0.000
## 46     0.000    0.000    0.000    0.000
## 47     0.000    0.000    0.000    0.000
## 48     0.000    0.000    0.000    0.000
## 49     0.000    0.000    0.000    0.000
## 50     0.000    0.000    0.000    0.000
## 51     0.243    0.212    0.266    0.266
## 52     0.327    0.286    0.369    0.369
## 53     0.300    0.262    0.338    0.338
## 54     0.324    0.283    0.334    0.334
## 55     0.388    0.343    0.478    0.478
## 56     0.211    0.175    0.235    0.235
## 57     0.316    0.270    0.373    0.373
## 58     0.290    0.249    0.423    0.423
## 59   122.179 -235.777 -337.933 -337.933
## 60     0.240    0.209    0.297    0.297
## 61     0.263    0.230    0.339    0.339
## 62     0.271    0.237    0.345    0.345
## 63     0.337    0.287    0.375    0.375
## 64     0.371    0.321    0.471    0.471
## 65     0.241    0.208    0.296    0.296
## 66     0.320    0.279    0.373    0.373
## 67     0.300    0.261    0.316    0.316
## 68     0.362    0.317    0.429    0.429
## 69     0.485    0.415    0.495    0.495
## 70     0.368    0.278    0.383    0.383
## 71     1.000    1.000    1.000    1.000
## 72     1.000    1.000    1.000    1.000
## 73     1.000    1.000    1.000    1.000
## 74     1.000    1.000    1.000    1.000
## 75     1.000    1.000    1.000    1.000
## 76     4.006    3.929    4.406    4.406
## 77     4.178    4.101    4.660    4.660
## 78     4.113    4.036    4.577    4.577
## 79     4.047    3.966    4.307    4.307
## 80     3.945    3.871    4.572    4.572
## 81     4.075    4.000    4.635    4.635
## 82     4.127    4.052    4.767    4.767
## 83     4.183    4.115    5.362    5.362
## 84     3.678    3.605    4.316    4.316
## 85     3.669    3.595    4.281    4.281
## 86     3.645    3.573    4.343    4.343
## 87     3.654    3.581    4.318    4.318
## 88     4.106    4.029    4.606    4.606
## 89     4.124    4.051    4.907    4.907
## 90     3.524    3.450    4.114    4.114
## 91     3.603    3.528    4.078    4.078
## 92     3.839    3.760    4.141    4.141
## 93     3.476    3.401    3.956    3.956
## 94     3.846    3.765    4.112    4.112
## 95     3.815    3.740    4.388    4.388
## 96     0.000    0.000    0.000    0.000
## 97     0.000    0.000    0.000    0.000
## 98     0.000    0.000    0.000    0.000
## 99     0.000    0.000    0.000    0.000
## 100    0.000    0.000    0.000    0.000

6.2.2 Convergent validity with method factors (CTUM-Model)

ctum_trus_mod <- 
  "exp =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06 + reas_exp + reas_alt_exp
   int =~ meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04 + reas_int + reas_alt_int
   ben =~ meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04 + reas_ben + reas_alt_ben
   
   meti =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06 + 
           meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04 +
           meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04

   si =~ reas_exp + reas_alt_exp + reas_int + reas_alt_int + reas_ben + reas_alt_ben

   si ~~ 0*meti + 0*exp + 0*int + 0*ben
   meti ~~ 0*exp + 0*int + 0*ben"

ctum_trus_fit <- sem(ctum_trus_mod, 
                data = data_mtmm,
                missing = "fiml", 
                std.lv = T)

fitmeasures(ctum_trus_fit)[c("chisq", "df", "tli", "cfi", "rmsea", "srmr")]
##        chisq           df          tli          cfi        rmsea         srmr 
## 424.68914246 147.00000000   0.95126617   0.96229540   0.06122172   0.02881346
semPlot::semPaths(ctum_trus_fit)

parameterEstimates(ctum_trus_fit, standardized = T) %>% 
  mutate_if(is.numeric, function(x) round(x, 3)) 
##              lhs op          rhs    est    se       z pvalue ci.lower ci.upper
## 1            exp =~  meti_exp_01  0.779 0.033  23.720  0.000    0.715    0.844
## 2            exp =~  meti_exp_02  0.712 0.034  21.177  0.000    0.647    0.778
## 3            exp =~  meti_exp_03  0.726 0.034  21.068  0.000    0.659    0.794
## 4            exp =~  meti_exp_04  0.761 0.036  20.963  0.000    0.689    0.832
## 5            exp =~  meti_exp_05  0.628 0.033  18.812  0.000    0.563    0.694
## 6            exp =~  meti_exp_06  0.743 0.038  19.609  0.000    0.669    0.817
## 7            exp =~     reas_exp  0.487 0.037  13.272  0.000    0.415    0.559
## 8            exp =~ reas_alt_exp  0.438 0.033  13.096  0.000    0.373    0.504
## 9            int =~  meti_int_01  0.701 0.033  21.411  0.000    0.637    0.765
## 10           int =~  meti_int_02  0.698 0.033  21.085  0.000    0.633    0.763
## 11           int =~  meti_int_03  0.643 0.035  18.294  0.000    0.574    0.712
## 12           int =~  meti_int_04  0.640 0.037  17.475  0.000    0.568    0.712
## 13           int =~     reas_int  0.459 0.038  12.026  0.000    0.384    0.533
## 14           int =~ reas_alt_int  0.404 0.036  11.207  0.000    0.333    0.475
## 15           ben =~  meti_ben_01  0.679 0.040  17.182  0.000    0.601    0.756
## 16           ben =~  meti_ben_02  0.684 0.036  19.060  0.000    0.614    0.754
## 17           ben =~  meti_ben_03  0.759 0.034  22.237  0.000    0.692    0.826
## 18           ben =~  meti_ben_04  0.627 0.040  15.516  0.000    0.547    0.706
## 19           ben =~     reas_ben  0.423 0.041  10.394  0.000    0.343    0.502
## 20           ben =~ reas_alt_ben  0.432 0.038  11.486  0.000    0.358    0.505
## 21          meti =~  meti_exp_01 -0.047 0.076  -0.615  0.539   -0.195    0.102
## 22          meti =~  meti_exp_02 -0.032 0.070  -0.466  0.641   -0.169    0.104
## 23          meti =~  meti_exp_03 -0.102 0.073  -1.400  0.161   -0.244    0.041
## 24          meti =~  meti_exp_04 -0.119 0.074  -1.610  0.107   -0.264    0.026
## 25          meti =~  meti_exp_05  0.043 0.067   0.632  0.527   -0.089    0.174
## 26          meti =~  meti_exp_06 -0.234 0.076  -3.066  0.002   -0.383   -0.084
## 27          meti =~  meti_int_01  0.150 0.065   2.309  0.021    0.023    0.278
## 28          meti =~  meti_int_02  0.147 0.065   2.251  0.024    0.019    0.275
## 29          meti =~  meti_int_03  0.191 0.065   2.939  0.003    0.064    0.319
## 30          meti =~  meti_int_04  0.222 0.064   3.448  0.001    0.096    0.349
## 31          meti =~  meti_ben_01  0.259 0.072   3.591  0.000    0.118    0.401
## 32          meti =~  meti_ben_02  0.138 0.069   2.011  0.044    0.003    0.273
## 33          meti =~  meti_ben_03 -0.017 0.074  -0.224  0.823   -0.162    0.129
## 34          meti =~  meti_ben_04  0.250 0.063   3.959  0.000    0.126    0.374
## 35            si =~     reas_exp  0.505 0.033  15.177  0.000    0.440    0.570
## 36            si =~ reas_alt_exp  0.421 0.031  13.433  0.000    0.359    0.482
## 37            si =~     reas_int  0.515 0.036  14.406  0.000    0.445    0.585
## 38            si =~ reas_alt_int  0.436 0.035  12.436  0.000    0.367    0.505
## 39            si =~     reas_ben  0.446 0.040  11.278  0.000    0.369    0.524
## 40            si =~ reas_alt_ben  0.374 0.037  10.028  0.000    0.301    0.447
## 41          meti ~~           si  0.000 0.000      NA     NA    0.000    0.000
## 42           exp ~~           si  0.000 0.000      NA     NA    0.000    0.000
## 43           int ~~           si  0.000 0.000      NA     NA    0.000    0.000
## 44           ben ~~           si  0.000 0.000      NA     NA    0.000    0.000
## 45           exp ~~         meti  0.000 0.000      NA     NA    0.000    0.000
## 46           int ~~         meti  0.000 0.000      NA     NA    0.000    0.000
## 47           ben ~~         meti  0.000 0.000      NA     NA    0.000    0.000
## 48   meti_exp_01 ~~  meti_exp_01  0.210 0.016  13.227  0.000    0.179    0.241
## 49   meti_exp_02 ~~  meti_exp_02  0.288 0.020  14.195  0.000    0.248    0.328
## 50   meti_exp_03 ~~  meti_exp_03  0.261 0.019  13.657  0.000    0.224    0.298
## 51   meti_exp_04 ~~  meti_exp_04  0.279 0.021  13.229  0.000    0.238    0.321
## 52   meti_exp_05 ~~  meti_exp_05  0.335 0.023  14.525  0.000    0.290    0.381
## 53   meti_exp_06 ~~  meti_exp_06  0.163 0.022   7.588  0.000    0.121    0.205
## 54      reas_exp ~~     reas_exp  0.261 0.024  10.953  0.000    0.214    0.307
## 55  reas_alt_exp ~~ reas_alt_exp  0.251 0.021  11.992  0.000    0.210    0.292
## 56   meti_int_01 ~~  meti_int_01  0.178 0.013  13.220  0.000    0.152    0.204
## 57   meti_int_02 ~~  meti_int_02  0.197 0.015  13.453  0.000    0.168    0.225
## 58   meti_int_03 ~~  meti_int_03  0.228 0.017  13.551  0.000    0.195    0.261
## 59   meti_int_04 ~~  meti_int_04  0.230 0.018  12.640  0.000    0.195    0.266
## 60      reas_int ~~     reas_int  0.292 0.026  11.308  0.000    0.242    0.343
## 61  reas_alt_int ~~ reas_alt_int  0.329 0.026  12.840  0.000    0.279    0.380
## 62   meti_ben_01 ~~  meti_ben_01  0.195 0.018  10.873  0.000    0.160    0.230
## 63   meti_ben_02 ~~  meti_ben_02  0.282 0.020  13.899  0.000    0.242    0.322
## 64   meti_ben_03 ~~  meti_ben_03  0.240 0.023  10.598  0.000    0.196    0.285
## 65   meti_ben_04 ~~  meti_ben_04  0.301 0.022  13.371  0.000    0.256    0.345
## 66      reas_ben ~~     reas_ben  0.464 0.035  13.408  0.000    0.396    0.532
## 67  reas_alt_ben ~~ reas_alt_ben  0.404 0.030  13.467  0.000    0.346    0.463
## 68           exp ~~          exp  1.000 0.000      NA     NA    1.000    1.000
## 69           int ~~          int  1.000 0.000      NA     NA    1.000    1.000
## 70           ben ~~          ben  1.000 0.000      NA     NA    1.000    1.000
## 71          meti ~~         meti  1.000 0.000      NA     NA    1.000    1.000
## 72            si ~~           si  1.000 0.000      NA     NA    1.000    1.000
## 73           exp ~~          int  0.936 0.016  59.750  0.000    0.906    0.967
## 74           exp ~~          ben  0.884 0.020  44.489  0.000    0.845    0.923
## 75           int ~~          ben  0.974 0.009 107.374  0.000    0.957    0.992
## 76   meti_exp_01 ~1               3.929 0.040  97.424  0.000    3.850    4.008
## 77   meti_exp_02 ~1               4.101 0.040 103.144  0.000    4.023    4.179
## 78   meti_exp_03 ~1               4.036 0.040 101.373  0.000    3.958    4.114
## 79   meti_exp_04 ~1               3.966 0.042  95.355  0.000    3.885    4.048
## 80   meti_exp_05 ~1               3.871 0.038 101.579  0.000    3.796    3.946
## 81   meti_exp_06 ~1               4.000 0.039 102.322  0.000    3.923    4.077
## 82      reas_exp ~1               4.042 0.039 103.385  0.000    3.966    4.119
## 83  reas_alt_exp ~1               4.107 0.036 115.637  0.000    4.037    4.177
## 84   meti_int_01 ~1               3.605 0.037  97.269  0.000    3.533    3.678
## 85   meti_int_02 ~1               3.595 0.037  96.044  0.000    3.522    3.669
## 86   meti_int_03 ~1               3.573 0.037  97.402  0.000    3.502    3.645
## 87   meti_int_04 ~1               3.581 0.037  96.846  0.000    3.509    3.654
## 88      reas_int ~1               4.019 0.040 101.665  0.000    3.942    4.097
## 89  reas_alt_int ~1               4.043 0.037 108.059  0.000    3.969    4.116
## 90   meti_ben_01 ~1               3.450 0.038  91.074  0.000    3.376    3.525
## 91   meti_ben_02 ~1               3.528 0.039  90.320  0.000    3.451    3.604
## 92   meti_ben_03 ~1               3.760 0.040  93.364  0.000    3.681    3.839
## 93   meti_ben_04 ~1               3.401 0.039  87.823  0.000    3.325    3.477
## 94      reas_ben ~1               3.757 0.041  90.773  0.000    3.676    3.838
## 95  reas_alt_ben ~1               3.728 0.039  96.408  0.000    3.653    3.804
## 96           exp ~1               0.000 0.000      NA     NA    0.000    0.000
## 97           int ~1               0.000 0.000      NA     NA    0.000    0.000
## 98           ben ~1               0.000 0.000      NA     NA    0.000    0.000
## 99          meti ~1               0.000 0.000      NA     NA    0.000    0.000
## 100           si ~1               0.000 0.000      NA     NA    0.000    0.000
##     std.lv std.all std.nox
## 1    0.779   0.861   0.861
## 2    0.712   0.798   0.798
## 3    0.726   0.813   0.813
## 4    0.761   0.815   0.815
## 5    0.628   0.734   0.734
## 6    0.743   0.847   0.847
## 7    0.487   0.561   0.561
## 8    0.438   0.557   0.557
## 9    0.701   0.843   0.843
## 10   0.698   0.831   0.831
## 11   0.643   0.781   0.781
## 12   0.640   0.771   0.771
## 13   0.459   0.523   0.523
## 14   0.404   0.489   0.489
## 15   0.679   0.798   0.798
## 16   0.684   0.780   0.780
## 17   0.759   0.840   0.840
## 18   0.627   0.721   0.721
## 19   0.423   0.461   0.461
## 20   0.432   0.505   0.505
## 21  -0.047  -0.051  -0.051
## 22  -0.032  -0.036  -0.036
## 23  -0.102  -0.114  -0.114
## 24  -0.119  -0.128  -0.128
## 25   0.043   0.050   0.050
## 26  -0.234  -0.266  -0.266
## 27   0.150   0.180   0.180
## 28   0.147   0.175   0.175
## 29   0.191   0.232   0.232
## 30   0.222   0.268   0.268
## 31   0.259   0.305   0.305
## 32   0.138   0.158   0.158
## 33  -0.017  -0.018  -0.018
## 34   0.250   0.288   0.288
## 35   0.505   0.582   0.582
## 36   0.421   0.534   0.534
## 37   0.515   0.588   0.588
## 38   0.436   0.528   0.528
## 39   0.446   0.486   0.486
## 40   0.374   0.437   0.437
## 41   0.000   0.000   0.000
## 42   0.000   0.000   0.000
## 43   0.000   0.000   0.000
## 44   0.000   0.000   0.000
## 45   0.000   0.000   0.000
## 46   0.000   0.000   0.000
## 47   0.000   0.000   0.000
## 48   0.210   0.256   0.256
## 49   0.288   0.362   0.362
## 50   0.261   0.327   0.327
## 51   0.279   0.320   0.320
## 52   0.335   0.458   0.458
## 53   0.163   0.212   0.212
## 54   0.261   0.346   0.346
## 55   0.251   0.405   0.405
## 56   0.178   0.257   0.257
## 57   0.197   0.279   0.279
## 58   0.228   0.336   0.336
## 59   0.230   0.334   0.334
## 60   0.292   0.381   0.381
## 61   0.329   0.482   0.482
## 62   0.195   0.270   0.270
## 63   0.282   0.367   0.367
## 64   0.240   0.294   0.294
## 65   0.301   0.398   0.398
## 66   0.464   0.551   0.551
## 67   0.404   0.554   0.554
## 68   1.000   1.000   1.000
## 69   1.000   1.000   1.000
## 70   1.000   1.000   1.000
## 71   1.000   1.000   1.000
## 72   1.000   1.000   1.000
## 73   0.936   0.936   0.936
## 74   0.884   0.884   0.884
## 75   0.974   0.974   0.974
## 76   3.929   4.340   4.340
## 77   4.101   4.594   4.594
## 78   4.036   4.516   4.516
## 79   3.966   4.247   4.247
## 80   3.871   4.525   4.525
## 81   4.000   4.558   4.558
## 82   4.042   4.657   4.657
## 83   4.107   5.217   5.217
## 84   3.605   4.333   4.333
## 85   3.595   4.278   4.278
## 86   3.573   4.339   4.339
## 87   3.581   4.314   4.314
## 88   4.019   4.585   4.585
## 89   4.043   4.893   4.893
## 90   3.450   4.057   4.057
## 91   3.528   4.023   4.023
## 92   3.760   4.159   4.159
## 93   3.401   3.912   3.912
## 94   3.757   4.095   4.095
## 95   3.728   4.362   4.362
## 96   0.000   0.000   0.000
## 97   0.000   0.000   0.000
## 98   0.000   0.000   0.000
## 99   0.000   0.000   0.000
## 100  0.000   0.000   0.000

6.2.3 Testing loadings

library(bain)

res_bain_subload_trust <- 
bain(ctum_trus_fit, standardize = T,
     "exp=~reas_exp > .4 & int=~reas_int > .4 & ben=~reas_ben > .4")

res_bain_eqload_trust <- 
bain(ctum_trus_fit, standardize = T,
     "-0.15 < exp=~reas_exp - exp=~reas_alt_exp < 0.15 &
      -0.15 < int=~reas_int - int=~reas_alt_int < 0.15 &
      -0.15 < ben=~reas_ben - ben=~reas_alt_ben < 0.15")

res_bain_subload_trust
## Bayesian informative hypothesis testing for an object of class lavaan:
## 
##    Fit   Com   BF.u  BF.c   PMPa  PMPb 
## H1 0.944 0.235 4.008 54.389 1.000 0.800
## Hu                                0.200
## 
## Hypotheses:
##   H1: exp=~reas_exp>.4&int=~reas_int>.4&ben=~reas_ben>.4
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
res_bain_eqload_trust
## Bayesian informative hypothesis testing for an object of class lavaan:
## 
##    Fit   Com   BF.u   BF.c     PMPa  PMPb 
## H1 0.993 0.023 44.005 6506.543 1.000 0.978
## Hu                                   0.022
## 
## Hypotheses:
##   H1: -0.15<exp=~reas_exp-exp=~reas_alt_exp<0.15&-0.15<int=~reas_int-int=~reas_alt_int<0.15&-0.15<ben=~reas_ben-ben=~reas_alt_ben<0.15
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.

6.3 Convergent Validity Single Items Distrust

6.3.1 Convergent Validity with method Factors (UTUM-Modell)

# Recode Items
data_mtmm_rec <- 
  data_mtmm %>% 
  mutate(reas_exp_r_rec = 6 - reas_exp_r,
         reas_alt_exp_r_rec = 6 - reas_alt_exp_r,
         reas_int_r_rec = 6 - reas_int_r,
         reas_alt_int_r_rec = 6 - reas_alt_int_r,
         reas_ben_r_rec = 6 - reas_ben_r,
         reas_alt_ben_r_rec = 6 - reas_alt_ben_r)

utum_dis_mod <- 
  "exp =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06 + reas_exp_r_rec + reas_alt_exp_r_rec
   int =~ meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04 + reas_int_r_rec + reas_alt_int_r_rec
   ben =~ meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04 + reas_ben_r_rec + reas_alt_ben_r_rec
   
   meti =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06 + 
           meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04 +
           meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04

   si =~ reas_exp_r_rec + reas_alt_exp_r_rec + reas_int_r_rec + reas_alt_int_r_rec + reas_ben_r_rec + reas_alt_ben_r_rec

   exp ~~ 0*int + 0*ben
   int ~~ 0*ben

   si ~~ 0*meti + 0*exp + 0*int + 0*ben
   meti ~~ 0*exp + 0*int + 0*ben"


utum_dis_fit <-
  cfa(utum_dis_mod,
      data = data_mtmm_rec,
      missing = "fiml",
      std.lv = T)

fitmeasures(utum_dis_fit)[c("chisq", "df", "tli", "cfi", "rmsea", "srmr")]
##        chisq           df          tli          cfi        rmsea         srmr 
## 504.82031073 150.00000000   0.93383784   0.94776672   0.06850832   0.12850829
semPlot::semPaths(utum_dis_fit)

parameterEstimates(utum_dis_fit, standardized = T) %>% 
  mutate_if(is.numeric, function(x) round(x, 3)) 
##                    lhs op                rhs    est    se       z pvalue
## 1                  exp =~        meti_exp_01  0.360 0.029  12.330  0.000
## 2                  exp =~        meti_exp_02  0.370 0.033  11.233  0.000
## 3                  exp =~        meti_exp_03  0.356 0.031  11.436  0.000
## 4                  exp =~        meti_exp_04  0.398 0.033  12.194  0.000
## 5                  exp =~        meti_exp_05  0.248 0.033   7.527  0.000
## 6                  exp =~        meti_exp_06  0.487 0.030  15.993  0.000
## 7                  exp =~     reas_exp_r_rec  0.141 0.042   3.383  0.001
## 8                  exp =~ reas_alt_exp_r_rec  0.095 0.041   2.336  0.019
## 9                  int =~        meti_int_01  0.082 0.052   1.571  0.116
## 10                 int =~        meti_int_02  0.136 0.071   1.918  0.055
## 11                 int =~        meti_int_03 -0.156 0.071  -2.208  0.027
## 12                 int =~        meti_int_04 -0.139 0.061  -2.285  0.022
## 13                 int =~     reas_int_r_rec  0.045 0.087   0.519  0.604
## 14                 int =~ reas_alt_int_r_rec  0.207 0.075   2.752  0.006
## 15                 ben =~        meti_ben_01  0.071 0.034   2.076  0.038
## 16                 ben =~        meti_ben_02  0.041 0.040   1.020  0.308
## 17                 ben =~        meti_ben_03 -0.028 0.035  -0.801  0.423
## 18                 ben =~        meti_ben_04  0.157 0.040   3.895  0.000
## 19                 ben =~     reas_ben_r_rec  0.531 0.079   6.739  0.000
## 20                 ben =~ reas_alt_ben_r_rec  0.495 0.074   6.671  0.000
## 21                meti =~        meti_exp_01  0.686 0.035  19.887  0.000
## 22                meti =~        meti_exp_02  0.609 0.035  17.196  0.000
## 23                meti =~        meti_exp_03  0.637 0.035  18.213  0.000
## 24                meti =~        meti_exp_04  0.658 0.037  17.960  0.000
## 25                meti =~        meti_exp_05  0.569 0.034  16.632  0.000
## 26                meti =~        meti_exp_06  0.601 0.035  17.273  0.000
## 27                meti =~        meti_int_01  0.714 0.030  23.785  0.000
## 28                meti =~        meti_int_02  0.711 0.031  23.162  0.000
## 29                meti =~        meti_int_03  0.676 0.031  21.738  0.000
## 30                meti =~        meti_int_04  0.680 0.031  21.665  0.000
## 31                meti =~        meti_ben_01  0.699 0.031  22.432  0.000
## 32                meti =~        meti_ben_02  0.678 0.033  20.384  0.000
## 33                meti =~        meti_ben_03  0.737 0.034  21.942  0.000
## 34                meti =~        meti_ben_04  0.639 0.033  19.262  0.000
## 35                  si =~     reas_exp_r_rec  0.673 0.042  16.056  0.000
## 36                  si =~ reas_alt_exp_r_rec  0.550 0.040  13.776  0.000
## 37                  si =~     reas_int_r_rec  0.747 0.047  15.909  0.000
## 38                  si =~ reas_alt_int_r_rec  0.715 0.045  15.889  0.000
## 39                  si =~     reas_ben_r_rec  0.497 0.045  11.066  0.000
## 40                  si =~ reas_alt_ben_r_rec  0.371 0.046   8.067  0.000
## 41                 exp ~~                int  0.000 0.000      NA     NA
## 42                 exp ~~                ben  0.000 0.000      NA     NA
## 43                 int ~~                ben  0.000 0.000      NA     NA
## 44                meti ~~                 si  0.000 0.000      NA     NA
## 45                 exp ~~                 si  0.000 0.000      NA     NA
## 46                 int ~~                 si  0.000 0.000      NA     NA
## 47                 ben ~~                 si  0.000 0.000      NA     NA
## 48                 exp ~~               meti  0.000 0.000      NA     NA
## 49                 int ~~               meti  0.000 0.000      NA     NA
## 50                 ben ~~               meti  0.000 0.000      NA     NA
## 51         meti_exp_01 ~~        meti_exp_01  0.216 0.016  13.174  0.000
## 52         meti_exp_02 ~~        meti_exp_02  0.287 0.021  13.549  0.000
## 53         meti_exp_03 ~~        meti_exp_03  0.265 0.019  13.767  0.000
## 54         meti_exp_04 ~~        meti_exp_04  0.279 0.021  13.313  0.000
## 55         meti_exp_05 ~~        meti_exp_05  0.344 0.023  15.008  0.000
## 56         meti_exp_06 ~~        meti_exp_06  0.171 0.018   9.397  0.000
## 57      reas_exp_r_rec ~~     reas_exp_r_rec  0.417 0.038  10.877  0.000
## 58  reas_alt_exp_r_rec ~~ reas_alt_exp_r_rec  0.419 0.034  12.335  0.000
## 59         meti_int_01 ~~        meti_int_01  0.171 0.015  11.532  0.000
## 60         meti_int_02 ~~        meti_int_02  0.174 0.023   7.715  0.000
## 61         meti_int_03 ~~        meti_int_03  0.203 0.026   7.889  0.000
## 62         meti_int_04 ~~        meti_int_04  0.213 0.023   9.252  0.000
## 63      reas_int_r_rec ~~     reas_int_r_rec  0.505 0.045  11.156  0.000
## 64  reas_alt_int_r_rec ~~ reas_alt_int_r_rec  0.389 0.047   8.356  0.000
## 65         meti_ben_01 ~~        meti_ben_01  0.224 0.016  13.863  0.000
## 66         meti_ben_02 ~~        meti_ben_02  0.304 0.021  14.570  0.000
## 67         meti_ben_03 ~~        meti_ben_03  0.275 0.020  14.039  0.000
## 68         meti_ben_04 ~~        meti_ben_04  0.312 0.023  13.789  0.000
## 69      reas_ben_r_rec ~~     reas_ben_r_rec  0.365 0.079   4.635  0.000
## 70  reas_alt_ben_r_rec ~~ reas_alt_ben_r_rec  0.487 0.071   6.871  0.000
## 71                 exp ~~                exp  1.000 0.000      NA     NA
## 72                 int ~~                int  1.000 0.000      NA     NA
## 73                 ben ~~                ben  1.000 0.000      NA     NA
## 74                meti ~~               meti  1.000 0.000      NA     NA
## 75                  si ~~                 si  1.000 0.000      NA     NA
## 76         meti_exp_01 ~1                     3.929 0.040  97.609  0.000
## 77         meti_exp_02 ~1                     4.101 0.040 103.342  0.000
## 78         meti_exp_03 ~1                     4.036 0.040 101.501  0.000
## 79         meti_exp_04 ~1                     3.966 0.042  95.476  0.000
## 80         meti_exp_05 ~1                     3.871 0.038 101.772  0.000
## 81         meti_exp_06 ~1                     4.000 0.039 102.387  0.000
## 82      reas_exp_r_rec ~1                     3.206 0.043  74.375  0.000
## 83  reas_alt_exp_r_rec ~1                     3.040 0.040  76.902  0.000
## 84         meti_int_01 ~1                     3.605 0.037  97.641  0.000
## 85         meti_int_02 ~1                     3.595 0.037  96.594  0.000
## 86         meti_int_03 ~1                     3.573 0.037  96.941  0.000
## 87         meti_int_04 ~1                     3.581 0.037  96.462  0.000
## 88      reas_int_r_rec ~1                     2.847 0.047  60.181  0.000
## 89  reas_alt_int_r_rec ~1                     3.050 0.045  67.937  0.000
## 90         meti_ben_01 ~1                     3.450 0.038  91.398  0.000
## 91         meti_ben_02 ~1                     3.528 0.039  90.489  0.000
## 92         meti_ben_03 ~1                     3.760 0.040  93.234  0.000
## 93         meti_ben_04 ~1                     3.401 0.038  88.458  0.000
## 94      reas_ben_r_rec ~1                     2.242 0.043  51.832  0.000
## 95  reas_alt_ben_r_rec ~1                     2.144 0.043  50.132  0.000
## 96                 exp ~1                     0.000 0.000      NA     NA
## 97                 int ~1                     0.000 0.000      NA     NA
## 98                 ben ~1                     0.000 0.000      NA     NA
## 99                meti ~1                     0.000 0.000      NA     NA
## 100                 si ~1                     0.000 0.000      NA     NA
##     ci.lower ci.upper std.lv std.all std.nox
## 1      0.302    0.417  0.360   0.398   0.398
## 2      0.305    0.434  0.370   0.415   0.415
## 3      0.295    0.417  0.356   0.399   0.399
## 4      0.334    0.462  0.398   0.426   0.426
## 5      0.184    0.313  0.248   0.291   0.291
## 6      0.427    0.547  0.487   0.555   0.555
## 7      0.059    0.222  0.141   0.149   0.149
## 8      0.015    0.175  0.095   0.112   0.112
## 9     -0.020    0.184  0.082   0.099   0.099
## 10    -0.003    0.274  0.136   0.162   0.162
## 11    -0.295   -0.018 -0.156  -0.189  -0.189
## 12    -0.259   -0.020 -0.139  -0.167  -0.167
## 13    -0.125    0.216  0.045   0.044   0.044
## 14     0.060    0.354  0.207   0.213   0.213
## 15     0.004    0.137  0.071   0.083   0.083
## 16    -0.037    0.119  0.041   0.046   0.046
## 17    -0.098    0.041 -0.028  -0.031  -0.031
## 18     0.078    0.236  0.157   0.182   0.182
## 19     0.376    0.685  0.531   0.561   0.561
## 20     0.349    0.640  0.495   0.531   0.531
## 21     0.619    0.754  0.686   0.760   0.760
## 22     0.539    0.678  0.609   0.683   0.683
## 23     0.568    0.705  0.637   0.713   0.713
## 24     0.586    0.730  0.658   0.705   0.705
## 25     0.502    0.636  0.569   0.666   0.666
## 26     0.533    0.669  0.601   0.685   0.685
## 27     0.655    0.772  0.714   0.861   0.861
## 28     0.651    0.771  0.711   0.851   0.851
## 29     0.615    0.737  0.676   0.817   0.817
## 30     0.618    0.741  0.680   0.816   0.816
## 31     0.638    0.760  0.699   0.825   0.825
## 32     0.613    0.744  0.678   0.775   0.775
## 33     0.671    0.803  0.737   0.814   0.814
## 34     0.574    0.704  0.639   0.741   0.741
## 35     0.590    0.755  0.673   0.713   0.713
## 36     0.472    0.628  0.550   0.643   0.643
## 37     0.655    0.839  0.747   0.724   0.724
## 38     0.627    0.803  0.715   0.736   0.736
## 39     0.409    0.585  0.497   0.526   0.526
## 40     0.281    0.461  0.371   0.398   0.398
## 41     0.000    0.000  0.000   0.000   0.000
## 42     0.000    0.000  0.000   0.000   0.000
## 43     0.000    0.000  0.000   0.000   0.000
## 44     0.000    0.000  0.000   0.000   0.000
## 45     0.000    0.000  0.000   0.000   0.000
## 46     0.000    0.000  0.000   0.000   0.000
## 47     0.000    0.000  0.000   0.000   0.000
## 48     0.000    0.000  0.000   0.000   0.000
## 49     0.000    0.000  0.000   0.000   0.000
## 50     0.000    0.000  0.000   0.000   0.000
## 51     0.184    0.248  0.216   0.265   0.265
## 52     0.245    0.328  0.287   0.361   0.361
## 53     0.227    0.302  0.265   0.332   0.332
## 54     0.238    0.320  0.279   0.321   0.321
## 55     0.299    0.389  0.344   0.471   0.471
## 56     0.135    0.207  0.171   0.222   0.222
## 57     0.342    0.492  0.417   0.469   0.469
## 58     0.353    0.486  0.419   0.574   0.574
## 59     0.142    0.200  0.171   0.249   0.249
## 60     0.130    0.218  0.174   0.249   0.249
## 61     0.153    0.254  0.203   0.297   0.297
## 62     0.168    0.258  0.213   0.306   0.306
## 63     0.417    0.594  0.505   0.474   0.474
## 64     0.298    0.480  0.389   0.413   0.413
## 65     0.193    0.256  0.224   0.312   0.312
## 66     0.263    0.345  0.304   0.397   0.397
## 67     0.237    0.314  0.275   0.336   0.336
## 68     0.267    0.356  0.312   0.418   0.418
## 69     0.210    0.519  0.365   0.408   0.408
## 70     0.348    0.626  0.487   0.560   0.560
## 71     1.000    1.000  1.000   1.000   1.000
## 72     1.000    1.000  1.000   1.000   1.000
## 73     1.000    1.000  1.000   1.000   1.000
## 74     1.000    1.000  1.000   1.000   1.000
## 75     1.000    1.000  1.000   1.000   1.000
## 76     3.850    4.007  3.929   4.348   4.348
## 77     4.023    4.179  4.101   4.603   4.603
## 78     3.958    4.114  4.036   4.521   4.521
## 79     3.885    4.048  3.966   4.253   4.253
## 80     3.796    3.946  3.871   4.533   4.533
## 81     3.923    4.077  4.000   4.561   4.561
## 82     3.121    3.290  3.206   3.401   3.401
## 83     2.963    3.118  3.040   3.557   3.557
## 84     3.533    3.678  3.605   4.349   4.349
## 85     3.522    3.668  3.595   4.303   4.303
## 86     3.501    3.646  3.573   4.318   4.318
## 87     3.509    3.654  3.581   4.297   4.297
## 88     2.754    2.939  2.847   2.757   2.757
## 89     2.962    3.138  3.050   3.141   3.141
## 90     3.376    3.524  3.450   4.071   4.071
## 91     3.451    3.604  3.528   4.031   4.031
## 92     3.681    3.839  3.760   4.153   4.153
## 93     3.325    3.476  3.401   3.940   3.940
## 94     2.157    2.327  2.242   2.372   2.372
## 95     2.060    2.227  2.144   2.299   2.299
## 96     0.000    0.000  0.000   0.000   0.000
## 97     0.000    0.000  0.000   0.000   0.000
## 98     0.000    0.000  0.000   0.000   0.000
## 99     0.000    0.000  0.000   0.000   0.000
## 100    0.000    0.000  0.000   0.000   0.000

6.3.2 Convergent Validity with method Factors (CTUM-Modell)

ctum_dis_mod <- 
  "exp =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06 + reas_exp_r_rec + reas_alt_exp_r_rec
   int =~ meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04 + reas_int_r_rec + reas_alt_int_r_rec
   ben =~ meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04 + reas_ben_r_rec + reas_alt_ben_r_rec
   
   meti =~ meti_exp_01 + meti_exp_02 + meti_exp_03 + meti_exp_04 + meti_exp_05 + meti_exp_06 + 
           meti_int_01 + meti_int_02 + meti_int_03 + meti_int_04 +
           meti_ben_01 + meti_ben_02 + meti_ben_03 + meti_ben_04

   si =~ reas_exp_r_rec + reas_alt_exp_r_rec + reas_int_r_rec + reas_alt_int_r_rec + reas_ben_r_rec + reas_alt_ben_r_rec

   si ~~ 0*meti + 0*exp + 0*int + 0*ben
   meti ~~ 0*exp + 0*int + 0*ben"


ctum_dis_fit <-
  cfa(ctum_dis_mod,
      data = data_mtmm_rec,
      estimator = "ML",
      std.lv = T)

fitmeasures(ctum_dis_fit)[c("chisq", "df", "tli", "cfi", "rmsea", "srmr")]
##        chisq           df          tli          cfi        rmsea         srmr 
## 417.30717242 147.00000000   0.93828740   0.95225393   0.06577724   0.08707447
semPlot::semPaths(ctum_dis_fit)

parameterEstimates(ctum_dis_fit, standardized = T) %>% 
  mutate_if(is.numeric, function(x) round(x, 3)) 
##                   lhs op                rhs   est    se      z pvalue ci.lower
## 1                 exp =~        meti_exp_01 0.406 0.035 11.554  0.000    0.337
## 2                 exp =~        meti_exp_02 0.400 0.037 10.803  0.000    0.327
## 3                 exp =~        meti_exp_03 0.426 0.037 11.516  0.000    0.354
## 4                 exp =~        meti_exp_04 0.407 0.039 10.469  0.000    0.331
## 5                 exp =~        meti_exp_05 0.311 0.038  8.131  0.000    0.236
## 6                 exp =~        meti_exp_06 0.550 0.035 15.817  0.000    0.482
## 7                 exp =~     reas_exp_r_rec 0.251 0.050  4.963  0.000    0.152
## 8                 exp =~ reas_alt_exp_r_rec 0.112 0.046  2.418  0.016    0.021
## 9                 int =~        meti_int_01 0.303 0.040  7.527  0.000    0.224
## 10                int =~        meti_int_02 0.250 0.041  6.124  0.000    0.170
## 11                int =~        meti_int_03 0.226 0.041  5.451  0.000    0.144
## 12                int =~        meti_int_04 0.250 0.042  5.941  0.000    0.168
## 13                int =~     reas_int_r_rec 0.441 0.060  7.382  0.000    0.324
## 14                int =~ reas_alt_int_r_rec 0.331 0.056  5.946  0.000    0.222
## 15                ben =~        meti_ben_01 0.214 0.042  5.045  0.000    0.131
## 16                ben =~        meti_ben_02 0.205 0.044  4.656  0.000    0.119
## 17                ben =~        meti_ben_03 0.182 0.045  4.057  0.000    0.094
## 18                ben =~        meti_ben_04 0.240 0.045  5.360  0.000    0.153
## 19                ben =~     reas_ben_r_rec 0.775 0.067 11.555  0.000    0.643
## 20                ben =~ reas_alt_ben_r_rec 0.485 0.057  8.526  0.000    0.373
## 21               meti =~        meti_exp_01 0.622 0.038 16.299  0.000    0.547
## 22               meti =~        meti_exp_02 0.540 0.039 13.987  0.000    0.464
## 23               meti =~        meti_exp_03 0.570 0.039 14.508  0.000    0.493
## 24               meti =~        meti_exp_04 0.610 0.041 14.946  0.000    0.530
## 25               meti =~        meti_exp_05 0.517 0.038 13.510  0.000    0.442
## 26               meti =~        meti_exp_06 0.494 0.038 12.852  0.000    0.419
## 27               meti =~        meti_int_01 0.633 0.033 18.939  0.000    0.568
## 28               meti =~        meti_int_02 0.648 0.034 19.296  0.000    0.582
## 29               meti =~        meti_int_03 0.601 0.034 17.703  0.000    0.534
## 30               meti =~        meti_int_04 0.607 0.035 17.478  0.000    0.539
## 31               meti =~        meti_ben_01 0.704 0.034 20.409  0.000    0.636
## 32               meti =~        meti_ben_02 0.674 0.037 18.417  0.000    0.602
## 33               meti =~        meti_ben_03 0.711 0.037 18.958  0.000    0.637
## 34               meti =~        meti_ben_04 0.626 0.037 16.813  0.000    0.553
## 35                 si =~     reas_exp_r_rec 0.621 0.046 13.420  0.000    0.531
## 36                 si =~ reas_alt_exp_r_rec 0.624 0.043 14.393  0.000    0.539
## 37                 si =~     reas_int_r_rec 0.587 0.054 10.923  0.000    0.482
## 38                 si =~ reas_alt_int_r_rec 0.641 0.049 12.952  0.000    0.544
## 39                 si =~     reas_ben_r_rec 0.232 0.054  4.312  0.000    0.126
## 40                 si =~ reas_alt_ben_r_rec 0.229 0.053  4.295  0.000    0.124
## 41               meti ~~                 si 0.000 0.000     NA     NA    0.000
## 42                exp ~~                 si 0.000 0.000     NA     NA    0.000
## 43                int ~~                 si 0.000 0.000     NA     NA    0.000
## 44                ben ~~                 si 0.000 0.000     NA     NA    0.000
## 45                exp ~~               meti 0.000 0.000     NA     NA    0.000
## 46                int ~~               meti 0.000 0.000     NA     NA    0.000
## 47                ben ~~               meti 0.000 0.000     NA     NA    0.000
## 48        meti_exp_01 ~~        meti_exp_01 0.222 0.018 12.283  0.000    0.186
## 49        meti_exp_02 ~~        meti_exp_02 0.282 0.022 12.872  0.000    0.239
## 50        meti_exp_03 ~~        meti_exp_03 0.266 0.021 12.501  0.000    0.224
## 51        meti_exp_04 ~~        meti_exp_04 0.308 0.024 12.942  0.000    0.261
## 52        meti_exp_05 ~~        meti_exp_05 0.343 0.025 13.698  0.000    0.294
## 53        meti_exp_06 ~~        meti_exp_06 0.161 0.020  8.213  0.000    0.123
## 54     reas_exp_r_rec ~~     reas_exp_r_rec 0.429 0.041 10.420  0.000    0.348
## 55 reas_alt_exp_r_rec ~~ reas_alt_exp_r_rec 0.329 0.038  8.740  0.000    0.255
## 56        meti_int_01 ~~        meti_int_01 0.182 0.015 11.773  0.000    0.152
## 57        meti_int_02 ~~        meti_int_02 0.196 0.016 12.449  0.000    0.165
## 58        meti_int_03 ~~        meti_int_03 0.239 0.018 13.112  0.000    0.204
## 59        meti_int_04 ~~        meti_int_04 0.249 0.019 13.034  0.000    0.211
## 60     reas_int_r_rec ~~     reas_int_r_rec 0.518 0.046 11.148  0.000    0.427
## 61 reas_alt_int_r_rec ~~ reas_alt_int_r_rec 0.417 0.039 10.591  0.000    0.340
## 62        meti_ben_01 ~~        meti_ben_01 0.209 0.018 11.729  0.000    0.174
## 63        meti_ben_02 ~~        meti_ben_02 0.287 0.023 12.703  0.000    0.243
## 64        meti_ben_03 ~~        meti_ben_03 0.293 0.023 12.508  0.000    0.247
## 65        meti_ben_04 ~~        meti_ben_04 0.326 0.025 13.126  0.000    0.278
## 66     reas_ben_r_rec ~~     reas_ben_r_rec 0.197 0.086  2.276  0.023    0.027
## 67 reas_alt_ben_r_rec ~~ reas_alt_ben_r_rec 0.574 0.051 11.265  0.000    0.474
## 68                exp ~~                exp 1.000 0.000     NA     NA    1.000
## 69                int ~~                int 1.000 0.000     NA     NA    1.000
## 70                ben ~~                ben 1.000 0.000     NA     NA    1.000
## 71               meti ~~               meti 1.000 0.000     NA     NA    1.000
## 72                 si ~~                 si 1.000 0.000     NA     NA    1.000
## 73                exp ~~                int 0.553 0.067  8.193  0.000    0.420
## 74                exp ~~                ben 0.275 0.077  3.574  0.000    0.124
## 75                int ~~                ben 0.759 0.060 12.618  0.000    0.641
##    ci.upper std.lv std.all std.nox
## 1     0.475  0.406   0.462   0.462
## 2     0.472  0.400   0.467   0.467
## 3     0.499  0.426   0.485   0.485
## 4     0.483  0.407   0.443   0.443
## 5     0.386  0.311   0.370   0.370
## 6     0.618  0.550   0.654   0.654
## 7     0.350  0.251   0.267   0.267
## 8     0.203  0.112   0.131   0.131
## 9     0.382  0.303   0.369   0.369
## 10    0.330  0.250   0.304   0.304
## 11    0.307  0.226   0.279   0.279
## 12    0.333  0.250   0.304   0.304
## 13    0.558  0.441   0.429   0.429
## 14    0.440  0.331   0.342   0.342
## 15    0.296  0.214   0.247   0.247
## 16    0.292  0.205   0.232   0.232
## 17    0.271  0.182   0.200   0.200
## 18    0.328  0.240   0.273   0.273
## 19    0.906  0.775   0.840   0.840
## 20    0.596  0.485   0.523   0.523
## 21    0.697  0.622   0.707   0.707
## 22    0.616  0.540   0.631   0.631
## 23    0.647  0.570   0.648   0.648
## 24    0.691  0.610   0.664   0.664
## 25    0.592  0.517   0.615   0.615
## 26    0.570  0.494   0.588   0.588
## 27    0.699  0.633   0.771   0.771
## 28    0.714  0.648   0.787   0.787
## 29    0.668  0.601   0.745   0.745
## 30    0.675  0.607   0.736   0.736
## 31    0.771  0.704   0.813   0.813
## 32    0.745  0.674   0.761   0.761
## 33    0.784  0.711   0.779   0.779
## 34    0.699  0.626   0.710   0.710
## 35    0.712  0.621   0.663   0.663
## 36    0.709  0.624   0.730   0.730
## 37    0.693  0.587   0.571   0.571
## 38    0.738  0.641   0.662   0.662
## 39    0.337  0.232   0.251   0.251
## 40    0.333  0.229   0.246   0.246
## 41    0.000  0.000   0.000   0.000
## 42    0.000  0.000   0.000   0.000
## 43    0.000  0.000   0.000   0.000
## 44    0.000  0.000   0.000   0.000
## 45    0.000  0.000   0.000   0.000
## 46    0.000  0.000   0.000   0.000
## 47    0.000  0.000   0.000   0.000
## 48    0.257  0.222   0.287   0.287
## 49    0.325  0.282   0.385   0.385
## 50    0.308  0.266   0.344   0.344
## 51    0.354  0.308   0.364   0.364
## 52    0.393  0.343   0.485   0.485
## 53    0.199  0.161   0.227   0.227
## 54    0.510  0.429   0.489   0.489
## 55    0.403  0.329   0.450   0.450
## 56    0.212  0.182   0.269   0.269
## 57    0.227  0.196   0.289   0.289
## 58    0.275  0.239   0.367   0.367
## 59    0.286  0.249   0.366   0.366
## 60    0.609  0.518   0.490   0.490
## 61    0.494  0.417   0.445   0.445
## 62    0.244  0.209   0.279   0.279
## 63    0.331  0.287   0.367   0.367
## 64    0.339  0.293   0.352   0.352
## 65    0.375  0.326   0.421   0.421
## 66    0.366  0.197   0.231   0.231
## 67    0.673  0.574   0.666   0.666
## 68    1.000  1.000   1.000   1.000
## 69    1.000  1.000   1.000   1.000
## 70    1.000  1.000   1.000   1.000
## 71    1.000  1.000   1.000   1.000
## 72    1.000  1.000   1.000   1.000
## 73    0.685  0.553   0.553   0.553
## 74    0.425  0.275   0.275   0.275
## 75    0.877  0.759   0.759   0.759
modificationindices(ctum_dis_fit, sort. = T)
##                    lhs op                rhs     mi    epc sepc.lv sepc.all
## 84                 exp =~        meti_ben_03 49.209  0.263   0.263    0.289
## 98                 int =~        meti_ben_03 37.356  0.502   0.502    0.550
## 94                 int =~     reas_exp_r_rec 28.223  0.374   0.374    0.399
## 41                meti ~~                 si 27.199  0.338   0.338    0.338
## 108                ben =~     reas_exp_r_rec 25.277  0.252   0.252    0.269
## 246     reas_exp_r_rec ~~     reas_ben_r_rec 21.155  0.134   0.134    0.462
## 309 reas_alt_int_r_rec ~~     reas_ben_r_rec 20.292 -0.158  -0.158   -0.553
## 241     reas_exp_r_rec ~~ reas_alt_int_r_rec 17.015 -0.155  -0.155   -0.366
## 185        meti_exp_03 ~~        meti_ben_02 16.478  0.063   0.063    0.227
## 304     reas_int_r_rec ~~ reas_alt_ben_r_rec 14.557 -0.133  -0.133   -0.245
## 130                 si =~        meti_int_03 13.496 -0.109  -0.109   -0.135
## 202        meti_exp_04 ~~        meti_ben_03 13.205  0.061   0.061    0.203
## 253 reas_alt_exp_r_rec ~~ reas_alt_int_r_rec 12.981  0.141   0.141    0.380
## 228        meti_exp_06 ~~ reas_alt_int_r_rec 12.066  0.062   0.062    0.240
## 281        meti_int_03 ~~        meti_int_04 11.373  0.046   0.046    0.187
## 312        meti_ben_01 ~~        meti_ben_03 10.727 -0.051  -0.051   -0.206
## 81                 exp =~ reas_alt_int_r_rec 10.546  0.183   0.183    0.189
## 226        meti_exp_06 ~~        meti_int_04 10.338 -0.041  -0.041   -0.205
## 158        meti_exp_02 ~~        meti_exp_06 10.309 -0.054  -0.054   -0.254
## 325     reas_ben_r_rec ~~ reas_alt_ben_r_rec 10.190  0.359   0.359    1.069
## 310 reas_alt_int_r_rec ~~ reas_alt_ben_r_rec 10.159  0.096   0.096    0.197
## 79                 exp =~        meti_int_04  9.942 -0.122  -0.122   -0.148
## 129                 si =~        meti_int_02  9.654  0.086   0.086    0.104
## 46                 int ~~               meti  9.572  0.271   0.271    0.271
## 252 reas_alt_exp_r_rec ~~     reas_int_r_rec  8.924 -0.103  -0.103   -0.249
## 150        meti_exp_01 ~~        meti_ben_02  8.863 -0.043  -0.043   -0.169
## 87                 exp =~ reas_alt_ben_r_rec  8.721 -0.142  -0.142   -0.153
## 240     reas_exp_r_rec ~~     reas_int_r_rec  8.546  0.100   0.100    0.213
## 113                ben =~        meti_int_04  8.535  0.178   0.178    0.215
## 215        meti_exp_05 ~~        meti_ben_01  8.282  0.044   0.044    0.163
## 311        meti_ben_01 ~~        meti_ben_02  8.169  0.043   0.043    0.177
## 206        meti_exp_05 ~~        meti_exp_06  7.552  0.045   0.045    0.193
## 168        meti_exp_02 ~~        meti_ben_02  7.468 -0.043  -0.043   -0.151
## 234        meti_exp_06 ~~ reas_alt_ben_r_rec  7.045 -0.051  -0.051   -0.168
## 187        meti_exp_03 ~~        meti_ben_04  6.728 -0.042  -0.042   -0.142
## 196        meti_exp_04 ~~        meti_int_03  6.692 -0.038  -0.038   -0.140
## 161        meti_exp_02 ~~        meti_int_01  6.616  0.033   0.033    0.145
## 239     reas_exp_r_rec ~~        meti_int_04  6.416  0.048   0.048    0.147
## 119               meti =~ reas_alt_int_r_rec  6.391  0.097   0.097    0.100
## 283        meti_int_03 ~~ reas_alt_int_r_rec  6.194 -0.046  -0.046   -0.145
## 302     reas_int_r_rec ~~        meti_ben_04  6.123 -0.058  -0.058   -0.142
## 275        meti_int_02 ~~        meti_ben_01  5.909  0.030   0.030    0.148
## 91                 int =~        meti_exp_04  5.501 -0.108  -0.108   -0.117
## 272        meti_int_02 ~~        meti_int_04  5.498 -0.030  -0.030   -0.135
## 301     reas_int_r_rec ~~        meti_ben_03  5.235  0.052   0.052    0.134
## 175        meti_exp_03 ~~        meti_exp_06  5.024  0.039   0.039    0.187
## 164        meti_exp_02 ~~        meti_int_04  5.019  0.032   0.032    0.121
## 162        meti_exp_02 ~~        meti_int_02  4.934 -0.029  -0.029   -0.123
## 146        meti_exp_01 ~~        meti_int_04  4.905 -0.029  -0.029   -0.123
## 231        meti_exp_06 ~~        meti_ben_03  4.823  0.031   0.031    0.143
## 136        meti_exp_01 ~~        meti_exp_02  4.810  0.032   0.032    0.129
## 145        meti_exp_01 ~~        meti_int_03  4.748  0.028   0.028    0.121
## 306 reas_alt_int_r_rec ~~        meti_ben_02  4.712  0.044   0.044    0.128
## 279        meti_int_02 ~~     reas_ben_r_rec  4.607 -0.045  -0.045   -0.228
## 291        meti_int_04 ~~ reas_alt_int_r_rec  4.597 -0.040  -0.040   -0.125
## 220        meti_exp_05 ~~ reas_alt_ben_r_rec  4.451 -0.049  -0.049   -0.111
## 85                 exp =~        meti_ben_04  4.333 -0.079  -0.079   -0.089
## 258 reas_alt_exp_r_rec ~~     reas_ben_r_rec  4.316 -0.062  -0.062   -0.243
## 103                ben =~        meti_exp_02  4.022 -0.066  -0.066   -0.077
## 260        meti_int_01 ~~        meti_int_02  3.933  0.024   0.024    0.125
## 221        meti_exp_06 ~~     reas_exp_r_rec  3.904 -0.038  -0.038   -0.145
## 230        meti_exp_06 ~~        meti_ben_02  3.849  0.027   0.027    0.127
## 261        meti_int_01 ~~        meti_int_03  3.847 -0.024  -0.024   -0.117
## 133                 si =~        meti_ben_02  3.730  0.063   0.063    0.072
## 182        meti_exp_03 ~~     reas_int_r_rec  3.612  0.041   0.041    0.109
## 101                int =~ reas_alt_ben_r_rec  3.599 -0.202  -0.202   -0.218
## 115                ben =~ reas_alt_int_r_rec  3.559 -0.169  -0.169   -0.174
## 139        meti_exp_01 ~~        meti_exp_05  3.544 -0.029  -0.029   -0.105
## 273        meti_int_02 ~~     reas_int_r_rec  3.373  0.035   0.035    0.110
## 247     reas_exp_r_rec ~~ reas_alt_ben_r_rec  3.363 -0.055  -0.055   -0.111
## 154        meti_exp_01 ~~ reas_alt_ben_r_rec  3.357  0.036   0.036    0.101
## 99                 int =~        meti_ben_04  3.278 -0.148  -0.148   -0.168
## 159        meti_exp_02 ~~     reas_exp_r_rec  3.183  0.036   0.036    0.104
## 42                 exp ~~                 si  3.084  0.144   0.144    0.144
## 47                 ben ~~               meti  3.057 -0.127  -0.127   -0.127
## 82                 exp =~        meti_ben_01  3.025 -0.059  -0.059   -0.068
## 135                 si =~        meti_ben_04  2.991 -0.060  -0.060   -0.068
## 219        meti_exp_05 ~~     reas_ben_r_rec  2.877  0.038   0.038    0.146
## 170        meti_exp_02 ~~        meti_ben_04  2.580  0.026   0.026    0.087
## 288        meti_int_03 ~~     reas_ben_r_rec  2.566  0.036   0.036    0.164
## 303     reas_int_r_rec ~~     reas_ben_r_rec  2.490  0.069   0.069    0.216
## 194        meti_exp_04 ~~        meti_int_01  2.477 -0.021  -0.021   -0.089
## 152        meti_exp_01 ~~        meti_ben_04  2.454  0.023   0.023    0.087
## 86                 exp =~     reas_ben_r_rec  2.424  0.110   0.110    0.119
## 105                ben =~        meti_exp_04  2.410 -0.054  -0.054   -0.058
## 121               meti =~ reas_alt_ben_r_rec  2.297 -0.069  -0.069   -0.074
## 285        meti_int_03 ~~        meti_ben_02  2.284 -0.022  -0.022   -0.084
## 205        meti_exp_04 ~~ reas_alt_ben_r_rec  2.271  0.034   0.034    0.081
## 109                ben =~ reas_alt_exp_r_rec  2.267 -0.074  -0.074   -0.086
## 134                 si =~        meti_ben_03  2.265  0.050   0.050    0.055
## 137        meti_exp_01 ~~        meti_exp_03  2.236 -0.022  -0.022   -0.091
## 249 reas_alt_exp_r_rec ~~        meti_int_02  2.234  0.024   0.024    0.094
## 167        meti_exp_02 ~~        meti_ben_01  2.232 -0.021  -0.021   -0.086
## 177        meti_exp_03 ~~ reas_alt_exp_r_rec  2.188 -0.027  -0.027   -0.091
## 250 reas_alt_exp_r_rec ~~        meti_int_03  2.153 -0.025  -0.025   -0.090
## 318        meti_ben_02 ~~     reas_ben_r_rec  2.142 -0.043  -0.043   -0.183
## 127                 si =~        meti_exp_06  2.127  0.044   0.044    0.052
## 95                 int =~ reas_alt_exp_r_rec  2.124 -0.098  -0.098   -0.114
## 266        meti_int_01 ~~        meti_ben_02  2.119 -0.019  -0.019   -0.085
## 287        meti_int_03 ~~        meti_ben_04  2.098  0.022   0.022    0.079
## 149        meti_exp_01 ~~        meti_ben_01  2.013 -0.018  -0.018   -0.084
## 151        meti_exp_01 ~~        meti_ben_03  1.995  0.021   0.021    0.081
## 112                ben =~        meti_int_03  1.995  0.083   0.083    0.103
## 156        meti_exp_02 ~~        meti_exp_04  1.806  0.022   0.022    0.076
## 259 reas_alt_exp_r_rec ~~ reas_alt_ben_r_rec  1.789  0.040   0.040    0.092
## 322        meti_ben_03 ~~ reas_alt_ben_r_rec  1.788 -0.030  -0.030   -0.074
## 211        meti_exp_05 ~~        meti_int_03  1.758  0.020   0.020    0.070
## 45                 exp ~~               meti  1.750  0.216   0.216    0.216
## 217        meti_exp_05 ~~        meti_ben_03  1.741 -0.023  -0.023   -0.072
## 122                 si =~        meti_exp_01  1.729 -0.038  -0.038   -0.044
## 118               meti =~     reas_int_r_rec  1.711  0.056   0.056    0.054
## 181        meti_exp_03 ~~        meti_int_04  1.710 -0.018  -0.018   -0.071
## 186        meti_exp_03 ~~        meti_ben_03  1.690  0.020   0.020    0.073
## 268        meti_int_01 ~~        meti_ben_04  1.678  0.018   0.018    0.074
## 204        meti_exp_04 ~~     reas_ben_r_rec  1.655 -0.028  -0.028   -0.114
## 213        meti_exp_05 ~~     reas_int_r_rec  1.606 -0.030  -0.030   -0.070
## 198        meti_exp_04 ~~     reas_int_r_rec  1.549 -0.028  -0.028   -0.071
## 315        meti_ben_01 ~~ reas_alt_ben_r_rec  1.527 -0.024  -0.024   -0.070
## 193        meti_exp_04 ~~ reas_alt_exp_r_rec  1.511  0.024   0.024    0.074
## 171        meti_exp_02 ~~     reas_ben_r_rec  1.476 -0.025  -0.025   -0.107
## 197        meti_exp_04 ~~        meti_int_04  1.474  0.018   0.018    0.066
## 286        meti_int_03 ~~        meti_ben_03  1.474 -0.018  -0.018   -0.069
## 218        meti_exp_05 ~~        meti_ben_04  1.408 -0.021  -0.021   -0.063
## 144        meti_exp_01 ~~        meti_int_02  1.408  0.014   0.014    0.067
## 212        meti_exp_05 ~~        meti_int_04  1.357  0.018   0.018    0.061
## 169        meti_exp_02 ~~        meti_ben_03  1.315 -0.018  -0.018   -0.064
## 225        meti_exp_06 ~~        meti_int_03  1.302 -0.014  -0.014   -0.072
## 297        meti_int_04 ~~ reas_alt_ben_r_rec  1.292  0.023   0.023    0.061
## 44                 ben ~~                 si  1.266  0.122   0.122    0.122
## 296        meti_int_04 ~~     reas_ben_r_rec  1.243  0.026   0.026    0.115
## 163        meti_exp_02 ~~        meti_int_03  1.237  0.016   0.016    0.060
## 114                ben =~     reas_int_r_rec  1.180 -0.114  -0.114   -0.111
## 263        meti_int_01 ~~     reas_int_r_rec  1.157 -0.021  -0.021   -0.068
## 203        meti_exp_04 ~~        meti_ben_04  1.138 -0.018  -0.018   -0.058
## 141        meti_exp_01 ~~     reas_exp_r_rec  1.103 -0.019  -0.019   -0.062
## 292        meti_int_04 ~~        meti_ben_01  1.063 -0.014  -0.014   -0.061
## 243     reas_exp_r_rec ~~        meti_ben_02  1.062 -0.021  -0.021   -0.061
## 90                 int =~        meti_exp_03  1.059  0.044   0.044    0.050
## 117               meti =~ reas_alt_exp_r_rec  1.051  0.037   0.037    0.043
## 298     reas_int_r_rec ~~ reas_alt_int_r_rec  1.024  0.037   0.037    0.080
## 178        meti_exp_03 ~~        meti_int_01  1.012 -0.013  -0.013   -0.057
## 271        meti_int_02 ~~        meti_int_03  1.012 -0.012  -0.012   -0.058
## 317        meti_ben_02 ~~        meti_ben_04  0.990 -0.017  -0.017   -0.056
## 320        meti_ben_03 ~~        meti_ben_04  0.980 -0.017  -0.017   -0.056
## 308 reas_alt_int_r_rec ~~        meti_ben_04  0.948 -0.021  -0.021   -0.056
## 305 reas_alt_int_r_rec ~~        meti_ben_01  0.935  0.018   0.018    0.059
## 324        meti_ben_04 ~~ reas_alt_ben_r_rec  0.909  0.023   0.023    0.053
## 245     reas_exp_r_rec ~~        meti_ben_04  0.890  0.020   0.020    0.055
## 148        meti_exp_01 ~~ reas_alt_int_r_rec  0.879 -0.017  -0.017   -0.055
## 232        meti_exp_06 ~~        meti_ben_04  0.877 -0.014  -0.014   -0.059
## 210        meti_exp_05 ~~        meti_int_02  0.856 -0.013  -0.013   -0.050
## 104                ben =~        meti_exp_03  0.804  0.029   0.029    0.033
## 89                 int =~        meti_exp_02  0.797 -0.039  -0.039   -0.045
## 102                ben =~        meti_exp_01  0.788  0.027   0.027    0.031
## 251 reas_alt_exp_r_rec ~~        meti_int_04  0.756 -0.015  -0.015   -0.053
## 293        meti_int_04 ~~        meti_ben_02  0.741  0.013   0.013    0.048
## 294        meti_int_04 ~~        meti_ben_03  0.727  0.013   0.013    0.048
## 264        meti_int_01 ~~ reas_alt_int_r_rec  0.704  0.014   0.014    0.052
## 277        meti_int_02 ~~        meti_ben_03  0.691 -0.012  -0.012   -0.048
## 174        meti_exp_03 ~~        meti_exp_05  0.661 -0.014  -0.014   -0.045
## 88                 int =~        meti_exp_01  0.637  0.032   0.032    0.037
## 242     reas_exp_r_rec ~~        meti_ben_01  0.603 -0.014  -0.014   -0.048
## 256 reas_alt_exp_r_rec ~~        meti_ben_03  0.596 -0.015  -0.015   -0.048
## 116               meti =~     reas_exp_r_rec  0.575  0.030   0.030    0.032
## 93                 int =~        meti_exp_06  0.535 -0.032  -0.032   -0.038
## 147        meti_exp_01 ~~     reas_int_r_rec  0.529 -0.014  -0.014   -0.042
## 172        meti_exp_02 ~~ reas_alt_ben_r_rec  0.527 -0.016  -0.016   -0.039
## 190        meti_exp_04 ~~        meti_exp_05  0.521 -0.013  -0.013   -0.039
## 43                 int ~~                 si  0.485  0.051   0.051    0.051
## 200        meti_exp_04 ~~        meti_ben_01  0.483 -0.010  -0.010   -0.040
## 289        meti_int_03 ~~ reas_alt_ben_r_rec  0.458  0.013   0.013    0.036
## 262        meti_int_01 ~~        meti_int_04  0.458  0.009   0.009    0.041
## 111                ben =~        meti_int_02  0.443 -0.037  -0.037   -0.045
## 125                 si =~        meti_exp_04  0.432  0.022   0.022    0.024
## 280        meti_int_02 ~~ reas_alt_ben_r_rec  0.428  0.012   0.012    0.036
## 233        meti_exp_06 ~~     reas_ben_r_rec  0.420  0.013   0.013    0.073
## 316        meti_ben_02 ~~        meti_ben_03  0.419  0.011   0.011    0.038
## 323        meti_ben_04 ~~     reas_ben_r_rec  0.391  0.020   0.020    0.080
## 106                ben =~        meti_exp_05  0.386  0.022   0.022    0.026
## 255 reas_alt_exp_r_rec ~~        meti_ben_02  0.385  0.012   0.012    0.038
## 184        meti_exp_03 ~~        meti_ben_01  0.382 -0.009  -0.009   -0.036
## 138        meti_exp_01 ~~        meti_exp_04  0.381  0.009   0.009    0.036
## 267        meti_int_01 ~~        meti_ben_03  0.346 -0.008  -0.008   -0.035
## 142        meti_exp_01 ~~ reas_alt_exp_r_rec  0.338  0.010   0.010    0.036
## 313        meti_ben_01 ~~        meti_ben_04  0.337  0.009   0.009    0.035
## 123                 si =~        meti_exp_02  0.331  0.018   0.018    0.022
## 110                ben =~        meti_int_01  0.324 -0.033  -0.033   -0.041
## 157        meti_exp_02 ~~        meti_exp_05  0.316 -0.009  -0.009   -0.030
## 248 reas_alt_exp_r_rec ~~        meti_int_01  0.311  0.009   0.009    0.036
## 180        meti_exp_03 ~~        meti_int_03  0.308  0.008   0.008    0.030
## 143        meti_exp_01 ~~        meti_int_01  0.305  0.006   0.006    0.032
## 295        meti_int_04 ~~        meti_ben_04  0.304  0.009   0.009    0.030
## 179        meti_exp_03 ~~        meti_int_02  0.296  0.007   0.007    0.031
## 128                 si =~        meti_int_01  0.294  0.015   0.015    0.018
## 92                 int =~        meti_exp_05  0.281  0.025   0.025    0.030
## 120               meti =~     reas_ben_r_rec  0.269 -0.026  -0.026   -0.029
## 83                 exp =~        meti_ben_02  0.262  0.019   0.019    0.021
## 321        meti_ben_03 ~~     reas_ben_r_rec  0.251  0.015   0.015    0.063
## 300     reas_int_r_rec ~~        meti_ben_02  0.250  0.011   0.011    0.029
## 216        meti_exp_05 ~~        meti_ben_02  0.244 -0.008  -0.008   -0.027
## 189        meti_exp_03 ~~ reas_alt_ben_r_rec  0.244 -0.010  -0.010   -0.027
## 107                ben =~        meti_exp_06  0.239 -0.016  -0.016   -0.019
## 183        meti_exp_03 ~~ reas_alt_int_r_rec  0.222  0.009   0.009    0.028
## 97                 int =~        meti_ben_02  0.210  0.037   0.037    0.041
## 274        meti_int_02 ~~ reas_alt_int_r_rec  0.198  0.008   0.008    0.027
## 192        meti_exp_04 ~~     reas_exp_r_rec  0.175  0.009   0.009    0.024
## 195        meti_exp_04 ~~        meti_int_02  0.168  0.006   0.006    0.023
## 173        meti_exp_03 ~~        meti_exp_04  0.164 -0.007  -0.007   -0.023
## 131                 si =~        meti_int_04  0.156  0.012   0.012    0.015
## 176        meti_exp_03 ~~     reas_exp_r_rec  0.155 -0.008  -0.008   -0.023
## 244     reas_exp_r_rec ~~        meti_ben_03  0.155  0.008   0.008    0.023
## 290        meti_int_04 ~~     reas_int_r_rec  0.113  0.007   0.007    0.020
## 214        meti_exp_05 ~~ reas_alt_int_r_rec  0.112  0.007   0.007    0.019
## 126                 si =~        meti_exp_05  0.104 -0.011  -0.011   -0.013
## 77                 exp =~        meti_int_02  0.096 -0.011  -0.011   -0.013
## 76                 exp =~        meti_int_01  0.095  0.011   0.011    0.014
## 307 reas_alt_int_r_rec ~~        meti_ben_03  0.089  0.006   0.006    0.018
## 269        meti_int_01 ~~     reas_ben_r_rec  0.087 -0.006  -0.006   -0.034
## 227        meti_exp_06 ~~     reas_int_r_rec  0.086  0.006   0.006    0.020
## 132                 si =~        meti_ben_01  0.086  0.009   0.009    0.010
## 208        meti_exp_05 ~~ reas_alt_exp_r_rec  0.086  0.006   0.006    0.017
## 165        meti_exp_02 ~~     reas_int_r_rec  0.072 -0.006  -0.006   -0.015
## 96                 int =~        meti_ben_01  0.070 -0.020  -0.020   -0.023
## 155        meti_exp_02 ~~        meti_exp_03  0.064 -0.004  -0.004   -0.015
## 299     reas_int_r_rec ~~        meti_ben_01  0.064  0.005   0.005    0.015
## 224        meti_exp_06 ~~        meti_int_02  0.058 -0.003  -0.003   -0.016
## 254 reas_alt_exp_r_rec ~~        meti_ben_01  0.055  0.004   0.004    0.015
## 166        meti_exp_02 ~~ reas_alt_int_r_rec  0.053 -0.005  -0.005   -0.013
## 207        meti_exp_05 ~~     reas_exp_r_rec  0.049  0.005   0.005    0.012
## 153        meti_exp_01 ~~     reas_ben_r_rec  0.047  0.004   0.004    0.020
## 223        meti_exp_06 ~~        meti_int_01  0.047 -0.002  -0.002   -0.014
## 188        meti_exp_03 ~~     reas_ben_r_rec  0.043  0.004   0.004    0.018
## 209        meti_exp_05 ~~        meti_int_01  0.038 -0.003  -0.003   -0.011
## 140        meti_exp_01 ~~        meti_exp_06  0.037  0.003   0.003    0.016
## 235     reas_exp_r_rec ~~ reas_alt_exp_r_rec  0.032 -0.009  -0.009   -0.023
## 238     reas_exp_r_rec ~~        meti_int_03  0.030 -0.003  -0.003   -0.010
## 80                 exp =~     reas_int_r_rec  0.028  0.010   0.010    0.010
## 278        meti_int_02 ~~        meti_ben_04  0.023 -0.002  -0.002   -0.009
## 201        meti_exp_04 ~~        meti_ben_02  0.019 -0.002  -0.002   -0.008
## 191        meti_exp_04 ~~        meti_exp_06  0.009  0.002   0.002    0.007
## 237     reas_exp_r_rec ~~        meti_int_02  0.009 -0.002  -0.002   -0.006
## 284        meti_int_03 ~~        meti_ben_01  0.007  0.001   0.001    0.005
## 222        meti_exp_06 ~~ reas_alt_exp_r_rec  0.006  0.001   0.001    0.006
## 282        meti_int_03 ~~     reas_int_r_rec  0.006 -0.002  -0.002   -0.004
## 276        meti_int_02 ~~        meti_ben_02  0.005 -0.001  -0.001   -0.004
## 236     reas_exp_r_rec ~~        meti_int_01  0.005  0.001   0.001    0.004
## 124                 si =~        meti_exp_03  0.004  0.002   0.002    0.002
## 265        meti_int_01 ~~        meti_ben_01  0.004 -0.001  -0.001   -0.004
## 314        meti_ben_01 ~~     reas_ben_r_rec  0.003  0.001   0.001    0.007
## 199        meti_exp_04 ~~ reas_alt_int_r_rec  0.003 -0.001  -0.001   -0.003
## 78                 exp =~        meti_int_03  0.001 -0.001  -0.001   -0.001
## 270        meti_int_01 ~~ reas_alt_ben_r_rec  0.001 -0.001  -0.001   -0.002
## 160        meti_exp_02 ~~ reas_alt_exp_r_rec  0.001  0.000   0.000   -0.001
## 319        meti_ben_02 ~~ reas_alt_ben_r_rec  0.000  0.000   0.000   -0.001
## 229        meti_exp_06 ~~        meti_ben_01  0.000  0.000   0.000    0.001
## 100                int =~     reas_ben_r_rec  0.000 -0.001  -0.001   -0.001
## 257 reas_alt_exp_r_rec ~~        meti_ben_04  0.000  0.000   0.000    0.000
##     sepc.nox
## 84     0.289
## 98     0.550
## 94     0.399
## 41     0.338
## 108    0.269
## 246    0.462
## 309   -0.553
## 241   -0.366
## 185    0.227
## 304   -0.245
## 130   -0.135
## 202    0.203
## 253    0.380
## 228    0.240
## 281    0.187
## 312   -0.206
## 81     0.189
## 226   -0.205
## 158   -0.254
## 325    1.069
## 310    0.197
## 79    -0.148
## 129    0.104
## 46     0.271
## 252   -0.249
## 150   -0.169
## 87    -0.153
## 240    0.213
## 113    0.215
## 215    0.163
## 311    0.177
## 206    0.193
## 168   -0.151
## 234   -0.168
## 187   -0.142
## 196   -0.140
## 161    0.145
## 239    0.147
## 119    0.100
## 283   -0.145
## 302   -0.142
## 275    0.148
## 91    -0.117
## 272   -0.135
## 301    0.134
## 175    0.187
## 164    0.121
## 162   -0.123
## 146   -0.123
## 231    0.143
## 136    0.129
## 145    0.121
## 306    0.128
## 279   -0.228
## 291   -0.125
## 220   -0.111
## 85    -0.089
## 258   -0.243
## 103   -0.077
## 260    0.125
## 221   -0.145
## 230    0.127
## 261   -0.117
## 133    0.072
## 182    0.109
## 101   -0.218
## 115   -0.174
## 139   -0.105
## 273    0.110
## 247   -0.111
## 154    0.101
## 99    -0.168
## 159    0.104
## 42     0.144
## 47    -0.127
## 82    -0.068
## 135   -0.068
## 219    0.146
## 170    0.087
## 288    0.164
## 303    0.216
## 194   -0.089
## 152    0.087
## 86     0.119
## 105   -0.058
## 121   -0.074
## 285   -0.084
## 205    0.081
## 109   -0.086
## 134    0.055
## 137   -0.091
## 249    0.094
## 167   -0.086
## 177   -0.091
## 250   -0.090
## 318   -0.183
## 127    0.052
## 95    -0.114
## 266   -0.085
## 287    0.079
## 149   -0.084
## 151    0.081
## 112    0.103
## 156    0.076
## 259    0.092
## 322   -0.074
## 211    0.070
## 45     0.216
## 217   -0.072
## 122   -0.044
## 118    0.054
## 181   -0.071
## 186    0.073
## 268    0.074
## 204   -0.114
## 213   -0.070
## 198   -0.071
## 315   -0.070
## 193    0.074
## 171   -0.107
## 197    0.066
## 286   -0.069
## 218   -0.063
## 144    0.067
## 212    0.061
## 169   -0.064
## 225   -0.072
## 297    0.061
## 44     0.122
## 296    0.115
## 163    0.060
## 114   -0.111
## 263   -0.068
## 203   -0.058
## 141   -0.062
## 292   -0.061
## 243   -0.061
## 90     0.050
## 117    0.043
## 298    0.080
## 178   -0.057
## 271   -0.058
## 317   -0.056
## 320   -0.056
## 308   -0.056
## 305    0.059
## 324    0.053
## 245    0.055
## 148   -0.055
## 232   -0.059
## 210   -0.050
## 104    0.033
## 89    -0.045
## 102    0.031
## 251   -0.053
## 293    0.048
## 294    0.048
## 264    0.052
## 277   -0.048
## 174   -0.045
## 88     0.037
## 242   -0.048
## 256   -0.048
## 116    0.032
## 93    -0.038
## 147   -0.042
## 172   -0.039
## 190   -0.039
## 43     0.051
## 200   -0.040
## 289    0.036
## 262    0.041
## 111   -0.045
## 125    0.024
## 280    0.036
## 233    0.073
## 316    0.038
## 323    0.080
## 106    0.026
## 255    0.038
## 184   -0.036
## 138    0.036
## 267   -0.035
## 142    0.036
## 313    0.035
## 123    0.022
## 110   -0.041
## 157   -0.030
## 248    0.036
## 180    0.030
## 143    0.032
## 295    0.030
## 179    0.031
## 128    0.018
## 92     0.030
## 120   -0.029
## 83     0.021
## 321    0.063
## 300    0.029
## 216   -0.027
## 189   -0.027
## 107   -0.019
## 183    0.028
## 97     0.041
## 274    0.027
## 192    0.024
## 195    0.023
## 173   -0.023
## 131    0.015
## 176   -0.023
## 244    0.023
## 290    0.020
## 214    0.019
## 126   -0.013
## 77    -0.013
## 76     0.014
## 307    0.018
## 269   -0.034
## 227    0.020
## 132    0.010
## 208    0.017
## 165   -0.015
## 96    -0.023
## 155   -0.015
## 299    0.015
## 224   -0.016
## 254    0.015
## 166   -0.013
## 207    0.012
## 153    0.020
## 223   -0.014
## 188    0.018
## 209   -0.011
## 140    0.016
## 235   -0.023
## 238   -0.010
## 80     0.010
## 278   -0.009
## 201   -0.008
## 191    0.007
## 237   -0.006
## 284    0.005
## 222    0.006
## 282   -0.004
## 276   -0.004
## 236    0.004
## 124    0.002
## 265   -0.004
## 314    0.007
## 199   -0.003
## 78    -0.001
## 270   -0.002
## 160   -0.001
## 319   -0.001
## 229    0.001
## 100   -0.001
## 257    0.000

6.3.3 Testing loadings

library(bain)

res_bain_subload_distrust <- 
bain(ctum_dis_fit, standardize = T,
     "int=~reas_int_r_rec > .3 & ben=~reas_ben_r_rec > .3")

res_bain_eqload_distrust <- 
bain(ctum_dis_fit, standardize = T,
     "-0.15 < exp=~reas_exp_r_rec - exp=~reas_alt_exp_r_rec < 0.15 &
      -0.15 < int=~reas_int_r_rec - int=~reas_alt_int_r_rec < 0.15 &
      -0.15 < ben=~reas_ben_r_rec - ben=~reas_alt_ben_r_rec < 0.15")

res_bain_subload_distrust
## Bayesian informative hypothesis testing for an object of class lavaan:
## 
##    Fit   Com   BF.u  BF.c    PMPa  PMPb 
## H1 0.991 0.240 4.129 333.960 1.000 0.805
## Hu                                 0.195
## 
## Hypotheses:
##   H1: int=~reas_int_r_rec>.3&ben=~reas_ben_r_rec>.3
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
res_bain_eqload_distrust
## Bayesian informative hypothesis testing for an object of class lavaan:
## 
##    Fit   Com   BF.u  BF.c  PMPa  PMPb 
## H1 0.026 0.004 6.104 6.239 1.000 0.859
## Hu                               0.141
## 
## Hypotheses:
##   H1: -0.15<exp=~reas_exp_r_rec-exp=~reas_alt_exp_r_rec<0.15&-0.15<int=~reas_int_r_rec-int=~reas_alt_int_r_rec<0.15&-0.15<ben=~reas_ben_r_rec-ben=~reas_alt_ben_r_rec<0.15
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.

7 Investigating Hypotheses 1 & 2: Teachers’ reasons for (dis-)trust in educational science Main Study

7.1 Graphical display

data_hyp1_2 <- data_ttest%>%
  select(f9_1, f9_2, f9_3, f10_1, f10_2, f10_3)%>%
  gather(variable, value)

library(patchwork)
library(hrbrthemes)
## NOTE: Either Arial Narrow or Roboto Condensed fonts are required to use these themes.
##       Please use hrbrthemes::import_roboto_condensed() to install Roboto Condensed and
##       if Arial Narrow is not on your system, please see https://bit.ly/arialnarrow
data_hyp1_2_freq <- as.data.frame(table(data_hyp1_2$variable, data_hyp1_2$value))%>%
  mutate(variable = fct_recode(Var1,
                               `Expertise\n(Trust)` = "f9_1",
                               `Integrity\n(Trust)` = "f9_2",
                               `Benevolence\n(Trust)` = "f9_3",
                               `Expertise\n(Distrust)` = "f10_1",
                               `Integrity\n(Distrust)` = "f10_2",
                               `Benevolence\n(Distrust)` = "f10_3"),
         variable = fct_relevel(variable, 
                                "Expertise\n(Trust)",
                                "Integrity\n(Trust)",
                                "Benevolence\n(Trust)",
                                "Expertise\n(Distrust)",
                                "Integrity\n(Distrust)",
                                "Benevolence\n(Distrust)"),
         value = as.numeric(Var2),
         Frequency = Freq)

plot1 <- ggplot(data = data_hyp1_2_freq,
       aes(variable, value)) +
  geom_point(aes(size = Frequency, color = Frequency, stat = "identity", 
                 position = "identity"), shape = 15) +
  scale_size_continuous(range = c(3,15)) + 
  scale_color_gradient(low = "grey95", high = "grey65") +
  stat_summary(data = data_hyp1_2%>%
                 mutate(variable = fct_recode(variable,
                               `Expertise\n(Trust)` = "f9_1",
                               `Integrity\n(Trust)` = "f9_2",
                               `Benevolence\n(Trust)` = "f9_3",
                               `Expertise\n(Distrust)` = "f10_1",
                               `Integrity\n(Distrust)` = "f10_2",
                               `Benevolence\n(Distrust)` = "f10_3"),
                        variable = fct_relevel(variable, 
                                "Expertise\n(Trust)",
                                "Integrity\n(Trust)",
                                "Benevolence\n(Trust)",
                                "Expertise\n(Distrust)",
                                "Integrity\n(Distrust)",
                                "Benevolence\n(Distrust)")),
                        aes(variable, value), 
               fun.data = "mean_sdl", fun.args = list(mult = 1), 
               color = "black")  +
  theme_ipsum_ps() +
  theme(panel.grid.major.x = element_blank(), panel.grid.minor.y = element_blank()) +
  guides(color=guide_legend(), size = guide_legend()) + 
  labs(title = "Reasons for trust and distrust in educational science",
       subtitle = "Product plot of the raw data and means ± 1*SD") + 
       xlab("") +
       ylab("")
## Warning: Ignoring unknown aesthetics: stat, position
#ggsave("plot1x.svg", plot1, width = 9.42, height = 5.71)

plot1
## Warning: Removed 45 rows containing non-finite values (stat_summary).

7.2 Effect sizes

7.2.1 Trust

Vargha & Delaney’s A Exp
Int 0.49
ben 0.57

7.2.2 Distrust

Vargha & Delaney’s A Exp
Int 0.31
ben 0.37

7.3 Approximate adjusted fractional Bayes factors

7.3.1 Reasons for trust in educational science: H1

library(bain)
within_h1 <- lm(cbind(f9_1, f9_2, f9_3)~1, data=data_ttest)
estimate_h1 <- coef(within_h1)[1:3]
names(estimate_h1) <- c("exp","int", "ben")
ngroup_h1 <- nrow(data_ttest)
covmatr_h1 <- list(vcov(within_h1))
results_h1 <- bain(estimate_h1,"exp=int=ben;exp>(int,ben);exp>int=ben",  
                n=ngroup_h1, Sigma=covmatr_h1,
                group_parameters=3,
                joint_parameters = 0)
print(results_h1)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c  PMPa  PMPb 
## H1 0.000 0.373 0.000 0.000 0.000 0.000
## H2 0.287 0.322 0.891 0.847 1.000 0.471
## H3 0.000 0.270 0.000 0.000 0.000 0.000
## Hu                               0.529
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp>(int,ben)
##   H3: exp>int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h1$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 3.842251e-05     1.533643
## H2 2.602641e+04 1.000000e+00 39915.218050
## H3 6.520423e-01 2.505310e-05     1.000000

7.3.1.1 Sensitivity analysis

results_h1f2 <- bain(estimate_h1,"exp=int=ben;exp>(int,ben);exp>int=ben",  
                n=ngroup_h1, Sigma=covmatr_h1,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 2)
print(results_h1f2)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c  PMPa  PMPb 
## H1 0.000 0.747 0.000 0.000 0.000 0.000
## H2 0.284 0.325 0.874 0.823 1.000 0.466
## H3 0.000 0.382 0.000 0.000 0.000 0.000
## Hu                               0.534
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp>(int,ben)
##   H3: exp>int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h1f2$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 1.959713e-05     1.084449
## H2 5.102789e+04 1.000000e+00 55337.154693
## H3 9.221271e-01 1.807104e-05     1.000000
results_h1f3 <- bain(estimate_h1,"exp=int=ben;exp>(int,ben);exp>int=ben",  
                n=ngroup_h1, Sigma=covmatr_h1,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 3)
print(results_h1f3)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c  PMPa  PMPb 
## H1 0.000 1.120 0.000 0.000 0.000 0.000
## H2 0.292 0.318 0.915 0.881 1.000 0.478
## H3 0.000 0.468 0.000 0.000 0.000 0.000
## Hu                               0.522
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp>(int,ben)
##   H3: exp>int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h1f3$BFmatrix
##             H1           H2           H3
## H1     1.00000 1.246693e-05     0.885449
## H2 80212.23153 1.000000e+00 71023.843500
## H3     1.12937 1.407978e-05     1.000000

7.3.2 Reasons for trust in educational science: H1a (Exploratory!)

within_h1a <- lm(cbind(f9_1, f9_2)~1, data=data_ttest)
estimate_h1a <- coef(within_h1a)[1:2]
names(estimate_h1a) <- c("exp","int")
ngroup_h1a <- nrow(data_ttest)
covmatr_h1a <- list(vcov(within_h1a))
results_h1a <- bain(estimate_h1a,"exp=int;exp>int", 
                n=ngroup_h1a, Sigma=covmatr_h1a,
                group_parameters=2,
                joint_parameters = 0)
print(results_h1a)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u   BF.c   PMPa  PMPb 
## H1 7.738 0.445 17.391 17.391 0.968 0.917
## H2 0.288 0.500 0.575  0.404  0.032 0.030
## Hu                                 0.053
## 
## Hypotheses:
##   H1: exp=int
##   H2: exp>int
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h1a$BFmatrix
##            H1       H2
## H1 1.00000000 30.23108
## H2 0.03307854  1.00000

7.3.2.1 Sensitivity analysis

results_h1af2 <- bain(estimate_h1a,"exp=int;exp>int", 
                n=ngroup_h1a, Sigma=covmatr_h1a,
                group_parameters=2,
                joint_parameters = 0,
                fraction = 2)
print(results_h1af2)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u   BF.c   PMPa  PMPb 
## H1 7.738 0.629 12.297 12.297 0.955 0.886
## H2 0.288 0.500 0.575  0.404  0.045 0.041
## Hu                                 0.072
## 
## Hypotheses:
##   H1: exp=int
##   H2: exp>int
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h1af2$BFmatrix
##            H1      H2
## H1 1.00000000 21.3766
## H2 0.04678012  1.0000
results_h1af3 <- bain(estimate_h1a,"exp=int;exp>int", 
                n=ngroup_h1a, Sigma=covmatr_h1a,
                group_parameters=2,
                joint_parameters = 0,
                fraction = 3)
print(results_h1af3)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u   BF.c   PMPa  PMPb 
## H1 7.738 0.771 10.041 10.041 0.946 0.864
## H2 0.288 0.500 0.575  0.404  0.054 0.050
## Hu                                 0.086
## 
## Hypotheses:
##   H1: exp=int
##   H2: exp>int
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h1af3$BFmatrix
##            H1       H2
## H1 1.00000000 17.45392
## H2 0.05729372  1.00000

7.3.3 Reasons for trust in educational science: H1b (Exploratory!)

library(bain)
within_h1b <- lm(cbind(f9_1, f9_3)~1, data=data_ttest)
estimate_h1b <- coef(within_h1b)[1:2]
names(estimate_h1b) <- c("exp","ben")
ngroup_h1b <- nrow(data_ttest)
covmatr_h1b <- list(vcov(within_h1b))
results_h1b <- bain(estimate_h1b,"exp=ben;exp>ben",  
                n=ngroup_h1b, Sigma=covmatr_h1b,
                group_parameters=2,
                joint_parameters = 0)
print(results_h1b)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c       PMPa  PMPb 
## H1 0.000 0.374 0.001 0.001      0.000 0.000
## H2 1.000 0.500 2.000 285136.432 1.000 0.666
## Hu                                    0.333
## 
## Hypotheses:
##   H1: exp=ben
##   H2: exp>ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h1b$BFmatrix
##          H1           H2
## H1    1.000 0.0004201512
## H2 2380.095 1.0000000000

7.3.3.1 Sensitivity analysis

results_h1bf2 <- bain(estimate_h1b,"exp=ben;exp>ben",  
                n=ngroup_h1b, Sigma=covmatr_h1b,
                group_parameters=2,
                joint_parameters = 0,
                fraction = 2)
print(results_h1bf2)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c       PMPa  PMPb 
## H1 0.000 0.528 0.001 0.001      0.000 0.000
## H2 1.000 0.500 2.000 285136.432 1.000 0.667
## Hu                                    0.333
## 
## Hypotheses:
##   H1: exp=ben
##   H2: exp>ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h1bf2$BFmatrix
##          H1           H2
## H1    1.000 0.0002970918
## H2 3365.963 1.0000000000
results_h1bf3 <- bain(estimate_h1b,"exp=ben;exp>ben",  
                n=ngroup_h1b, Sigma=covmatr_h1b,
                group_parameters=2,
                joint_parameters = 0,
                fraction = 3)
print(results_h1bf3)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c       PMPa  PMPb 
## H1 0.000 0.647 0.000 0.000      0.000 0.000
## H2 1.000 0.500 2.000 285136.432 1.000 0.667
## Hu                                    0.333
## 
## Hypotheses:
##   H1: exp=ben
##   H2: exp>ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h1bf3$BFmatrix
##          H1           H2
## H1    1.000 0.0002425744
## H2 4122.446 1.0000000000

7.3.4 Reasons for distrust in educational science: H2

within_h2 <- lm(cbind(f10_1, f10_2, f10_3)~1, data=data_ttest)
estimate_h2 <- coef(within_h2)[1:3]
names(estimate_h2) <- c("exp","int", "ben")
ngroup_h2 <- nrow(data_ttest)
covmatr_h2 <- list(vcov(within_h2))
results_h2 <- bain(estimate_h2,"exp=int=ben;exp<(int,ben);exp<int=ben",  
                n=ngroup_h2, Sigma=covmatr_h2,
                group_parameters=3,
                joint_parameters = 0)
print(results_h2)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c               PMPa  PMPb 
## H1 0.000 0.273 0.000 0.000              0.000 0.000
## H2 1.000 0.330 3.032 22878074224672.238 0.983 0.742
## H3 0.013 0.240 0.052 0.052              0.017 0.013
## Hu                                            0.245
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp<(int,ben)
##   H3: exp<int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h2$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 1.296213e-38 7.532838e-37
## H2 7.714782e+37 1.000000e+00 5.811421e+01
## H3 1.327521e+36 1.720750e-02 1.000000e+00

7.3.4.1 Sensitivity analysis

results_h2f2 <- bain(estimate_h2,"exp=int=ben;exp<(int,ben);exp<int=ben",  
                n=ngroup_h2, Sigma=covmatr_h2,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 2)
print(results_h2f2)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c               PMPa  PMPb 
## H1 0.000 0.546 0.000 0.000              0.000 0.000
## H2 1.000 0.335 2.982 22372085646463.426 0.988 0.742
## H3 0.013 0.339 0.037 0.037              0.012 0.009
## Hu                                            0.249
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp<(int,ben)
##   H3: exp<int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h2f2$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 6.589533e-39 5.326521e-37
## H2 1.517558e+38 1.000000e+00 8.083306e+01
## H3 1.877398e+36 1.237118e-02 1.000000e+00
results_h2f3 <- bain(estimate_h2,"exp=int=ben;exp<(int,ben);exp<int=ben",  
                n=ngroup_h2, Sigma=covmatr_h2,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 3)
print(results_h2f3)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c               PMPa  PMPb 
## H1 0.000 0.819 0.000 0.000              0.000 0.000
## H2 1.000 0.331 3.020 21583946898072.125 0.990 0.746
## H3 0.013 0.415 0.030 0.030              0.010 0.007
## Hu                                            0.247
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp<(int,ben)
##   H3: exp<int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h2f3$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 4.337736e-39 4.349086e-37
## H2 2.305350e+38 1.000000e+00 1.002617e+02
## H3 2.299334e+36 9.973901e-03 1.000000e+00

8 Investigating Hypotheses 3 & 4: Teachers’ reasons for (dis-)trust in science Main Study

8.1 Graphical display

data_hyp3_4 <- data_ttest%>%
  select(f4_1, f4_2, f4_3, f5_1, f5_2, f5_3)%>%
  gather(variable, value)

data_hyp3_4_freq <- as.data.frame(table(data_hyp3_4$variable, data_hyp3_4$value))%>%
  mutate(variable = fct_recode(Var1,
                               `Expertise\n(Trust)` = "f4_1",
                               `Integrity\n(Trust)` = "f4_2",
                               `Benevolence\n(Trust)` = "f4_3",
                               `Expertise\n(Distrust)` = "f5_1",
                               `Integrity\n(Distrust)` = "f5_2",
                               `Benevolence\n(Distrust)` = "f5_3"),
         variable = fct_relevel(variable, 
                                "Expertise\n(Trust)",
                                "Integrity\n(Trust)",
                                "Benevolence\n(Trust)",
                                "Expertise\n(Distrust)",
                                "Integrity\n(Distrust)",
                                "Benevolence\n(Distrust)"),
         value = as.numeric(Var2),
         Frequency = Freq)

plot2 <- ggplot(data = data_hyp3_4_freq,
       aes(variable, value)) +
  geom_point(aes(size = Frequency, color = Frequency, stat = "identity", 
                 position = "identity"), shape = 15) +
  scale_size_continuous(range = c(3,15)) + 
  scale_color_gradient(low = "grey95", high = "grey65") +
  stat_summary(data = data_hyp3_4%>%
                 mutate(variable = fct_recode(variable,
                               `Expertise\n(Trust)` = "f4_1",
                               `Integrity\n(Trust)` = "f4_2",
                               `Benevolence\n(Trust)` = "f4_3",
                               `Expertise\n(Distrust)` = "f5_1",
                               `Integrity\n(Distrust)` = "f5_2",
                               `Benevolence\n(Distrust)` = "f5_3"),
                        variable = fct_relevel(variable, 
                                "Expertise\n(Trust)",
                                "Integrity\n(Trust)",
                                "Benevolence\n(Trust)",
                                "Expertise\n(Distrust)",
                                "Integrity\n(Distrust)",
                                "Benevolence\n(Distrust)")),
                        aes(variable, value), 
               fun.data = "mean_sdl", fun.args = list(mult = 1), 
               color = "black")  +
  theme_ipsum_ps() +
  theme(panel.grid.major.x = element_blank(), panel.grid.minor.y = element_blank()) +
  guides(color=guide_legend(), size = guide_legend()) + 
  labs(title = "Reasons for trust and distrust in science",
       subtitle = "Product plot of the raw data and means ± 1*SD") + 
       xlab("") +
       ylab("")
## Warning: Ignoring unknown aesthetics: stat, position
#ggsave("plot2.svg", plot2, width = 9.42, height = 5.71)

plot2
## Warning: Removed 24 rows containing non-finite values (stat_summary).

8.2 Effect sizes

8.2.1 Trust

Vargha & Delaney’s A Exp
Int 0.54
ben 0.81

8.2.2 Distrust

Vargha & Delaney’s A Exp
Int 0.28
ben 0.1

8.3 Approximate adjusted fractional Bayes factors

8.3.1 Reasons for trust in science: H3

within_h3 <- lm(cbind(f4_1, f4_2, f4_3)~1, data=data_ttest)
estimate_h3 <- coef(within_h3)[1:3]
names(estimate_h3) <- c("exp","int", "ben")
ngroup_h3 <- nrow(data_ttest)
covmatr_h3 <- list(vcov(within_h3))
results_h3 <- bain(estimate_h3,"exp=int=ben;exp>(int,ben);exp>int=ben",  
                n=ngroup_h3, Sigma=covmatr_h3,
                group_parameters=3,
                joint_parameters = 0)
print(results_h3)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c      PMPa  PMPb 
## H1 0.000 0.447 0.000 0.000     0.000 0.000
## H2 1.000 0.293 3.415 69578.818 1.000 0.773
## H3 0.000 0.264 0.000 0.000     0.000 0.000
## Hu                                   0.227
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp>(int,ben)
##   H3: exp>int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h3$BFmatrix
##               H1            H2           H3
## H1  1.000000e+00 1.929058e-112 2.526982e-42
## H2 5.183878e+111  1.000000e+00 1.309957e+70
## H3  3.957290e+41  7.633841e-71 1.000000e+00

8.3.1.1 Sensitivity analysis

results_h3f2 <- bain(estimate_h3,"exp=int=ben;exp>(int,ben);exp>int=ben",  
                n=ngroup_h3, Sigma=covmatr_h3,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 2)
print(results_h3f2)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c      PMPa  PMPb 
## H1 0.000 0.893 0.000 0.000     0.000 0.000
## H2 1.000 0.292 3.421 66094.458 1.000 0.774
## H3 0.000 0.373 0.000 0.000     0.000 0.000
## Hu                                   0.226
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp>(int,ben)
##   H3: exp>int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h3f2$BFmatrix
##               H1            H2           H3
## H1  1.000000e+00 9.628475e-113 1.786846e-42
## H2 1.038586e+112  1.000000e+00 1.855793e+70
## H3  5.596453e+41  5.388531e-71 1.000000e+00
results_h3f3 <- bain(estimate_h3,"exp=int=ben;exp>(int,ben);exp>int=ben",  
                n=ngroup_h3, Sigma=covmatr_h3,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 3)
print(results_h3f3)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c      PMPa  PMPb 
## H1 0.000 1.340 0.000 0.000     0.000 0.000
## H2 1.000 0.289 3.461 69204.031 1.000 0.776
## H3 0.000 0.457 0.000 0.000     0.000 0.000
## Hu                                   0.224
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp>(int,ben)
##   H3: exp>int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h3f3$BFmatrix
##               H1            H2           H3
## H1  1.000000e+00 6.344082e-113 1.458954e-42
## H2 1.576272e+112  1.000000e+00 2.299708e+70
## H3  6.854228e+41  4.348378e-71 1.000000e+00

8.3.2 Reasons for distrust in science: H4

within_h4 <- lm(cbind(f5_1, f5_2, f5_3)~1, data=data_ttest)
estimate_h4 <- coef(within_h4)[1:3]
names(estimate_h4) <- c("exp","int", "ben")
ngroup_h4 <- nrow(data_ttest)
covmatr_h4 <- list(vcov(within_h4))
results_h4 <- bain(estimate_h4,"exp=int=ben;exp<(int,ben);exp<int=ben",  
                n=ngroup_h4, Sigma=covmatr_h4,
                group_parameters=3,
                joint_parameters = 0)
print(results_h4)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c               PMPa  PMPb 
## H1 0.000 0.366 0.000 0.000              0.000 0.000
## H2 1.000 0.331 3.022 23171390218021.137 1.000 0.751
## H3 0.000 0.280 0.000 0.000              0.000 0.000
## Hu                                            0.249
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp<(int,ben)
##   H3: exp<int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h4$BFmatrix
##               H1            H2            H3
## H1  1.000000e+00 1.247116e-234 1.166343e-169
## H2 8.018498e+233  1.000000e+00  9.352321e+64
## H3 8.573806e+168  1.069253e-65  1.000000e+00

8.3.2.1 Sensitivity analysis

results_h4f2 <- bain(estimate_h4,"exp=int=ben;exp<(int,ben);exp<int=ben",  
                n=ngroup_h4, Sigma=covmatr_h4,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 2)
print(results_h4f2)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c               PMPa  PMPb 
## H1 0.000 0.731 0.000 0.000              0.000 0.000
## H2 1.000 0.332 3.013 23070728595198.426 1.000 0.751
## H3 0.000 0.396 0.000 0.000              0.000 0.000
## Hu                                            0.249
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp<(int,ben)
##   H3: exp<int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h4f2$BFmatrix
##               H1            H2            H3
## H1  1.000000e+00 6.253759e-235 8.247292e-170
## H2 1.599038e+234  1.000000e+00  1.318773e+65
## H3 1.212519e+169  7.582804e-66  1.000000e+00
results_h4f3 <- bain(estimate_h4,"exp=int=ben;exp<(int,ben);exp<int=ben",  
                n=ngroup_h4, Sigma=covmatr_h4,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 3)
print(results_h4f3)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c               PMPa  PMPb 
## H1 0.000 1.097 0.000 0.000              0.000 0.000
## H2 1.000 0.332 3.015 23087751457239.219 1.000 0.751
## H3 0.000 0.485 0.000 0.000              0.000 0.000
## Hu                                            0.249
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp<(int,ben)
##   H3: exp<int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h4f3$BFmatrix
##               H1            H2            H3
## H1  1.000000e+00 4.167119e-235 6.733885e-170
## H2 2.399740e+234  1.000000e+00  1.615957e+65
## H3 1.485027e+169  6.188283e-66  1.000000e+00

9 Investigating Hypotheses 5 & 6: Germans’ reasons for (dis-)trust in science Main Study

9.1 Preparing the Science Barometer (Wissenschaftsbarometer) data

data_merged <- data_wb%>%
  # filter(bild == 16)%>% # only those with higher education
  mutate(altq = alter,
         f1_1 = V1_1,  # Interesse an Politik | recoded below
         f1_2 = V1_4,  # Interesse an Sport | recoded below
         f1_3 = V1_5,  # Interesse an Wissenschaft und Forschung | 
         f4_1 = V9_1,  # Trust: Exp    | recoded below
         f4_2 = V9_2,  # Trust: Int    | recoded below
         f4_3 = V9_3,  # Trust: Ben    | recoded below
         f5_1 = V10_1, # Distrust: Exp | recoded below
         f5_2 = V10_2, # Distrust: Int | recoded below
         f5_3 = V10_3, # Distrust: Ben | recoded below
         population = "general",
         bild = as.factor(bild))%>%
    mutate_at(vars(c("f1_1", "f1_2", "f1_3",
                     "f4_1", "f4_2", "f4_3", "f5_1", "f5_2", "f5_3")),
            list(~ifelse(. == 9, NA, .)))%>% # 9 = weiß nicht/keine Angabe
  select(altq, f1_1, f1_2, f1_3, f4_1, f4_2, 
         f4_3, f5_1, f5_2, f5_3, population, bild)%>%
  mutate(f1_1 = 6 - f1_1, # RECODING
         f1_2 = 6 - f1_2,
         f1_3 = 6 - f1_3,
         f4_1 = 6 - f4_1, 
         f4_2 = 6 - f4_2,
         f4_3 = 6 - f4_3,
         f5_1 = 6 - f5_1,
         f5_2 = 6 - f5_2,
         f5_3 = 6 - f5_3,
         bild = as.factor(bild))%>%
  full_join(., 
            data_ttest%>%
              mutate(population = "teachers",
                     bild = as.factor("16")))%>%
  mutate(population_n = as.numeric(as.factor(population)) - 1)%>%
  select(altq, f1_1, f1_2, f1_3, f4_1, f4_2, 
         f4_3, f5_1, f5_2, f5_3, population, bild, population_n)%>%
  mutate(bild = as.factor(bild))
## Joining, by = c("altq", "f1_1", "f1_2", "f1_3", "f4_1", "f4_2", "f4_3", "f5_1", "f5_2", "f5_3", "population", "bild")

9.2 Matching teachers and the general population

set.seed(31415)
match1 <- MatchIt::matchit(population_n ~ altq + bild + f1_1 + f1_2 + f1_3, 
                           replace = T, 
                           data = na.omit(data_merged), 
                           method = "genetic",
                           pop.size = 250)
summary(match1)

9.2.1 Standardized summary of data before matching (copypasteable)

summary_match1 <- summary(match1, standardize = T)
knitr::kable(summary_match1$sum.all, digits = 3)
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean eCDF Max Std. Pair Dist.
distance 0.587 0.181 2.861 0.311 0.375 0.690 NA
altq 47.690 54.565 -0.637 0.379 0.116 0.294 NA
bild11 0.000 0.014 -0.144 NA 0.014 0.014 NA
bild12 0.000 0.159 -0.507 NA 0.159 0.159 NA
bild14 0.000 0.277 -0.702 NA 0.277 0.277 NA
bild15 0.000 0.159 -0.507 NA 0.159 0.159 NA
bild16 1.000 0.391 1.233 NA 0.609 0.609 NA
f1_1 4.020 3.773 0.280 0.620 0.049 0.113 NA
f1_2 2.982 3.207 -0.176 0.993 0.045 0.085 NA
f1_3 3.822 3.787 0.042 0.644 0.034 0.068 NA

9.2.2 Standardized summary of data after matching (copypasteable)

knitr::kable(summary_match1$sum.matched, digits = 3)
Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean eCDF Max Std. Pair Dist.
distance 0.587 0.587 -0.002 0.993 0.004 0.033 0.107
altq 47.690 47.635 0.005 0.959 0.006 0.035 0.094
bild11 0.000 0.000 0.000 NA 0.000 0.000 0.000
bild12 0.000 0.000 0.000 NA 0.000 0.000 0.000
bild14 0.000 0.000 0.000 NA 0.000 0.000 0.000
bild15 0.000 0.000 0.000 NA 0.000 0.000 0.000
bild16 1.000 1.000 0.000 NA 0.000 0.000 0.000
f1_1 4.020 4.058 -0.042 1.084 0.021 0.060 0.902
f1_2 2.982 3.000 -0.014 1.078 0.018 0.035 0.159
f1_3 3.822 3.823 0.000 0.993 0.000 0.000 0.000
data_hyp5_6 <- na.omit(data_merged)%>%
  mutate(matching_weights = match1$weights,
         PID = 1:n())%>%
  filter(population == "general" &
           matching_weights > 0)

data_hyp5_6_long <- data_hyp5_6%>%
  gather(variable, value, f4_1, f4_2, f4_3, f5_1, f5_2, f5_3)

9.3 Graphical display

# create a {survey}-design-object which allows to compute
# frequency tables with weighted data
wght_design <- survey::svydesign(id = ~PID, weights = ~matching_weights, data = data_hyp5_6_long)

data_hyp5_6_freq <- survey::svytable(~variable+value, wght_design)%>%
  as.data.frame(.)%>%
  mutate(variable = fct_recode(variable,
                              `Expertise\n(Trust)` = "f4_1",
                              `Integrity\n(Trust)` = "f4_2",
                              `Benevolence\n(Trust)` = "f4_3",
                              `Expertise\n(Distrust)` = "f5_1",
                              `Integrity\n(Distrust)` = "f5_2",
                              `Benevolence\n(Distrust)` = "f5_3"),
        variable = fct_relevel(variable, 
                               "Expertise\n(Trust)",
                               "Integrity\n(Trust)",
                               "Benevolence\n(Trust)",
                               "Expertise\n(Distrust)",
                               "Integrity\n(Distrust)",
                               "Benevolence\n(Distrust)"),
        value = as.numeric(value),
        Frequency = Freq)

plot3 <- data_hyp5_6_long%>%
  group_by(variable)%>%
  summarize(mean = weighted.mean(value, w = matching_weights),
            sd = sqrt(Hmisc::wtd.var(value, weights = matching_weights)))%>%
  mutate(variable = fct_recode(variable,
                              `Expertise\n(Trust)` = "f4_1",
                              `Integrity\n(Trust)` = "f4_2",
                              `Benevolence\n(Trust)` = "f4_3",
                              `Expertise\n(Distrust)` = "f5_1",
                              `Integrity\n(Distrust)` = "f5_2",
                              `Benevolence\n(Distrust)` = "f5_3"),
         variable = fct_relevel(variable, 
                               "Expertise\n(Trust)",
                               "Integrity\n(Trust)",
                               "Benevolence\n(Trust)",
                               "Expertise\n(Distrust)",
                               "Integrity\n(Distrust)",
                               "Benevolence\n(Distrust)"))%>%
  ggplot(.) + 
  geom_point(data = data_hyp5_6_freq, aes(variable, value, size = Frequency, color = Frequency, stat = "identity", 
                 position = "identity"), shape = 15) +
  scale_size_continuous(range = c(3,15)) + 
  scale_color_gradient(low = "grey95", high = "grey65") +
  geom_point(aes(variable, mean), shape = 19, size = 2.5) +
  geom_errorbar(aes(variable, mean, ymin=mean-sd, ymax=mean+sd), width=.0) + 
  labs(subtitle = "Means ±1SD in matched general population") +
  coord_cartesian(ylim = c(1,5)) +
  theme_ipsum_ps() +
  theme(panel.grid.major.x = element_blank(), panel.grid.minor.y = element_blank()) +
  guides(color=guide_legend(), size = guide_legend()) + 
  labs(title = "Reasons for trust and distrust in science",
       subtitle = "Product plot of the raw data and means ± 1*SD  (matched general Population)") + 
       xlab("") +
       ylab("")
## Warning: Ignoring unknown aesthetics: stat, position
# ggsave("plot3.svg", plot3, width = 9.42, height = 5.71)
plot3

9.4 Effect sizes

9.4.1 Trust

library(RProbSup)

weightedA_trust_Exp_Int <- 
  A2(data_hyp5_6$f4_1,
     data_hyp5_6$f4_2,
     weights = T,
     w = data_hyp5_6$matching_weights)

weightedA_trust_Exp_Ben <- 
    A2(data_hyp5_6$f4_1,
     data_hyp5_6$f4_3,
     weights = T,
     w = data_hyp5_6$matching_weights)

weightedA_distrust_Exp_Int <- 
  A2(data_hyp5_6$f5_1,
     data_hyp5_6$f5_2,
     weights = T,
     w = data_hyp5_6$matching_weights)

weightedA_distrust_Exp_Ben <- 
    A2(data_hyp5_6$f5_1,
     data_hyp5_6$f5_3,
     weights = T,
     w = data_hyp5_6$matching_weights)
Vargha & Delaney’s A Exp
Int 0.58
ben 0.85

9.4.2 Distrust

Vargha & Delaney’s A Exp
Int 0.24
ben 0.09

9.5 Approximate adjusted fractional Bayes factors

9.5.1 Reasons for trust in science: H5

library(heplots)
## Loading required package: car
## Loading required package: carData
## Registered S3 methods overwritten by 'car':
##   method                          from
##   influence.merMod                lme4
##   cooks.distance.influence.merMod lme4
##   dfbeta.influence.merMod         lme4
##   dfbetas.influence.merMod        lme4
## 
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
## 
##     recode
## The following object is masked from 'package:purrr':
## 
##     some
within_h5 <- robmlm(cbind(f4_1, f4_2, f4_3)~1, 
                      data=data_hyp5_6, 
                      weights = matching_weights)
estimate_h5 <- coef(within_h5)[1:3]
names(estimate_h5) <- c("exp","int", "ben")
ngroup_h5 <- nrow(data_hyp5_6)
covmatr_h5 <- list(heplots:::vcov.mlm(within_h5))
results_h5 <- bain(estimate_h5,"exp=int=ben;exp>(int,ben);exp>int=ben",  
                n=ngroup_h5, Sigma=covmatr_h5,
                group_parameters=3,
                joint_parameters = 0)
print(results_h5)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c     PMPa  PMPb 
## H1 0.000 0.323 0.000 0.000    0.000 0.000
## H2 0.999 0.297 3.361 3404.742 1.000 0.771
## H3 0.000 0.232 0.000 0.000    0.000 0.000
## Hu                                  0.229
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp>(int,ben)
##   H3: exp>int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h5$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 1.179326e-36 2.401340e-19
## H2 8.479423e+35 1.000000e+00 2.036198e+17
## H3 4.164342e+18 4.911115e-18 1.000000e+00

9.5.1.1 Sensitivity analysis

results_h5f2 <- bain(estimate_h5,"exp=int=ben;exp>(int,ben);exp>int=ben",  
                n=ngroup_h5, Sigma=covmatr_h5,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 2)
print(results_h5f2)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c     PMPa  PMPb 
## H1 0.000 0.647 0.000 0.000    0.000 0.000
## H2 0.999 0.298 3.357 3180.731 1.000 0.770
## H3 0.000 0.328 0.000 0.000    0.000 0.000
## Hu                                  0.230
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp>(int,ben)
##   H3: exp>int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h5f2$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 5.904281e-37 1.698004e-19
## H2 1.693686e+36 1.000000e+00 2.875885e+17
## H3 5.889269e+18 3.477190e-18 1.000000e+00
results_h5f3 <- bain(estimate_h5,"exp=int=ben;exp>(int,ben);exp>int=ben",  
                n=ngroup_h5, Sigma=covmatr_h5,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 3)
print(results_h5f3)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c     PMPa  PMPb 
## H1 0.000 0.970 0.000 0.000    0.000 0.000
## H2 0.999 0.298 3.356 3327.421 1.000 0.770
## H3 0.000 0.402 0.000 0.000    0.000 0.000
## Hu                                  0.230
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp>(int,ben)
##   H3: exp>int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h5f3$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 3.937193e-37 1.386414e-19
## H2 2.539880e+36 1.000000e+00 3.521326e+17
## H3 7.212852e+18 2.839839e-18 1.000000e+00

9.5.2 Reasons for trust in science: H6

within_h6 <- robmlm(cbind(f5_1, f5_2, f5_3)~1, 
                      data=data_hyp5_6, 
                      weights = matching_weights)
estimate_h6 <- coef(within_h6)[1:3]
names(estimate_h6) <- c("exp","int", "ben")
ngroup_h6 <- nrow(data_hyp5_6)
covmatr_h6 <- list(heplots:::vcov.mlm(within_h6))
results_h6 <- bain(estimate_h6,"exp=int=ben;exp<(int,ben);exp<int=ben",  
                n=ngroup_h6, Sigma=covmatr_h6,
                group_parameters=3,
                joint_parameters = 0)
print(results_h6)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c               PMPa  PMPb 
## H1 0.000 0.307 0.000 0.000              0.000 0.000
## H2 1.000 0.332 3.012 23061462699880.293 1.000 0.751
## H3 0.000 0.256 0.000 0.000              0.000 0.000
## Hu                                            0.249
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp<(int,ben)
##   H3: exp<int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h6$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 2.320264e-86 1.665417e-59
## H2 4.309855e+85 1.000000e+00 7.177707e+26
## H3 6.004501e+58 1.393202e-27 1.000000e+00

9.5.2.1 Sensitivity analysis

results_h6f2 <- bain(estimate_h6,"exp=int=ben;exp<(int,ben);exp<int=ben",  
                n=ngroup_h6, Sigma=covmatr_h6,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 2)
print(results_h6f2)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c               PMPa  PMPb 
## H1 0.000 0.614 0.000 0.000              0.000 0.000
## H2 1.000 0.329 3.036 23333554981422.871 1.000 0.752
## H3 0.000 0.362 0.000 0.000              0.000 0.000
## Hu                                            0.248
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp<(int,ben)
##   H3: exp<int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h6f2$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 1.151059e-86 1.177628e-59
## H2 8.687650e+85 1.000000e+00 1.023082e+27
## H3 8.491646e+58 9.774388e-28 1.000000e+00
results_h6f3 <- bain(estimate_h6,"exp=int=ben;exp<(int,ben);exp<int=ben",  
                n=ngroup_h6, Sigma=covmatr_h6,
                group_parameters=3,
                joint_parameters = 0,
                fraction = 3)
print(results_h6f3)
## Bayesian informative hypothesis testing for an object of class numeric:
## 
##    Fit   Com   BF.u  BF.c               PMPa  PMPb 
## H1 0.000 0.921 0.000 0.000              0.000 0.000
## H2 1.000 0.337 2.971 22589850575949.270 1.000 0.748
## H3 0.000 0.444 0.000 0.000              0.000 0.000
## Hu                                            0.252
## 
## Hypotheses:
##   H1: exp=int=ben
##   H2: exp<(int,ben)
##   H3: exp<int=ben
## 
## Note: BF.u denotes the Bayes factor of the hypothesis at hand versus the unconstrained hypothesis Hu. BF.c denotes the Bayes factor of the hypothesis at hand versus its complement.
results_h6f3$BFmatrix
##              H1           H2           H3
## H1 1.000000e+00 7.841337e-87 9.615292e-60
## H2 1.275293e+86 1.000000e+00 1.226231e+27
## H3 1.040010e+59 8.155070e-28 1.000000e+00

10 Session Info

sessionInfo()
## R version 4.0.4 (2021-02-15)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Big Sur 10.16
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] de_DE.UTF-8/de_DE.UTF-8/de_DE.UTF-8/C/de_DE.UTF-8/de_DE.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] heplots_1.3-8    car_3.0-10       carData_3.0-4    RProbSup_3.0    
##  [5] hrbrthemes_0.8.0 patchwork_1.1.1  bain_0.2.4       semTools_0.5-4  
##  [9] lavaan_0.6-8     corrplot_0.84    skimr_2.1.3      haven_2.3.1     
## [13] forcats_0.5.1    stringr_1.4.0    dplyr_1.0.5      purrr_0.3.4     
## [17] readr_1.4.0      tidyr_1.1.3      tibble_3.1.0     ggplot2_3.3.3   
## [21] tidyverse_1.3.0 
## 
## loaded via a namespace (and not attached):
##   [1] readxl_1.3.1        backports_1.2.1     Hmisc_4.5-0        
##   [4] semPlot_1.1.2       systemfonts_1.0.1   igraph_1.2.6       
##   [7] plyr_1.8.6          repr_1.1.3          splines_4.0.4      
##  [10] crosstalk_1.1.1     digest_0.6.27       htmltools_0.5.1.1  
##  [13] matrixcalc_1.0-3    fansi_0.4.2         magrittr_2.0.1     
##  [16] Rsolnp_1.16         checkmate_2.0.0     lisrelToR_0.1.4    
##  [19] cluster_2.1.0       openxlsx_4.2.3      extrafont_0.17     
##  [22] modelr_0.1.8        extrafontdb_1.0     jpeg_0.1-8.1       
##  [25] sem_3.1-11          colorspace_2.0-0    rvest_1.0.0        
##  [28] mitools_2.4         xfun_0.22           crayon_1.4.1       
##  [31] jsonlite_1.7.2      Exact_2.1           lme4_1.1-26        
##  [34] regsem_1.6.2        survival_3.2-7      glue_1.4.2         
##  [37] gtable_0.3.0        mi_1.0              Rttf2pt1_1.3.8     
##  [40] abind_1.4-5         scales_1.1.1        mvtnorm_1.1-1      
##  [43] DBI_1.1.1           Rcpp_1.0.6          xtable_1.8-4       
##  [46] htmlTable_2.1.0     tmvnsim_1.0-2       effsize_0.8.1      
##  [49] foreign_0.8-81      proxy_0.4-25        Formula_1.2-4      
##  [52] survey_4.0          stats4_4.0.4        truncnorm_1.0-8    
##  [55] htmlwidgets_1.5.3   httr_1.4.2          RColorBrewer_1.1-2 
##  [58] ellipsis_0.3.1      farver_2.1.0        pkgconfig_2.0.3    
##  [61] XML_3.99-0.6        nnet_7.3-15         kutils_1.70        
##  [64] dbplyr_2.1.0        utf8_1.1.4          labeling_0.4.2     
##  [67] reshape2_1.4.4      tidyselect_1.1.0    rlang_0.4.10       
##  [70] munsell_0.5.0       reactR_0.4.4        cellranger_1.1.0   
##  [73] tools_4.0.4         cli_2.3.1           generics_0.1.0     
##  [76] sjlabelled_1.1.7    broom_0.7.5         fdrtool_1.2.16     
##  [79] evaluate_0.14       arm_1.11-2          yaml_2.2.1         
##  [82] knitr_1.31          fs_1.5.0            zip_2.1.1          
##  [85] glasso_1.11         rootSolve_1.8.2.1   pbapply_1.4-3      
##  [88] nlme_3.1-152        reactable_0.2.3     mime_0.10          
##  [91] xml2_1.3.2          compiler_4.0.4      rstudioapi_0.13    
##  [94] curl_4.3            png_0.1-7           e1071_1.7-6        
##  [97] reprex_1.0.0        statmod_1.4.35      pbivnorm_0.6.0     
## [100] DescTools_0.99.40   stringi_1.5.3       highr_0.8          
## [103] qgraph_1.6.9        rockchalk_1.8.144   gdtools_0.2.3      
## [106] lattice_0.20-41     Matrix_1.3-2        psych_2.1.3        
## [109] nloptr_1.2.2.2      vctrs_0.3.6         pillar_1.5.1       
## [112] lifecycle_1.0.0     OpenMx_2.19.1       corpcor_1.6.9      
## [115] data.table_1.14.0   insight_0.13.1      lmom_2.8           
## [118] R6_2.5.0            latticeExtra_0.6-29 rio_0.5.26         
## [121] gridExtra_2.3       gld_2.6.2           gtools_3.8.2       
## [124] boot_1.3-26         MASS_7.3-53         assertthat_0.2.1   
## [127] withr_2.4.1         mnormt_2.0.2        expm_0.999-6       
## [130] parallel_4.0.4      hms_1.0.0           grid_4.0.4         
## [133] rpart_4.1-15        coda_0.19-4         class_7.3-18       
## [136] minqa_1.2.4         rmarkdown_2.7       lubridate_1.7.10   
## [139] base64enc_0.1-3