#install.packages("lavaan")
#install.packages("MIIVsem")
#install.packages("tidyverse")
library(lavaan)
library(MIIVsem)
library(tidyverse)data_study1 <- read_csv("./Study 1 data.csv")This is the initial model.
Abbeviations:
VIRUS_WORRY: Virus-related worries
WORRY_EMPL: Economic worries: Employment
WORRY_REC: Economic worries: Recession/Economy
ACC: Acceptance of social distancing measures (e.g., stay-at-home orders)
REJ: General rejection of social distancing measures
cfa1 <- '
VIRUS_WORRY =~ aw01 + aw02 + aw03
WORRY_EMPL =~ ewj01 + ewj02 + ewj03
WORRY_REC = ~ ewe01 + ewe02 + ewe03
ACC =~ acc01 + acc02 + acc03
REJ =~ rej01 + rej02 + rej03
'
fit.cfa1 <- sem(cfa1, data = data_study1, estimator="MLR", missing="FIML")
summary(fit.cfa1, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6-7 ended normally after 84 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 55
##
## Number of observations 612
## Number of missing patterns 3
##
## Model Test User Model:
## Standard Robust
## Test Statistic 218.488 192.179
## Degrees of freedom 80 80
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.137
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 8195.180 5681.932
## Degrees of freedom 105 105
## P-value 0.000 0.000
## Scaling correction factor 1.442
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.983 0.980
## Tucker-Lewis Index (TLI) 0.978 0.974
##
## Robust Comparative Fit Index (CFI) 0.984
## Robust Tucker-Lewis Index (TLI) 0.979
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -14638.911 -14638.911
## Scaling correction factor 1.577
## for the MLR correction
## Loglikelihood unrestricted model (H1) -14529.667 -14529.667
## Scaling correction factor 1.316
## for the MLR correction
##
## Akaike (AIC) 29387.823 29387.823
## Bayesian (BIC) 29630.743 29630.743
## Sample-size adjusted Bayesian (BIC) 29456.129 29456.129
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.053 0.048
## 90 Percent confidence interval - lower 0.045 0.040
## 90 Percent confidence interval - upper 0.062 0.056
## P-value RMSEA <= 0.05 0.257 0.655
##
## Robust RMSEA 0.051
## 90 Percent confidence interval - lower 0.042
## 90 Percent confidence interval - upper 0.060
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.038 0.038
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## VIRUS_WORRY =~
## aw01 1.000 1.401 0.787
## aw02 1.232 0.058 21.107 0.000 1.726 0.913
## aw03 1.182 0.059 20.006 0.000 1.656 0.882
## WORRY_EMPL =~
## ewj01 1.000 1.761 0.914
## ewj02 1.089 0.033 33.297 0.000 1.917 0.903
## ewj03 1.111 0.030 36.717 0.000 1.956 0.957
## WORRY_REC =~
## ewe01 1.000 1.338 0.878
## ewe02 0.878 0.035 25.244 0.000 1.175 0.877
## ewe03 0.939 0.034 27.561 0.000 1.257 0.876
## ACC =~
## acc01 1.000 1.585 0.783
## acc02 1.056 0.036 29.293 0.000 1.674 0.905
## acc03 1.163 0.036 32.461 0.000 1.843 0.944
## REJ =~
## rej01 1.000 1.885 0.912
## rej02 0.983 0.030 33.267 0.000 1.853 0.898
## rej03 0.977 0.026 38.265 0.000 1.841 0.931
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## VIRUS_WORRY ~~
## WORRY_EMPL 0.052 0.115 0.452 0.651 0.021 0.021
## WORRY_REC 0.455 0.099 4.599 0.000 0.243 0.243
## ACC 1.339 0.146 9.180 0.000 0.603 0.603
## REJ -1.270 0.164 -7.761 0.000 -0.481 -0.481
## WORRY_EMPL ~~
## WORRY_REC 0.537 0.099 5.409 0.000 0.228 0.228
## ACC -0.535 0.129 -4.139 0.000 -0.192 -0.192
## REJ 1.015 0.160 6.325 0.000 0.306 0.306
## WORRY_REC ~~
## ACC 0.073 0.111 0.659 0.510 0.034 0.034
## REJ 0.323 0.118 2.730 0.006 0.128 0.128
## ACC ~~
## REJ -2.428 0.173 -14.028 0.000 -0.813 -0.813
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .aw01 4.960 0.072 68.923 0.000 4.960 2.785
## .aw02 3.945 0.076 51.610 0.000 3.945 2.088
## .aw03 3.629 0.076 47.775 0.000 3.629 1.933
## .ewj01 2.408 0.078 30.925 0.000 2.408 1.250
## .ewj02 2.881 0.086 33.581 0.000 2.881 1.357
## .ewj03 2.706 0.083 32.748 0.000 2.706 1.324
## .ewe01 5.093 0.062 82.667 0.000 5.093 3.342
## .ewe02 5.523 0.054 102.065 0.000 5.523 4.126
## .ewe03 5.436 0.058 93.783 0.000 5.436 3.791
## .acc01 4.296 0.082 52.523 0.000 4.296 2.123
## .acc02 5.208 0.075 69.635 0.000 5.208 2.815
## .acc03 5.054 0.079 64.033 0.000 5.054 2.588
## .rej01 2.961 0.084 35.434 0.000 2.961 1.432
## .rej02 2.920 0.083 35.012 0.000 2.920 1.415
## .rej03 2.974 0.080 37.200 0.000 2.974 1.504
## VIRUS_WORRY 0.000 0.000 0.000
## WORRY_EMPL 0.000 0.000 0.000
## WORRY_REC 0.000 0.000 0.000
## ACC 0.000 0.000 0.000
## REJ 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .aw01 1.208 0.128 9.431 0.000 1.208 0.381
## .aw02 0.592 0.085 6.967 0.000 0.592 0.166
## .aw03 0.786 0.095 8.290 0.000 0.786 0.223
## .ewj01 0.612 0.097 6.311 0.000 0.612 0.165
## .ewj02 0.828 0.148 5.608 0.000 0.828 0.184
## .ewj03 0.354 0.083 4.260 0.000 0.354 0.085
## .ewe01 0.532 0.082 6.513 0.000 0.532 0.229
## .ewe02 0.412 0.053 7.765 0.000 0.412 0.230
## .ewe03 0.477 0.074 6.431 0.000 0.477 0.232
## .acc01 1.582 0.122 12.960 0.000 1.582 0.386
## .acc02 0.621 0.077 8.066 0.000 0.621 0.181
## .acc03 0.415 0.098 4.253 0.000 0.415 0.109
## .rej01 0.720 0.117 6.135 0.000 0.720 0.168
## .rej02 0.823 0.143 5.753 0.000 0.823 0.193
## .rej03 0.523 0.083 6.330 0.000 0.523 0.134
## VIRUS_WORRY 1.963 0.184 10.672 0.000 1.000 1.000
## WORRY_EMPL 3.100 0.224 13.823 0.000 1.000 1.000
## WORRY_REC 1.791 0.134 13.352 0.000 1.000 1.000
## ACC 2.512 0.179 14.030 0.000 1.000 1.000
## REJ 3.553 0.207 17.185 0.000 1.000 1.000miive(cfa1, data_study1)## MIIVsem (0.5.5) results
##
## Number of observations 610
## Number of equations 10
## Estimator MIIV-2SLS
## Standard Errors standard
## Missing listwise
##
##
## Parameter Estimates:
##
##
## STRUCTURAL COEFFICIENTS:
## Estimate Std.Err z-value P(>|z|) Sargan df P(Chi)
## ACC =~
## acc01 1.000
## acc02 1.046 0.040 25.916 0.000 13.130 12 0.360
## acc03 1.151 0.043 26.814 0.000 11.828 12 0.460
## REJ =~
## rej01 1.000
## rej02 0.967 0.028 34.542 0.000 29.478 12 0.003
## rej03 0.956 0.025 38.315 0.000 36.037 12 0.000
## VIRUS_WORRY =~
## aw01 1.000
## aw02 1.075 0.043 24.967 0.000 91.454 12 0.000
## aw03 1.039 0.044 23.725 0.000 84.312 12 0.000
## WORRY_EMPL =~
## ewj01 1.000
## ewj02 1.083 0.030 36.327 0.000 13.661 12 0.323
## ewj03 1.104 0.027 41.613 0.000 16.909 12 0.153
## WORRY_REC =~
## ewe01 1.000
## ewe02 0.871 0.031 28.304 0.000 10.442 12 0.577
## ewe03 0.933 0.033 28.190 0.000 22.945 12 0.028
##
## INTERCEPTS:
## Estimate Std.Err z-value P(>|z|)
## acc01 0.000
## acc02 0.713 0.184 3.873 0.000
## acc03 0.103 0.195 0.526 0.599
## aw01 0.000
## aw02 -1.388 0.221 -6.266 0.000
## aw03 -1.523 0.225 -6.756 0.000
## ewe01 0.000
## ewe02 1.088 0.161 6.770 0.000
## ewe03 0.685 0.173 3.958 0.000
## ewj01 0.000
## ewj02 0.274 0.088 3.119 0.002
## ewj03 0.049 0.077 0.631 0.528
## rej01 0.000
## rej02 0.051 0.097 0.522 0.602
## rej03 0.139 0.086 1.617 0.106–> Result: the model does not fit according to the chisquare omnibus test as well as to the equation specific Sargan tests. Besides, the factor loadings of VIRUS_WORRY show an interesting declining pattern (.787, .913, .882). This does not have to mean something but is a bit strange as all items do not differ with regard to clearness (which would explain the pattern). For the moment, we note that without further conclusions.
The standardized residuasl represent differences between empirical covariances and model-implied covariances (i.e., those covariances that would exist if the model was true).
resid(fit.cfa1, "standardized")## $type
## [1] "standardized"
##
## $cov
## aw01 aw02 aw03 ewj01 ewj02 ewj03 ewe01 ewe02 ewe03 acc01
## aw01 -0.042
## aw02 -1.679 -0.007
## aw03 -2.348 2.044 -0.003
## ewj01 -2.536 1.034 0.545 0.000
## ewj02 -1.819 1.474 2.463 -0.026 0.000
## ewj03 -3.168 0.286 0.702 -0.016 0.030 0.000
## ewe01 0.435 -1.469 -1.154 -0.172 0.456 1.665 0.000
## ewe02 1.908 -0.138 -0.373 -1.403 -0.611 0.119 0.012 0.000
## ewe03 2.454 -0.800 0.956 -1.745 -0.212 0.074 -0.057 0.053 0.000
## acc01 3.945 -1.111 -0.859 0.081 0.912 0.842 -0.090 0.670 0.163 0.000
## acc02 5.381 -1.640 -1.929 -0.812 0.852 0.578 -0.202 0.182 1.863 0.339
## acc03 5.939 -2.204 -2.717 -1.134 0.598 -0.400 -1.456 -0.252 0.431 0.096
## rej01 -6.416 0.819 1.694 1.173 0.070 -0.155 -0.502 -1.558 -1.977 -0.544
## rej02 -4.724 1.263 2.440 1.178 -0.661 0.303 2.319 0.080 -0.332 1.611
## rej03 -5.321 2.116 2.615 0.261 -1.252 -0.453 1.444 -0.026 0.101 1.681
## acc02 acc03 rej01 rej02 rej03
## aw01
## aw02
## aw03
## ewj01
## ewj02
## ewj03
## ewe01
## ewe02
## ewe03
## acc01
## acc02 0.000
## acc03 -0.105 0.000
## rej01 -1.576 -1.795 0.000
## rej02 0.612 0.333 -0.616 0.000
## rej03 0.842 0.728 -0.136 0.604 0.000
##
## $mean
## aw01 aw02 aw03 ewj01 ewj02 ewj03 ewe01 ewe02 ewe03 acc01 acc02
## -3.636 -1.342 -1.362 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## acc03 rej01 rej02 rej03
## 0.000 0.000 0.000 0.000Most notworthy are the symmetrical and systematic differences in the first three columns. This is a typical sign that items are forced in one factor model that measure different things.
Based on the significant Sargan tests and strong deviation in the standardized residuals between these items and the COSMO target item, aw02 und rej03 are eliminated.
cfa2 <- '
VIRUS_WORRY =~ aw01 + aw03
WORRY_EMPL =~ ewj02 + ewj01 + ewj03
WORRY_REC = ~ ewe02 + ewe01 + ewe03
ACC =~ acc01 + acc02 + acc02
REJ =~ rej01 + rej02
'
fit.cfa2 <- sem(cfa2, data = data_study1, estimator="MLR", missing="FIML")
summary(fit.cfa2, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6-7 ended normally after 78 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 46
##
## Number of observations 612
## Number of missing patterns 3
##
## Model Test User Model:
## Standard Robust
## Test Statistic 67.362 60.001
## Degrees of freedom 44 44
## P-value (Chi-square) 0.013 0.054
## Scaling correction factor 1.123
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 5427.774 3695.470
## Degrees of freedom 66 66
## P-value 0.000 0.000
## Scaling correction factor 1.469
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.996 0.996
## Tucker-Lewis Index (TLI) 0.993 0.993
##
## Robust Comparative Fit Index (CFI) 0.997
## Robust Tucker-Lewis Index (TLI) 0.995
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12127.295 -12127.295
## Scaling correction factor 1.500
## for the MLR correction
## Loglikelihood unrestricted model (H1) -12093.614 -12093.614
## Scaling correction factor 1.315
## for the MLR correction
##
## Akaike (AIC) 24346.589 24346.589
## Bayesian (BIC) 24549.759 24549.759
## Sample-size adjusted Bayesian (BIC) 24403.718 24403.718
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.029 0.024
## 90 Percent confidence interval - lower 0.014 0.004
## 90 Percent confidence interval - upper 0.043 0.038
## P-value RMSEA <= 0.05 0.996 1.000
##
## Robust RMSEA 0.026
## 90 Percent confidence interval - lower NA
## 90 Percent confidence interval - upper 0.041
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.022 0.022
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## VIRUS_WORRY =~
## aw01 1.000 1.654 0.929
## aw03 0.819 0.053 15.401 0.000 1.354 0.721
## WORRY_EMPL =~
## ewj02 1.000 1.917 0.903
## ewj01 0.918 0.028 33.321 0.000 1.760 0.914
## ewj03 1.020 0.020 52.044 0.000 1.956 0.957
## WORRY_REC =~
## ewe02 1.000 1.175 0.878
## ewe01 1.137 0.045 25.108 0.000 1.335 0.876
## ewe03 1.072 0.043 25.076 0.000 1.259 0.878
## ACC =~
## acc01 1.000 1.563 0.773
## acc02 1.098 0.045 24.523 0.000 1.716 0.927
## REJ =~
## rej01 1.000 1.929 0.933
## rej02 0.924 0.029 32.198 0.000 1.782 0.864
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## VIRUS_WORRY ~~
## WORRY_EMPL -0.165 0.155 -1.068 0.285 -0.052 -0.052
## WORRY_REC 0.522 0.115 4.526 0.000 0.268 0.268
## ACC 1.736 0.157 11.024 0.000 0.671 0.671
## REJ -1.845 0.182 -10.130 0.000 -0.578 -0.578
## WORRY_EMPL ~~
## WORRY_REC 0.513 0.095 5.424 0.000 0.228 0.228
## ACC -0.533 0.141 -3.771 0.000 -0.178 -0.178
## REJ 1.155 0.173 6.678 0.000 0.312 0.312
## WORRY_REC ~~
## ACC 0.095 0.099 0.963 0.336 0.052 0.052
## REJ 0.245 0.108 2.260 0.024 0.108 0.108
## ACC ~~
## REJ -2.461 0.173 -14.226 0.000 -0.816 -0.816
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .aw01 4.958 0.072 68.919 0.000 4.958 2.786
## .aw03 3.630 0.076 47.775 0.000 3.630 1.932
## .ewj02 2.881 0.086 33.581 0.000 2.881 1.357
## .ewj01 2.408 0.078 30.925 0.000 2.408 1.250
## .ewj03 2.706 0.083 32.748 0.000 2.706 1.324
## .ewe02 5.523 0.054 102.065 0.000 5.523 4.126
## .ewe01 5.093 0.062 82.667 0.000 5.093 3.342
## .ewe03 5.436 0.058 93.783 0.000 5.436 3.791
## .acc01 4.296 0.082 52.523 0.000 4.296 2.123
## .acc02 5.208 0.075 69.635 0.000 5.208 2.815
## .rej01 2.961 0.084 35.434 0.000 2.961 1.432
## .rej02 2.920 0.083 35.012 0.000 2.920 1.415
## VIRUS_WORRY 0.000 0.000 0.000
## WORRY_EMPL 0.000 0.000 0.000
## WORRY_REC 0.000 0.000 0.000
## ACC 0.000 0.000 0.000
## REJ 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .aw01 0.433 0.189 2.285 0.022 0.433 0.137
## .aw03 1.696 0.134 12.628 0.000 1.696 0.481
## .ewj02 0.828 0.148 5.609 0.000 0.828 0.184
## .ewj01 0.613 0.097 6.323 0.000 0.613 0.165
## .ewj03 0.354 0.083 4.268 0.000 0.354 0.085
## .ewe02 0.412 0.054 7.652 0.000 0.412 0.230
## .ewe01 0.540 0.082 6.607 0.000 0.540 0.232
## .ewe03 0.471 0.074 6.381 0.000 0.471 0.229
## .acc01 1.650 0.141 11.706 0.000 1.650 0.403
## .acc02 0.479 0.104 4.617 0.000 0.479 0.140
## .rej01 0.552 0.120 4.591 0.000 0.552 0.129
## .rej02 1.080 0.169 6.396 0.000 1.080 0.254
## VIRUS_WORRY 2.735 0.239 11.443 0.000 1.000 1.000
## WORRY_EMPL 3.676 0.203 18.149 0.000 1.000 1.000
## WORRY_REC 1.380 0.129 10.712 0.000 1.000 1.000
## ACC 2.443 0.189 12.916 0.000 1.000 1.000
## REJ 3.721 0.201 18.515 0.000 1.000 1.000miive(cfa2, data_study1)## MIIVsem (0.5.5) results
##
## Number of observations 610
## Number of equations 7
## Estimator MIIV-2SLS
## Standard Errors standard
## Missing listwise
##
##
## Parameter Estimates:
##
##
## STRUCTURAL COEFFICIENTS:
## Estimate Std.Err z-value P(>|z|) Sargan df P(Chi)
## ACC =~
## acc01 1.000
## acc02 1.083 0.048 22.344 0.000 9.639 9 0.380
## REJ =~
## rej01 1.000
## rej02 0.916 0.032 28.787 0.000 17.159 9 0.046
## VIRUS_WORRY =~
## aw01 1.000
## aw03 0.816 0.049 16.706 0.000 16.515 9 0.057
## WORRY_EMPL =~
## ewj02 1.000
## ewj01 0.915 0.025 36.334 0.000 10.077 9 0.344
## ewj03 1.016 0.025 40.187 0.000 11.746 9 0.228
## WORRY_REC =~
## ewe02 1.000
## ewe01 1.134 0.040 28.224 0.000 9.925 9 0.357
## ewe03 1.068 0.038 28.235 0.000 10.501 9 0.311
##
## INTERCEPTS:
## Estimate Std.Err z-value P(>|z|)
## acc01 0.000
## acc02 0.555 0.218 2.549 0.011
## aw01 0.000
## aw03 -0.418 0.249 -1.681 0.093
## ewe01 -1.172 0.226 -5.191 0.000
## ewe02 0.000
## ewe03 -0.463 0.212 -2.178 0.029
## ewj01 -0.229 0.086 -2.650 0.008
## ewj02 0.000
## ewj03 -0.222 0.086 -2.598 0.009
## rej01 0.000
## rej02 0.200 0.107 1.877 0.061–> Model fits slightly. The Sargan test for awv03 is slightly n.s. (p = .057) At this time not conspicuous as p-values in Sargan test should be interpreted with regard to the number of performed tests (the same is true for rej02, that has a sign. p-value)
Now, predictors are included. This approach has to goals:
Test of a model with real predictors (instead of simple covariates) with their effects representing unique effects adjusted for spurious correlations due to the other predictors
Generation of new, not-yet tested restrictions and implications which the model has to fulfill IF the respecified model is correct. This reduces the danger to wrongly adapt the model to a stable part of the data
sem1 <- '
VIRUS_WORRY =~ aw01 + aw03
WORRY_EMPL =~ ewj02 + ewj01 + ewj03
WORRY_REC = ~ ewe02 + ewe01 + ewe03
ACC =~ acc01 + acc02 + acc03
REJ =~ rej01 + rej02
VIRUS_WORRY ~ health_anx_XS + worries_trait_XS + reactance_trait_XS + lonely_XS + affected_econ_XS
WORRY_EMPL ~ health_anx_XS + worries_trait_XS + reactance_trait_XS + lonely_XS + affected_econ_XS
WORRY_REC ~ health_anx_XS + worries_trait_XS + reactance_trait_XS + lonely_XS + affected_econ_XS
ACC ~ health_anx_XS + worries_trait_XS + reactance_trait_XS + lonely_XS + affected_econ_XS
REJ ~ health_anx_XS + worries_trait_XS + reactance_trait_XS + lonely_XS + affected_econ_XS
'
fit.sem1 <- sem(sem1, data = data_study1, estimator="MLR", missing="FIML")
summary(fit.sem1, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6-7 ended normally after 109 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 74
##
## Used Total
## Number of observations 611 612
## Number of missing patterns 3
##
## Model Test User Model:
## Standard Robust
## Test Statistic 150.734 138.198
## Degrees of freedom 95 95
## P-value (Chi-square) 0.000 0.003
## Scaling correction factor 1.091
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 7219.527 5635.481
## Degrees of freedom 143 143
## P-value 0.000 0.000
## Scaling correction factor 1.281
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.992 0.992
## Tucker-Lewis Index (TLI) 0.988 0.988
##
## Robust Comparative Fit Index (CFI) 0.993
## Robust Tucker-Lewis Index (TLI) 0.990
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12524.079 -12524.079
## Scaling correction factor 1.388
## for the MLR correction
## Loglikelihood unrestricted model (H1) -12448.712 -12448.712
## Scaling correction factor 1.221
## for the MLR correction
##
## Akaike (AIC) 25196.158 25196.158
## Bayesian (BIC) 25522.876 25522.876
## Sample-size adjusted Bayesian (BIC) 25287.941 25287.941
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.031 0.027
## 90 Percent confidence interval - lower 0.021 0.017
## 90 Percent confidence interval - upper 0.040 0.036
## P-value RMSEA <= 0.05 1.000 1.000
##
## Robust RMSEA 0.028
## 90 Percent confidence interval - lower 0.017
## 90 Percent confidence interval - upper 0.038
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.024 0.024
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## VIRUS_WORRY =~
## aw01 1.000 1.560 0.877
## aw03 0.917 0.054 17.098 0.000 1.431 0.763
## WORRY_EMPL =~
## ewj02 1.000 1.920 0.905
## ewj01 0.922 0.027 33.952 0.000 1.770 0.918
## ewj03 1.014 0.018 55.203 0.000 1.946 0.952
## WORRY_REC =~
## ewe02 1.000 1.172 0.876
## ewe01 1.139 0.045 25.198 0.000 1.335 0.876
## ewe03 1.075 0.043 25.115 0.000 1.260 0.879
## ACC =~
## acc01 1.000 1.587 0.784
## acc02 1.050 0.036 29.484 0.000 1.667 0.901
## acc03 1.166 0.035 33.208 0.000 1.850 0.948
## REJ =~
## rej01 1.000 1.914 0.926
## rej02 0.938 0.025 37.264 0.000 1.796 0.870
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## VIRUS_WORRY ~
## health_anx_XS 0.339 0.048 7.034 0.000 0.217 0.344
## worries_trt_XS 0.193 0.051 3.786 0.000 0.124 0.198
## reactnc_trt_XS -0.311 0.052 -5.951 0.000 -0.199 -0.307
## lonely_XS -0.058 0.040 -1.443 0.149 -0.037 -0.070
## affected_cn_XS -0.382 0.216 -1.769 0.077 -0.245 -0.066
## WORRY_EMPL ~
## health_anx_XS -0.032 0.048 -0.652 0.514 -0.016 -0.026
## worries_trt_XS 0.254 0.049 5.188 0.000 0.133 0.212
## reactnc_trt_XS 0.028 0.041 0.691 0.490 0.015 0.022
## lonely_XS 0.103 0.037 2.819 0.005 0.054 0.100
## affected_cn_XS 4.144 0.264 15.713 0.000 2.158 0.585
## WORRY_REC ~
## health_anx_XS -0.058 0.035 -1.650 0.099 -0.049 -0.078
## worries_trt_XS 0.158 0.038 4.157 0.000 0.135 0.216
## reactnc_trt_XS 0.027 0.036 0.754 0.451 0.023 0.036
## lonely_XS 0.036 0.029 1.270 0.204 0.031 0.058
## affected_cn_XS 0.172 0.174 0.989 0.322 0.146 0.040
## ACC ~
## health_anx_XS 0.205 0.044 4.643 0.000 0.129 0.204
## worries_trt_XS 0.100 0.047 2.136 0.033 0.063 0.101
## reactnc_trt_XS -0.419 0.046 -9.170 0.000 -0.264 -0.406
## lonely_XS -0.148 0.039 -3.768 0.000 -0.093 -0.174
## affected_cn_XS -0.297 0.238 -1.249 0.212 -0.187 -0.051
## REJ ~
## health_anx_XS -0.133 0.050 -2.682 0.007 -0.070 -0.110
## worries_trt_XS -0.082 0.052 -1.573 0.116 -0.043 -0.068
## reactnc_trt_XS 0.650 0.049 13.171 0.000 0.340 0.523
## lonely_XS 0.159 0.045 3.542 0.000 0.083 0.155
## affected_cn_XS 1.076 0.269 4.002 0.000 0.562 0.153
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VIRUS_WORRY ~~
## .WORRY_EMPL -0.082 0.087 -0.949 0.343 -0.045 -0.045
## .WORRY_REC 0.485 0.093 5.209 0.000 0.322 0.322
## .ACC 1.158 0.118 9.833 0.000 0.647 0.647
## .REJ -1.083 0.128 -8.464 0.000 -0.553 -0.553
## .WORRY_EMPL ~~
## .WORRY_REC 0.253 0.068 3.722 0.000 0.162 0.162
## .ACC -0.244 0.083 -2.955 0.003 -0.132 -0.132
## .REJ 0.318 0.094 3.382 0.001 0.157 0.157
## .WORRY_REC ~~
## .ACC 0.136 0.081 1.690 0.091 0.089 0.089
## .REJ 0.090 0.082 1.100 0.271 0.053 0.053
## .ACC ~~
## .REJ -1.588 0.122 -12.974 0.000 -0.792 -0.792
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .aw01 4.509 0.217 20.758 0.000 4.509 2.534
## .aw03 3.214 0.211 15.255 0.000 3.214 1.714
## .ewj02 1.109 0.177 6.257 0.000 1.109 0.522
## .ewj01 0.774 0.157 4.921 0.000 0.774 0.402
## .ewj03 0.909 0.175 5.200 0.000 0.909 0.445
## .ewe02 4.968 0.163 30.506 0.000 4.968 3.712
## .ewe01 4.461 0.180 24.749 0.000 4.461 2.928
## .ewe03 4.840 0.169 28.557 0.000 4.840 3.376
## .acc01 5.143 0.191 26.966 0.000 5.143 2.540
## .acc02 6.094 0.197 30.909 0.000 6.094 3.294
## .acc03 6.038 0.218 27.749 0.000 6.038 3.093
## .rej01 0.969 0.193 5.010 0.000 0.969 0.469
## .rej02 1.051 0.194 5.424 0.000 1.051 0.509
## .VIRUS_WORRY 0.000 0.000 0.000
## .WORRY_EMPL 0.000 0.000 0.000
## .WORRY_REC 0.000 0.000 0.000
## .ACC 0.000 0.000 0.000
## .REJ 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .aw01 0.734 0.154 4.770 0.000 0.734 0.232
## .aw03 1.467 0.132 11.109 0.000 1.467 0.417
## .ewj02 0.819 0.144 5.683 0.000 0.819 0.182
## .ewj01 0.582 0.090 6.446 0.000 0.582 0.157
## .ewj03 0.393 0.084 4.682 0.000 0.393 0.094
## .ewe02 0.417 0.054 7.728 0.000 0.417 0.233
## .ewe01 0.539 0.082 6.570 0.000 0.539 0.232
## .ewe03 0.468 0.074 6.354 0.000 0.468 0.227
## .acc01 1.582 0.121 13.029 0.000 1.582 0.386
## .acc02 0.645 0.076 8.533 0.000 0.645 0.188
## .acc03 0.389 0.092 4.225 0.000 0.389 0.102
## .rej01 0.610 0.102 5.994 0.000 0.610 0.143
## .rej02 1.032 0.166 6.233 0.000 1.032 0.242
## .VIRUS_WORRY 1.750 0.200 8.764 0.000 0.719 0.719
## .WORRY_EMPL 1.874 0.147 12.714 0.000 0.508 0.508
## .WORRY_REC 1.295 0.118 10.966 0.000 0.942 0.942
## .ACC 1.833 0.142 12.869 0.000 0.728 0.728
## .REJ 2.190 0.162 13.497 0.000 0.598 0.598miive(sem1, data_study1)## MIIVsem (0.5.5) results
##
## Number of observations 609
## Number of equations 13
## Estimator MIIV-2SLS
## Standard Errors standard
## Missing listwise
##
##
## Parameter Estimates:
##
##
## STRUCTURAL COEFFICIENTS:
## Estimate Std.Err z-value P(>|z|) Sargan df P(Chi)
## ACC =~
## acc01 1.000
## acc02 1.039 0.040 25.984 0.000 17.301 15 0.301
## acc03 1.147 0.042 27.010 0.000 14.687 15 0.474
## REJ =~
## rej01 1.000
## rej02 0.930 0.030 31.098 0.000 22.696 15 0.091
## VIRUS_WORRY =~
## aw01 1.000
## aw03 0.885 0.047 19.035 0.000 48.136 15 0.000
## WORRY_EMPL =~
## ewj02 1.000
## ewj01 0.916 0.025 36.497 0.000 15.844 15 0.392
## ewj03 1.011 0.025 40.457 0.000 16.639 15 0.341
## WORRY_REC =~
## ewe02 1.000
## ewe01 1.133 0.040 28.193 0.000 12.614 15 0.632
## ewe03 1.067 0.038 28.177 0.000 16.915 15 0.324
##
## ACC ~
## health_anx_XS 0.267 0.056 4.793 0.000
## worries_trt_XS 0.075 0.059 1.278 0.201
## reactnc_trt_XS -0.406 0.053 -7.608 0.000
## lonely_XS -0.134 0.046 -2.918 0.004
## affected_cn_XS -0.222 0.289 -0.769 0.442
## REJ ~
## health_anx_XS -0.133 0.051 -2.625 0.009
## worries_trt_XS -0.105 0.053 -1.966 0.049
## reactnc_trt_XS 0.635 0.049 13.094 0.000
## lonely_XS 0.170 0.042 4.095 0.000
## affected_cn_XS 1.128 0.262 4.298 0.000
## VIRUS_WORRY ~
## health_anx_XS 0.302 0.048 6.282 0.000
## worries_trt_XS 0.164 0.051 3.235 0.001
## reactnc_trt_XS -0.336 0.046 -7.284 0.000
## lonely_XS -0.060 0.040 -1.519 0.129
## affected_cn_XS -0.386 0.250 -1.545 0.122
## WORRY_EMPL ~
## health_anx_XS -0.043 0.049 -0.878 0.380
## worries_trt_XS 0.259 0.052 4.992 0.000
## reactnc_trt_XS 0.010 0.047 0.201 0.841
## lonely_XS 0.126 0.041 3.117 0.002
## affected_cn_XS 4.118 0.256 16.103 0.000
## WORRY_REC ~
## health_anx_XS -0.030 0.039 -0.765 0.444
## worries_trt_XS 0.154 0.042 3.714 0.000
## reactnc_trt_XS 0.025 0.038 0.651 0.515
## lonely_XS 0.028 0.032 0.862 0.389
## affected_cn_XS 0.177 0.205 0.867 0.386
##
## INTERCEPTS:
## Estimate Std.Err z-value P(>|z|)
## ACC 4.947 0.223 22.193 0.000
## acc01 0.000
## acc02 0.737 0.183 4.040 0.000
## acc03 0.120 0.193 0.622 0.534
## aw01 0.000
## aw03 -0.765 0.237 -3.222 0.001
## ewe01 -1.163 0.226 -5.156 0.000
## ewe02 0.000
## ewe03 -0.458 0.213 -2.153 0.031
## ewj01 -0.232 0.086 -2.691 0.007
## ewj02 0.000
## ewj03 -0.208 0.085 -2.450 0.014
## REJ 1.038 0.203 5.126 0.000
## rej01 0.000
## rej02 0.160 0.102 1.575 0.115
## VIRUS_WORRY 4.795 0.193 24.883 0.000
## WORRY_EMPL 1.124 0.197 5.691 0.000
## WORRY_REC 4.927 0.158 31.201 0.000The results show that adding predictors again causes misfit. As the predictors were added as composites with a saturated pattern of effects (every effect is estimated), the reason can only be in the measurement model. Let’s look onto the standardized residuals:
resid(fit.sem1, "standardized")## $type
## [1] "standardized"
##
## $cov
## aw01 aw03 ewj02 ewj01 ewj03 ewe02 ewe01 ewe03
## aw01 -0.003
## aw03 -0.022 -0.016
## ewj02 -0.558 3.459 0.000
## ewj01 -1.651 1.928 -0.543 0.000
## ewj03 -3.084 2.245 0.304 -0.019 0.000
## ewe02 0.562 -0.298 -0.572 -1.444 0.252 0.000
## ewe01 -1.939 -0.951 0.542 -0.165 1.897 0.235 0.000
## ewe03 1.364 0.787 -0.208 -1.844 0.150 -0.048 -0.175 0.000
## acc01 0.018 -0.901 1.033 0.107 0.922 0.823 -0.031 0.254
## acc02 1.669 -1.920 1.063 -0.958 0.733 0.217 -0.218 2.136
## acc03 1.855 -2.848 0.893 -1.383 -0.562 -0.313 -1.810 0.573
## rej01 -3.332 3.529 -0.556 0.860 -1.015 -1.241 0.033 -1.772
## rej02 -0.924 2.344 -0.753 1.306 0.467 0.790 3.044 0.329
## health_anx_XS -5.352 4.123 -0.261 1.039 -0.756 1.464 -0.197 -1.128
## worries_trait_XS -5.649 4.194 0.111 0.850 -0.991 0.484 0.371 -0.840
## reactance_trait_XS -2.926 2.923 -0.341 0.762 -0.586 -0.358 1.834 -1.748
## lonely_XS -2.542 2.251 0.876 0.136 -1.069 -0.590 0.599 -0.068
## affected_econ_XS -1.572 1.400 -0.050 1.273 -1.743 -0.053 0.900 -0.923
## acc01 acc02 acc03 rej01 rej02 hl__XS wr__XS rc__XS
## aw01
## aw03
## ewj02
## ewj01
## ewj03
## ewe02
## ewe01
## ewe03
## acc01 0.000
## acc02 0.928 0.000
## acc03 -0.007 -0.248 0.000
## rej01 0.718 -0.940 -0.902 0.000
## rej02 2.054 0.741 0.719 0.000 0.000
## health_anx_XS 1.719 -1.026 -0.129 -0.488 0.560 0.000
## worries_trait_XS 0.548 -0.405 0.023 -1.497 1.677 0.000 0.000
## reactance_trait_XS 0.982 -0.258 -0.197 -1.608 1.394 0.000 0.000 0.000
## lonely_XS 0.980 1.313 -1.290 0.012 -0.012 0.000 0.000 0.000
## affected_econ_XS 0.855 -1.973 1.401 0.175 -0.167 0.000 0.000 0.000
## lnl_XS af__XS
## aw01
## aw03
## ewj02
## ewj01
## ewj03
## ewe02
## ewe01
## ewe03
## acc01
## acc02
## acc03
## rej01
## rej02
## health_anx_XS
## worries_trait_XS
## reactance_trait_XS
## lonely_XS 0.000
## affected_econ_XS 0.000 0.000
##
## $mean
## aw01 aw03 ewj02 ewj01
## 0.090 -1.588 0.000 0.000
## ewj03 ewe02 ewe01 ewe03
## 0.000 0.000 0.000 0.000
## acc01 acc02 acc03 rej01
## 0.000 0.000 0.000 0.000
## rej02 health_anx_XS worries_trait_XS reactance_trait_XS
## 0.000 0.000 0.000 0.000
## lonely_XS affected_econ_XS
## 0.000 0.000This model shows the same pattern as in the initial CFA: the residuals show quite clearly that both virus-related worries indicators do not work in a synchronous fashion. This is most striking in the case of health_anxiety and trait worries, whose correlations with the COSMO target item (aw01) is greatly overestimated, while that with the infection-oriented item (aw03) is strongly underestimated. This is evidence that a) a single latent variable as the response-generating mechanism is wrong and that the first item is not as health-related as the second.
This fits with the initial observation of the varying pattern of descending loadings.
It is unfortunate but we have to eliminate a further indicator of virus-related worries. As an alternative it would possible to break virus-related worries in two latent variables–one with infection-related worries as intended initially and one with overall worries stemming from the COSMO survey. As the goal of study 1, however, consisted in validating the COSMO study, we decided to eliminate infection-related worries.
Having one indicator, however, poses the challenge how to identify the measurement model. Hence, the error variance has to be fixed to some value. The routine scheme is to fix it to zero but this would equate the indicator with the latent variable which also implies perfect measurement. Better, hence is to fix the error variance to a reasonable value.
We decided to fix the error variance of the latent virus-related/overall worry single-indicator variable to the variance of the indicator times one minus its reliability (Lin et al.). From a strict perspective, using Cronbach’s alpha in this case is not exactly correct as both items on which alpha was calculated are no convergent measures of the same factor. But at least it is a lower boundary for the error variance.
Lin, C.-H., Sher, P. J., & Shih, H.-Y. (2005). Past progress and future directions in conceptualizing customer perceived value. International Journal of Service Industry Management, 16(4), 318-336.
data_study1 %>%
summarise(var = var(aw01, na.rm=TRUE)) %>%
mutate(fixed.error = var*(1-.80))## # A tibble: 1 x 2
## var fixed.error
## <dbl> <dbl>
## 1 3.18 0.635sem2 <- '
VIRUS_WORRY =~ aw01
WORRY_EMPL =~ ewj02 + ewj01 + ewj03
WORRY_REC = ~ ewe02 + ewe01 + ewe03
ACC =~ acc01 + acc02 + acc03
REJ =~ rej01 + rej02
VIRUS_WORRY ~ health_anx_XS + worries_trait_XS + reactance_trait_XS + lonely_XS + affected_econ_XS
WORRY_EMPL ~ health_anx_XS + worries_trait_XS + reactance_trait_XS + lonely_XS + affected_econ_XS
WORRY_REC ~ health_anx_XS + worries_trait_XS + reactance_trait_XS + lonely_XS + affected_econ_XS
ACC ~ health_anx_XS + worries_trait_XS + reactance_trait_XS + lonely_XS + affected_econ_XS
REJ ~ health_anx_XS + worries_trait_XS + reactance_trait_XS + lonely_XS + affected_econ_XS
#Error correction
aw01~~.635*aw01
'
fit.sem2 <- sem(sem2, data = data_study1, estimator="MLR", missing="FIML")
summary(fit.sem2, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6-7 ended normally after 103 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 70
##
## Used Total
## Number of observations 611 612
## Number of missing patterns 2
##
## Model Test User Model:
## Standard Robust
## Test Statistic 100.241 92.280
## Degrees of freedom 80 80
## P-value (Chi-square) 0.063 0.164
## Scaling correction factor 1.086
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 6770.375 5235.021
## Degrees of freedom 126 126
## P-value 0.000 0.000
## Scaling correction factor 1.293
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.997 0.998
## Tucker-Lewis Index (TLI) 0.995 0.996
##
## Robust Comparative Fit Index (CFI) 0.998
## Robust Tucker-Lewis Index (TLI) 0.997
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11474.299 -11474.299
## Scaling correction factor 1.396
## for the MLR correction
## Loglikelihood unrestricted model (H1) -11424.178 -11424.178
## Scaling correction factor 1.231
## for the MLR correction
##
## Akaike (AIC) 23088.598 23088.598
## Bayesian (BIC) 23397.655 23397.655
## Sample-size adjusted Bayesian (BIC) 23175.420 23175.420
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.020 0.016
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.032 0.028
## P-value RMSEA <= 0.05 1.000 1.000
##
## Robust RMSEA 0.017
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.030
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.015 0.015
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## VIRUS_WORRY =~
## aw01 1.000 1.591 0.894
## WORRY_EMPL =~
## ewj02 1.000 1.920 0.904
## ewj01 0.922 0.027 33.964 0.000 1.770 0.918
## ewj03 1.014 0.018 55.219 0.000 1.946 0.952
## WORRY_REC =~
## ewe02 1.000 1.173 0.876
## ewe01 1.138 0.045 25.159 0.000 1.335 0.876
## ewe03 1.074 0.043 25.151 0.000 1.260 0.878
## ACC =~
## acc01 1.000 1.586 0.783
## acc02 1.050 0.036 29.450 0.000 1.666 0.901
## acc03 1.167 0.035 33.197 0.000 1.851 0.948
## REJ =~
## rej01 1.000 1.916 0.927
## rej02 0.937 0.025 37.050 0.000 1.795 0.870
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## VIRUS_WORRY ~
## health_anx_XS 0.300 0.049 6.154 0.000 0.188 0.298
## worries_trt_XS 0.166 0.053 3.126 0.002 0.104 0.167
## reactnc_trt_XS -0.335 0.054 -6.180 0.000 -0.210 -0.324
## lonely_XS -0.061 0.043 -1.425 0.154 -0.038 -0.071
## affected_cn_XS -0.387 0.236 -1.638 0.101 -0.243 -0.066
## WORRY_EMPL ~
## health_anx_XS -0.032 0.048 -0.653 0.514 -0.016 -0.026
## worries_trt_XS 0.254 0.049 5.188 0.000 0.133 0.212
## reactnc_trt_XS 0.028 0.040 0.691 0.490 0.015 0.022
## lonely_XS 0.103 0.037 2.818 0.005 0.054 0.100
## affected_cn_XS 4.144 0.264 15.711 0.000 2.158 0.585
## WORRY_REC ~
## health_anx_XS -0.058 0.035 -1.647 0.099 -0.049 -0.078
## worries_trt_XS 0.158 0.038 4.156 0.000 0.135 0.216
## reactnc_trt_XS 0.027 0.036 0.754 0.451 0.023 0.036
## lonely_XS 0.036 0.029 1.269 0.204 0.031 0.058
## affected_cn_XS 0.172 0.174 0.990 0.322 0.146 0.040
## ACC ~
## health_anx_XS 0.205 0.044 4.644 0.000 0.129 0.204
## worries_trt_XS 0.100 0.047 2.137 0.033 0.063 0.101
## reactnc_trt_XS -0.418 0.046 -9.170 0.000 -0.264 -0.406
## lonely_XS -0.148 0.039 -3.772 0.000 -0.093 -0.174
## affected_cn_XS -0.296 0.238 -1.246 0.213 -0.187 -0.051
## REJ ~
## health_anx_XS -0.133 0.050 -2.681 0.007 -0.070 -0.110
## worries_trt_XS -0.082 0.052 -1.579 0.114 -0.043 -0.068
## reactnc_trt_XS 0.650 0.049 13.167 0.000 0.339 0.522
## lonely_XS 0.159 0.045 3.544 0.000 0.083 0.155
## affected_cn_XS 1.078 0.269 4.004 0.000 0.563 0.153
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .VIRUS_WORRY ~~
## .WORRY_EMPL -0.126 0.091 -1.379 0.168 -0.066 -0.066
## .WORRY_REC 0.508 0.100 5.062 0.000 0.322 0.322
## .ACC 1.211 0.115 10.541 0.000 0.646 0.646
## .REJ -1.150 0.125 -9.161 0.000 -0.560 -0.560
## .WORRY_EMPL ~~
## .WORRY_REC 0.253 0.068 3.722 0.000 0.162 0.162
## .ACC -0.244 0.082 -2.959 0.003 -0.132 -0.132
## .REJ 0.318 0.094 3.381 0.001 0.157 0.157
## .WORRY_REC ~~
## .ACC 0.136 0.081 1.687 0.092 0.088 0.088
## .REJ 0.090 0.082 1.094 0.274 0.053 0.053
## .ACC ~~
## .REJ -1.588 0.122 -12.966 0.000 -0.792 -0.792
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .aw01 4.793 0.215 22.299 0.000 4.793 2.694
## .ewj02 1.109 0.177 6.257 0.000 1.109 0.522
## .ewj01 0.775 0.157 4.923 0.000 0.775 0.402
## .ewj03 0.909 0.175 5.199 0.000 0.909 0.445
## .ewe02 4.968 0.163 30.486 0.000 4.968 3.712
## .ewe01 4.461 0.180 24.756 0.000 4.461 2.928
## .ewe03 4.840 0.169 28.566 0.000 4.840 3.376
## .acc01 5.143 0.191 26.973 0.000 5.143 2.540
## .acc02 6.094 0.197 30.915 0.000 6.094 3.294
## .acc03 6.039 0.218 27.749 0.000 6.039 3.093
## .rej01 0.969 0.194 5.006 0.000 0.969 0.469
## .rej02 1.054 0.194 5.435 0.000 1.054 0.511
## .VIRUS_WORRY 0.000 0.000 0.000
## .WORRY_EMPL 0.000 0.000 0.000
## .WORRY_REC 0.000 0.000 0.000
## .ACC 0.000 0.000 0.000
## .REJ 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .aw01 0.635 0.635 0.201
## .ewj02 0.819 0.144 5.688 0.000 0.819 0.182
## .ewj01 0.583 0.090 6.448 0.000 0.583 0.157
## .ewj03 0.392 0.084 4.667 0.000 0.392 0.094
## .ewe02 0.415 0.054 7.681 0.000 0.415 0.232
## .ewe01 0.539 0.082 6.615 0.000 0.539 0.232
## .ewe03 0.469 0.074 6.365 0.000 0.469 0.228
## .acc01 1.584 0.122 13.035 0.000 1.584 0.386
## .acc02 0.647 0.076 8.525 0.000 0.647 0.189
## .acc03 0.386 0.091 4.252 0.000 0.386 0.101
## .rej01 0.604 0.102 5.948 0.000 0.604 0.141
## .rej02 1.037 0.166 6.240 0.000 1.037 0.244
## .VIRUS_WORRY 1.918 0.140 13.734 0.000 0.758 0.758
## .WORRY_EMPL 1.874 0.147 12.718 0.000 0.509 0.509
## .WORRY_REC 1.297 0.118 10.960 0.000 0.942 0.942
## .ACC 1.832 0.143 12.851 0.000 0.728 0.728
## .REJ 2.195 0.163 13.502 0.000 0.598 0.598miive(sem2, data_study1)## MIIVsem (0.5.5) results
##
## Number of observations 610
## Number of equations 12
## Estimator MIIV-2SLS
## Standard Errors standard
## Missing listwise
##
##
## Parameter Estimates:
##
##
## STRUCTURAL COEFFICIENTS:
## Estimate Std.Err z-value P(>|z|) Sargan df P(Chi)
## ACC =~
## acc01 1.000
## acc02 1.040 0.040 25.936 0.000 16.965 14 0.258
## acc03 1.148 0.043 26.950 0.000 13.870 14 0.459
## REJ =~
## rej01 1.000
## rej02 0.929 0.030 30.853 0.000 21.553 14 0.088
## WORRY_EMPL =~
## ewj02 1.000
## ewj01 0.918 0.025 36.551 0.000 12.480 14 0.568
## ewj03 1.014 0.025 40.477 0.000 13.711 14 0.471
## WORRY_REC =~
## ewe02 1.000
## ewe01 1.134 0.040 28.267 0.000 12.006 14 0.606
## ewe03 1.068 0.038 28.252 0.000 15.134 14 0.369
##
## ACC ~
## health_anx_XS 0.270 0.056 4.858 0.000
## worries_trt_XS 0.070 0.059 1.204 0.228
## reactnc_trt_XS -0.407 0.053 -7.611 0.000
## lonely_XS -0.132 0.046 -2.880 0.004
## affected_cn_XS -0.213 0.289 -0.738 0.460
## REJ ~
## health_anx_XS -0.132 0.050 -2.613 0.009
## worries_trt_XS -0.106 0.053 -1.991 0.046
## reactnc_trt_XS 0.635 0.048 13.102 0.000
## lonely_XS 0.171 0.042 4.110 0.000
## affected_cn_XS 1.130 0.262 4.311 0.000
## VIRUS_WORRY ~
## health_anx_XS 0.301 0.048 6.262 0.000
## worries_trt_XS 0.166 0.051 3.281 0.001
## reactnc_trt_XS -0.336 0.046 -7.284 0.000
## lonely_XS -0.061 0.040 -1.540 0.124
## affected_cn_XS -0.389 0.249 -1.562 0.118
## WORRY_EMPL ~
## health_anx_XS -0.041 0.049 -0.836 0.403
## worries_trt_XS 0.256 0.052 4.949 0.000
## reactnc_trt_XS 0.009 0.047 0.197 0.844
## lonely_XS 0.128 0.041 3.146 0.002
## affected_cn_XS 4.124 0.256 16.133 0.000
## WORRY_REC ~
## health_anx_XS -0.032 0.039 -0.816 0.415
## worries_trt_XS 0.157 0.041 3.782 0.000
## reactnc_trt_XS 0.025 0.038 0.656 0.512
## lonely_XS 0.027 0.032 0.832 0.406
## affected_cn_XS 0.172 0.204 0.842 0.400
##
## INTERCEPTS:
## Estimate Std.Err z-value P(>|z|)
## ACC 4.941 0.223 22.162 0.000
## acc01 0.000
## acc02 0.736 0.183 4.027 0.000
## acc03 0.117 0.194 0.606 0.545
## ewe01 -1.170 0.225 -5.193 0.000
## ewe02 0.000
## ewe03 -0.461 0.212 -2.173 0.030
## ewj01 -0.237 0.086 -2.750 0.006
## ewj02 0.000
## ewj03 -0.215 0.085 -2.528 0.011
## REJ 1.037 0.202 5.124 0.000
## rej01 0.000
## rej02 0.169 0.103 1.644 0.100
## VIRUS_WORRY 4.797 0.193 24.913 0.000
## WORRY_EMPL 1.120 0.197 5.676 0.000
## WORRY_REC 4.930 0.158 31.228 0.000resid(fit.sem2, "standardized")## $type
## [1] "standardized"
##
## $cov
## aw01 ewj02 ewj01 ewj03 ewe02 ewe01 ewe03 acc01
## aw01 -0.001
## ewj02 1.256 0.000
## ewj01 -0.012 -1.250 0.000
## ewj03 -1.075 0.555 -0.036 0.000
## ewe02 0.525 -0.576 -1.494 0.255 0.000
## ewe01 -2.242 0.536 -0.165 1.985 0.198 0.000
## ewe03 1.475 -0.203 -1.902 0.160 -0.069 -0.127 0.000
## acc01 -0.803 1.049 0.105 0.934 0.831 -0.028 0.261 0.000
## acc02 0.415 1.083 -0.974 0.760 0.220 -0.213 2.132 0.998
## acc03 0.044 0.928 -1.416 -0.587 -0.314 -1.826 0.588 -0.007
## rej01 -0.734 -0.585 0.902 -1.148 -1.248 0.042 -1.769 0.729
## rej02 0.825 -0.745 1.344 0.500 0.818 3.136 0.354 2.073
## health_anx_XS -0.004 -0.277 1.112 -0.940 1.587 -0.217 -1.241 1.784
## worries_trait_XS 0.001 0.121 0.919 -1.292 0.496 0.394 -0.927 0.565
## reactance_trait_XS 0.008 -0.351 0.798 -0.692 -0.367 1.882 -1.826 0.990
## lonely_XS 0.004 0.898 0.144 -1.196 -0.608 0.618 -0.065 0.990
## affected_econ_XS 0.004 -0.045 1.311 -1.989 -0.059 0.918 -0.940 0.855
## acc02 acc03 rej01 rej02 hl__XS wr__XS rc__XS lnl_XS
## aw01
## ewj02
## ewj01
## ewj03
## ewe02
## ewe01
## ewe03
## acc01
## acc02 0.000
## acc03 -0.284 0.000
## rej01 -0.988 -0.898 0.000
## rej02 0.707 0.733 0.000 0.000
## health_anx_XS -1.104 -0.161 -0.569 0.590 0.000
## worries_trait_XS -0.426 0.026 -1.838 1.759 0.000 0.000
## reactance_trait_XS -0.277 -0.190 -1.788 1.477 0.000 0.000 0.000
## lonely_XS 1.354 -1.345 -0.010 0.009 0.000 0.000 0.000 0.000
## affected_econ_XS -2.042 1.421 0.167 -0.156 0.000 0.000 0.000 0.000
## af__XS
## aw01
## ewj02
## ewj01
## ewj03
## ewe02
## ewe01
## ewe03
## acc01
## acc02
## acc03
## rej01
## rej02
## health_anx_XS
## worries_trait_XS
## reactance_trait_XS
## lonely_XS
## affected_econ_XS 0.000
##
## $mean
## aw01 ewj02 ewj01 ewj03
## -0.586 0.000 0.000 0.000
## ewe02 ewe01 ewe03 acc01
## 0.000 0.000 0.000 0.000
## acc02 acc03 rej01 rej02
## 0.000 0.000 0.000 0.000
## health_anx_XS worries_trait_XS reactance_trait_XS lonely_XS
## 0.000 0.000 0.000 0.000
## affected_econ_XS
## 0.000This model cleanly fits from the perspective of the chisquare test as well as the Sargan tests. The test for rej02 is now non-significant (albeit not as ideal). We decide to keep it due to the multi-test implications and capitilization on chance