Vom Großen ins Kleine - Übertragbarkeit eines Modells der epistemischen Lebensspannenentwicklung auf den epistemischen Wandel in Kurzzeitinterventionen
August 19, 2019
Data
Read Data
## 'data.frame': 221 obs. of 31 variables:
## $ FRG_A_01_t1: int 4 3 4 3 1 5 2 5 3 1 ...
## $ FRG_A_02_t1: int 3 4 4 3 2 3 2 2 2 1 ...
## $ FRG_A_03_t1: int 3 4 2 3 2 3 2 2 3 4 ...
## $ FRG_A_04_t1: int 4 4 3 3 2 2 2 3 2 1 ...
## $ FRG_A_05_t1: int 3 1 3 3 1 1 2 1 1 1 ...
## $ FRG_M_01_t1: int 4 3 4 5 5 4 3 5 4 2 ...
## $ FRG_M_02_t1: int 4 3 3 3 3 3 4 2 3 1 ...
## $ FRG_M_03_t1: int 3 3 3 4 3 5 5 3 6 2 ...
## $ FRG_M_04_t1: int 4 3 4 4 4 3 4 4 2 3 ...
## $ FRG_M_05_t1: int 3 2 4 3 1 3 3 2 2 2 ...
## $ FRG_E_01_t1: int 4 4 5 3 6 4 5 6 6 5 ...
## $ FRG_E_02_t1: int 4 4 5 4 5 4 5 5 4 1 ...
## $ FRG_E_03_t1: int 4 3 5 4 5 5 5 6 6 4 ...
## $ FRG_E_04_t1: int 4 4 4 5 6 5 5 6 6 6 ...
## $ FRG_E_05_t1: int 4 4 5 4 4 5 5 6 6 6 ...
## $ FRG_A_01_t2: int 3 2 3 4 4 2 2 4 1 1 ...
## $ FRG_A_02_t2: int 3 3 2 2 3 1 2 1 1 1 ...
## $ FRG_A_03_t2: int 3 3 2 2 3 1 2 1 1 3 ...
## $ FRG_A_04_t2: int 3 4 3 2 2 1 2 1 1 3 ...
## $ FRG_A_05_t2: int 2 1 2 2 1 1 1 1 1 1 ...
## $ FRG_M_01_t2: int 4 3 4 4 5 5 5 2 2 2 ...
## $ FRG_M_02_t2: int 3 2 4 2 4 2 5 2 2 1 ...
## $ FRG_M_03_t2: int 3 4 4 2 4 2 5 4 5 1 ...
## $ FRG_M_04_t2: int 3 4 4 3 2 4 4 2 2 1 ...
## $ FRG_M_05_t2: int 3 3 3 3 3 2 3 2 3 2 ...
## $ FRG_E_01_t2: int 4 4 5 4 5 5 5 6 5 4 ...
## $ FRG_E_02_t2: int 4 4 4 6 5 4 5 4 4 1 ...
## $ FRG_E_03_t2: int 5 5 5 4 5 2 5 3 6 2 ...
## $ FRG_E_04_t2: int 6 5 6 6 5 5 5 6 1 6 ...
## $ FRG_E_05_t2: int 6 5 6 4 4 4 4 5 4 6 ...
## $ study : Factor w/ 3 levels "s1","s2","s3": 3 3 3 3 3 3 3 3 3 3 ...Descriptives Item Level
library(psych)
describe(data)## vars n mean sd median trimmed mad min max range skew
## FRG_A_01_t1 1 221 3.18 1.26 3 3.17 1.48 1 6 5 0.16
## FRG_A_02_t1 2 221 2.51 1.15 2 2.44 1.48 1 6 5 0.47
## FRG_A_03_t1 3 221 2.95 1.19 3 2.92 1.48 1 6 5 0.22
## FRG_A_04_t1 4 221 2.93 0.95 3 2.97 1.48 1 5 4 -0.15
## FRG_A_05_t1 5 221 2.15 1.05 2 2.04 1.48 1 6 5 0.66
## FRG_M_01_t1 6 221 3.84 1.15 4 3.89 1.48 1 6 5 -0.34
## FRG_M_02_t1 7 221 2.57 1.05 3 2.54 1.48 1 5 4 0.24
## FRG_M_03_t1 8 221 3.72 1.20 4 3.73 1.48 1 6 5 -0.06
## FRG_M_04_t1 9 221 3.22 1.08 3 3.25 1.48 1 6 5 -0.27
## FRG_M_05_t1 10 221 2.68 0.99 3 2.69 1.48 1 5 4 0.16
## FRG_E_01_t1 11 221 4.81 0.91 5 4.85 1.48 2 6 4 -0.58
## FRG_E_02_t1 12 221 4.75 1.04 5 4.87 1.48 1 6 5 -0.98
## FRG_E_03_t1 13 221 4.79 0.99 5 4.88 1.48 1 6 5 -0.83
## FRG_E_04_t1 14 221 4.67 1.03 5 4.76 1.48 1 6 5 -0.70
## FRG_E_05_t1 15 221 4.90 0.84 5 4.93 1.48 3 6 3 -0.23
## FRG_A_01_t2 16 221 2.41 1.29 2 2.28 1.48 1 6 5 0.65
## FRG_A_02_t2 17 221 1.95 1.00 2 1.83 1.48 1 6 5 0.93
## FRG_A_03_t2 18 221 2.33 1.11 2 2.23 1.48 1 6 5 0.52
## FRG_A_04_t2 19 221 2.57 1.11 3 2.55 1.48 1 5 4 0.11
## FRG_A_05_t2 20 221 1.77 0.93 2 1.63 1.48 1 5 4 1.11
## FRG_M_01_t2 21 221 3.29 1.25 3 3.32 1.48 1 6 5 -0.13
## FRG_M_02_t2 22 221 2.45 1.11 2 2.37 1.48 1 6 5 0.61
## FRG_M_03_t2 23 221 3.67 1.27 4 3.71 1.48 1 6 5 -0.28
## FRG_M_04_t2 24 221 2.67 1.10 3 2.66 1.48 1 6 5 0.15
## FRG_M_05_t2 25 221 2.48 1.03 2 2.43 1.48 1 5 4 0.39
## FRG_E_01_t2 26 221 5.10 0.83 5 5.16 1.48 3 6 3 -0.43
## FRG_E_02_t2 27 221 4.70 0.99 5 4.79 1.48 1 6 5 -0.85
## FRG_E_03_t2 28 221 4.87 0.95 5 4.94 1.48 2 6 4 -0.73
## FRG_E_04_t2 29 221 5.34 0.95 6 5.49 0.00 1 6 5 -1.60
## FRG_E_05_t2 30 221 5.40 0.79 6 5.52 0.00 2 6 4 -1.11
## study* 31 221 2.08 0.58 2 2.10 0.00 1 3 2 -0.01
## kurtosis se
## FRG_A_01_t1 -0.68 0.08
## FRG_A_02_t1 -0.26 0.08
## FRG_A_03_t1 -0.48 0.08
## FRG_A_04_t1 -0.72 0.06
## FRG_A_05_t1 0.03 0.07
## FRG_M_01_t1 -0.27 0.08
## FRG_M_02_t1 -0.63 0.07
## FRG_M_03_t1 -0.49 0.08
## FRG_M_04_t1 -0.38 0.07
## FRG_M_05_t1 -0.49 0.07
## FRG_E_01_t1 0.40 0.06
## FRG_E_02_t1 1.16 0.07
## FRG_E_03_t1 0.88 0.07
## FRG_E_04_t1 0.58 0.07
## FRG_E_05_t1 -0.75 0.06
## FRG_A_01_t2 -0.56 0.09
## FRG_A_02_t2 0.61 0.07
## FRG_A_03_t2 -0.21 0.07
## FRG_A_04_t2 -0.89 0.07
## FRG_A_05_t2 0.59 0.06
## FRG_M_01_t2 -0.76 0.08
## FRG_M_02_t2 -0.15 0.07
## FRG_M_03_t2 -0.52 0.09
## FRG_M_04_t2 -0.56 0.07
## FRG_M_05_t2 -0.46 0.07
## FRG_E_01_t2 -0.82 0.06
## FRG_E_02_t2 1.23 0.07
## FRG_E_03_t2 0.52 0.06
## FRG_E_04_t2 3.04 0.06
## FRG_E_05_t2 0.64 0.05
## study* -0.12 0.04Compute Scales and Unstandardized Descriptives/Reliabilities
##FREE-GST
data$FRG_A_t1 <- rowMeans(data[,c("FRG_A_01_t1","FRG_A_02_t1","FRG_A_03_t1","FRG_A_04_t1","FRG_A_05_t1")])
data$FRG_M_t1 <- rowMeans(data[,c("FRG_M_01_t1","FRG_M_02_t1","FRG_M_03_t1","FRG_M_04_t1","FRG_M_05_t1")])
data$FRG_E_t1 <- rowMeans(data[,c("FRG_E_01_t1","FRG_E_02_t1","FRG_E_03_t1","FRG_E_04_t1","FRG_E_05_t1")])
data$FRG_A_t2 <- rowMeans(data[,c("FRG_A_01_t2","FRG_A_02_t2","FRG_A_03_t2","FRG_A_04_t2","FRG_A_05_t2")])
data$FRG_M_t2 <- rowMeans(data[,c("FRG_M_01_t2","FRG_M_02_t2","FRG_M_03_t2","FRG_M_04_t2","FRG_M_05_t2")])
data$FRG_E_t2 <- rowMeans(data[,c("FRG_E_01_t2","FRG_E_02_t2","FRG_E_03_t2","FRG_E_04_t2","FRG_E_05_t2")])
alpha(data[,c("FRG_A_01_t1","FRG_A_02_t1","FRG_A_03_t1","FRG_A_04_t1","FRG_A_05_t1")])##
## Reliability analysis
## Call: alpha(x = data[, c("FRG_A_01_t1", "FRG_A_02_t1", "FRG_A_03_t1",
## "FRG_A_04_t1", "FRG_A_05_t1")])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.66 0.66 0.63 0.28 1.9 0.035 2.7 0.74 0.25
##
## lower alpha upper 95% confidence boundaries
## 0.59 0.66 0.73
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## FRG_A_01_t1 0.57 0.57 0.52 0.25 1.3 0.046 0.0145
## FRG_A_02_t1 0.54 0.53 0.47 0.22 1.1 0.050 0.0091
## FRG_A_03_t1 0.59 0.58 0.54 0.26 1.4 0.043 0.0187
## FRG_A_04_t1 0.65 0.64 0.60 0.31 1.8 0.038 0.0193
## FRG_A_05_t1 0.68 0.68 0.63 0.35 2.1 0.034 0.0107
## med.r
## FRG_A_01_t1 0.25
## FRG_A_02_t1 0.22
## FRG_A_03_t1 0.23
## FRG_A_04_t1 0.29
## FRG_A_05_t1 0.33
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## FRG_A_01_t1 221 0.73 0.70 0.61 0.49 3.2 1.26
## FRG_A_02_t1 221 0.76 0.75 0.70 0.57 2.5 1.15
## FRG_A_03_t1 221 0.69 0.68 0.57 0.46 2.9 1.19
## FRG_A_04_t1 221 0.55 0.59 0.40 0.33 2.9 0.95
## FRG_A_05_t1 221 0.50 0.52 0.29 0.24 2.2 1.05
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## FRG_A_01_t1 0.09 0.24 0.27 0.24 0.13 0.03 0
## FRG_A_02_t1 0.22 0.30 0.30 0.14 0.04 0.01 0
## FRG_A_03_t1 0.12 0.25 0.31 0.23 0.08 0.02 0
## FRG_A_04_t1 0.06 0.28 0.35 0.29 0.02 0.00 0
## FRG_A_05_t1 0.33 0.30 0.27 0.07 0.02 0.00 0alpha(data[,c("FRG_M_01_t1","FRG_M_02_t1","FRG_M_03_t1","FRG_M_04_t1","FRG_M_05_t1")])##
## Reliability analysis
## Call: alpha(x = data[, c("FRG_M_01_t1", "FRG_M_02_t1", "FRG_M_03_t1",
## "FRG_M_04_t1", "FRG_M_05_t1")])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.62 0.63 0.6 0.25 1.7 0.04 3.2 0.69 0.27
##
## lower alpha upper 95% confidence boundaries
## 0.55 0.62 0.7
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## FRG_M_01_t1 0.57 0.58 0.54 0.26 1.4 0.048 0.0138
## FRG_M_02_t1 0.52 0.53 0.49 0.22 1.1 0.053 0.0132
## FRG_M_03_t1 0.59 0.59 0.53 0.26 1.4 0.046 0.0062
## FRG_M_04_t1 0.59 0.59 0.53 0.26 1.4 0.045 0.0066
## FRG_M_05_t1 0.58 0.58 0.53 0.26 1.4 0.046 0.0116
## med.r
## FRG_M_01_t1 0.27
## FRG_M_02_t1 0.20
## FRG_M_03_t1 0.27
## FRG_M_04_t1 0.28
## FRG_M_05_t1 0.30
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## FRG_M_01_t1 221 0.64 0.63 0.47 0.38 3.8 1.15
## FRG_M_02_t1 221 0.69 0.70 0.59 0.47 2.6 1.05
## FRG_M_03_t1 221 0.64 0.61 0.46 0.35 3.7 1.20
## FRG_M_04_t1 221 0.60 0.62 0.47 0.34 3.2 1.08
## FRG_M_05_t1 221 0.59 0.62 0.47 0.36 2.7 0.99
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## FRG_M_01_t1 0.03 0.11 0.20 0.37 0.24 0.05 0
## FRG_M_02_t1 0.16 0.33 0.31 0.16 0.03 0.00 0
## FRG_M_03_t1 0.03 0.11 0.29 0.29 0.20 0.07 0
## FRG_M_04_t1 0.07 0.18 0.30 0.37 0.07 0.01 0
## FRG_M_05_t1 0.11 0.33 0.36 0.17 0.03 0.00 0alpha(data[,c("FRG_E_01_t1","FRG_E_02_t1","FRG_E_03_t1","FRG_E_04_t1","FRG_E_05_t1")])##
## Reliability analysis
## Call: alpha(x = data[, c("FRG_E_01_t1", "FRG_E_02_t1", "FRG_E_03_t1",
## "FRG_E_04_t1", "FRG_E_05_t1")])
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.61 0.62 0.6 0.24 1.6 0.042 4.8 0.6 0.21
##
## lower alpha upper 95% confidence boundaries
## 0.53 0.61 0.69
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## FRG_E_01_t1 0.58 0.59 0.57 0.26 1.4 0.047 0.0238
## FRG_E_02_t1 0.58 0.58 0.54 0.26 1.4 0.047 0.0169
## FRG_E_03_t1 0.56 0.57 0.54 0.25 1.3 0.049 0.0215
## FRG_E_04_t1 0.57 0.57 0.50 0.25 1.3 0.047 0.0039
## FRG_E_05_t1 0.50 0.50 0.44 0.20 1.0 0.055 0.0080
## med.r
## FRG_E_01_t1 0.23
## FRG_E_02_t1 0.21
## FRG_E_03_t1 0.23
## FRG_E_04_t1 0.24
## FRG_E_05_t1 0.19
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## FRG_E_01_t1 221 0.58 0.59 0.40 0.32 4.8 0.91
## FRG_E_02_t1 221 0.62 0.60 0.43 0.33 4.7 1.04
## FRG_E_03_t1 221 0.63 0.62 0.46 0.36 4.8 0.99
## FRG_E_04_t1 221 0.63 0.62 0.51 0.34 4.7 1.03
## FRG_E_05_t1 221 0.69 0.71 0.64 0.49 4.9 0.84
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## FRG_E_01_t1 0.00 0.02 0.03 0.30 0.41 0.24 0
## FRG_E_02_t1 0.01 0.03 0.06 0.24 0.43 0.23 0
## FRG_E_03_t1 0.00 0.03 0.05 0.26 0.42 0.24 0
## FRG_E_04_t1 0.00 0.04 0.04 0.33 0.36 0.23 0
## FRG_E_05_t1 0.00 0.00 0.04 0.28 0.42 0.26 0data <- data[,c("FRG_A_t1","FRG_A_t2","FRG_M_t1","FRG_M_t2","FRG_E_t1","FRG_E_t2")]
describe(data)## vars n mean sd median trimmed mad min max range skew
## FRG_A_t1 1 221 2.74 0.74 2.8 2.75 0.89 1.0 5.0 4.0 0.07
## FRG_A_t2 2 221 2.21 0.82 2.2 2.17 0.89 1.0 4.8 3.8 0.35
## FRG_M_t1 3 221 3.21 0.69 3.2 3.22 0.59 1.6 4.8 3.2 -0.13
## FRG_M_t2 4 221 2.91 0.82 3.0 2.91 0.89 1.0 5.2 4.2 0.03
## FRG_E_t1 5 221 4.78 0.60 4.8 4.79 0.59 3.2 6.0 2.8 -0.17
## FRG_E_t2 6 221 5.08 0.56 5.2 5.11 0.59 3.6 6.0 2.4 -0.30
## kurtosis se
## FRG_A_t1 0.01 0.05
## FRG_A_t2 -0.48 0.06
## FRG_M_t1 -0.48 0.05
## FRG_M_t2 -0.21 0.06
## FRG_E_t1 -0.52 0.04
## FRG_E_t2 -0.58 0.04library(corrplot)## corrplot 0.84 loadedsource("http://www.sthda.com/upload/rquery_cormat.r")
rquery.cormat(data)
## $r
## FRG_E_t1 FRG_E_t2 FRG_A_t1 FRG_A_t2 FRG_M_t1 FRG_M_t2
## FRG_E_t1 1
## FRG_E_t2 0.51 1
## FRG_A_t1 -0.25 0.011 1
## FRG_A_t2 -0.35 -0.19 0.58 1
## FRG_M_t1 0.0038 -0.11 0.0058 0.016 1
## FRG_M_t2 -0.15 -0.1 0.12 0.22 0.55 1
##
## $p
## FRG_E_t1 FRG_E_t2 FRG_A_t1 FRG_A_t2 FRG_M_t1 FRG_M_t2
## FRG_E_t1 0
## FRG_E_t2 9.9e-16 0
## FRG_A_t1 0.00018 0.87 0
## FRG_A_t2 9e-08 0.0052 7.1e-21 0
## FRG_M_t1 0.96 0.096 0.93 0.82 0
## FRG_M_t2 0.022 0.13 0.067 0.00099 5.3e-19 0
##
## $sym
## FRG_E_t1 FRG_E_t2 FRG_A_t1 FRG_A_t2 FRG_M_t1 FRG_M_t2
## FRG_E_t1 1
## FRG_E_t2 . 1
## FRG_A_t1 1
## FRG_A_t2 . . 1
## FRG_M_t1 1
## FRG_M_t2 . 1
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1Standardization and Standardized Descriptives
data$FRG_A_t2 <- (data$FRG_A_t2 - mean(data$FRG_A_t1,na.rm = T))/sd(data$FRG_A_t1,na.rm = T)
data$FRG_A_t1 <- (data$FRG_A_t1 - mean(data$FRG_A_t1,na.rm = T))/sd(data$FRG_A_t1,na.rm = T)
data$FRG_M_t2 <- (data$FRG_M_t2 - mean(data$FRG_M_t1,na.rm = T))/sd(data$FRG_M_t1,na.rm = T)
data$FRG_M_t1 <- (data$FRG_M_t1 - mean(data$FRG_M_t1,na.rm = T))/sd(data$FRG_M_t1,na.rm = T)
data$FRG_E_t2 <- (data$FRG_E_t2 - mean(data$FRG_E_t1,na.rm = T))/sd(data$FRG_E_t1,na.rm = T)
data$FRG_E_t1 <- (data$FRG_E_t1 - mean(data$FRG_E_t1,na.rm = T))/sd(data$FRG_E_t1,na.rm = T)
describe(data)## vars n mean sd median trimmed mad min max range skew
## FRG_A_t1 1 221 0.00 1.00 0.08 0.01 1.21 -2.37 3.06 5.44 0.07
## FRG_A_t2 2 221 -0.73 1.11 -0.74 -0.78 1.21 -2.37 2.79 5.16 0.35
## FRG_M_t1 3 221 0.00 1.00 -0.01 0.02 0.86 -2.32 2.30 4.62 -0.13
## FRG_M_t2 4 221 -0.43 1.18 -0.30 -0.43 1.29 -3.19 2.88 6.07 0.03
## FRG_E_t1 5 221 0.00 1.00 0.03 0.02 0.99 -2.63 2.02 4.65 -0.17
## FRG_E_t2 6 221 0.50 0.94 0.69 0.54 0.99 -1.97 2.02 3.99 -0.30
## kurtosis se
## FRG_A_t1 0.01 0.07
## FRG_A_t2 -0.48 0.07
## FRG_M_t1 -0.48 0.07
## FRG_M_t2 -0.21 0.08
## FRG_E_t1 -0.52 0.07
## FRG_E_t2 -0.58 0.06Analysis
Latent Difference Score Model
library(lavaan)## This is lavaan 0.6-4## lavaan is BETA software! Please report any bugs.##
## Attaching package: 'lavaan'## The following object is masked from 'package:psych':
##
## cor2covcov_model <- ' # Define latent difference Factor
delta_A =~ 1*FRG_A_t2
# Set autoregressive paths to 1
FRG_A_t2 ~ 1*FRG_A_t1
# Means and Intercept
delta_A ~ 1
FRG_A_t1 ~ 1
FRG_A_t2 ~ 0
# Exogenous (Co)Variances
delta_A ~ FRG_A_t1
delta_A ~~ delta_A
FRG_A_t1 ~~ FRG_A_t1
# Disturbances
FRG_A_t2 ~~ 0*FRG_A_t2
# Covariate
delta_M =~ 1*FRG_M_t2
# Set autoregressive paths to 1
FRG_M_t2 ~ 1*FRG_M_t1
# Means and Intercept
delta_M ~ 1
FRG_M_t1 ~ 1
FRG_M_t2 ~ 0
# Exogenous (Co)Variances
delta_M ~ FRG_M_t1
delta_M ~~ delta_M
FRG_M_t1 ~~ FRG_M_t1
# Disturbances
FRG_M_t2 ~~ 0*FRG_M_t2
# Covariate
delta_E =~ 1*FRG_E_t2
# Set autoregressive paths to 1
FRG_E_t2 ~ 1*FRG_E_t1
# Means and Intercept
delta_E ~ 1
FRG_E_t1 ~ 1
FRG_E_t2 ~ 0
# Exogenous (Co)Variances
delta_E ~ FRG_E_t1
delta_E ~~ delta_E
FRG_E_t1 ~~ FRG_E_t1
# Disturbances
FRG_E_t2 ~~ 0*FRG_E_t2
delta_E ~~ delta_M
delta_A ~~ delta_M
delta_A ~~ delta_E
delta_A ~ FRG_M_t1
delta_A ~ FRG_E_t1
delta_M ~ FRG_A_t1
delta_M ~ FRG_E_t1
delta_E ~ FRG_A_t1
delta_E ~ FRG_M_t1
FRG_A_t1 ~~ FRG_M_t1
FRG_A_t1 ~~ FRG_E_t1
FRG_E_t1 ~~ FRG_M_t1
'
fit_cov <- sem(cov_model,
data = data)
summary(fit_cov, rsquare = T, standardized=TRUE)## lavaan 0.6-4 ended normally after 33 iterations
##
## Optimization method NLMINB
## Number of free parameters 27
##
## Number of observations 221
##
## Estimator ML
## Model Fit Test Statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Structured
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## delta_A =~
## FRG_A_t2 1.000 0.978 0.879
## delta_M =~
## FRG_M_t2 1.000 1.045 0.884
## delta_E =~
## FRG_E_t2 1.000 0.963 1.029
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FRG_A_t2 ~
## FRG_A_t1 1.000 1.000 0.897
## delta_A ~
## FRG_A_t1 -0.420 0.061 -6.871 0.000 -0.430 -0.429
## FRG_M_t2 ~
## FRG_M_t1 1.000 1.000 0.844
## delta_M ~
## FRG_M_t1 -0.346 0.065 -5.332 0.000 -0.332 -0.331
## FRG_E_t2 ~
## FRG_E_t1 1.000 1.000 1.066
## delta_E ~
## FRG_E_t1 -0.491 0.055 -8.940 0.000 -0.510 -0.509
## delta_A ~
## FRG_M_t1 0.015 0.059 0.253 0.800 0.015 0.015
## FRG_E_t1 -0.246 0.061 -4.019 0.000 -0.251 -0.251
## delta_M ~
## FRG_A_t1 0.103 0.067 1.536 0.124 0.099 0.098
## FRG_E_t1 -0.159 0.067 -2.365 0.018 -0.152 -0.151
## delta_E ~
## FRG_A_t1 0.138 0.055 2.510 0.012 0.143 0.143
## FRG_M_t1 -0.108 0.053 -2.032 0.042 -0.112 -0.112
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_M ~~
## .delta_E 0.029 0.051 0.563 0.574 0.038 0.038
## .delta_A ~~
## .delta_M 0.151 0.058 2.606 0.009 0.178 0.178
## .delta_E -0.083 0.047 -1.778 0.075 -0.120 -0.120
## FRG_A_t1 ~~
## FRG_M_t1 0.006 0.067 0.086 0.931 0.006 0.006
## FRG_E_t1 -0.248 0.069 -3.597 0.000 -0.248 -0.249
## FRG_M_t1 ~~
## FRG_E_t1 0.004 0.067 0.056 0.955 0.004 0.004
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_A -0.732 0.059 -12.388 0.000 -0.749 -0.749
## FRG_A_t1 0.000 0.067 0.000 1.000 0.000 0.000
## .FRG_A_t2 0.000 0.000 0.000
## .delta_M -0.428 0.065 -6.599 0.000 -0.409 -0.409
## FRG_M_t1 -0.000 0.067 -0.000 1.000 -0.000 -0.000
## .FRG_M_t2 0.000 0.000 0.000
## .delta_E 0.499 0.053 9.406 0.000 0.518 0.518
## FRG_E_t1 0.000 0.067 0.000 1.000 0.000 0.000
## .FRG_E_t2 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_A 0.771 0.073 10.512 0.000 0.807 0.807
## FRG_A_t1 0.995 0.095 10.512 0.000 0.995 1.000
## .FRG_A_t2 0.000 0.000 0.000
## .delta_M 0.928 0.088 10.512 0.000 0.851 0.851
## FRG_M_t1 0.995 0.095 10.512 0.000 0.995 1.000
## .FRG_M_t2 0.000 0.000 0.000
## .delta_E 0.623 0.059 10.512 0.000 0.672 0.672
## FRG_E_t1 0.995 0.095 10.512 0.000 0.995 1.000
## .FRG_E_t2 0.000 0.000 0.000
##
## R-Square:
## Estimate
## delta_A 0.193
## FRG_A_t2 1.000
## delta_M 0.149
## FRG_M_t2 1.000
## delta_E 0.328
## FRG_E_t2 1.000Cluster Analysis
NbClust
test.data <- data[,c("FRG_A_t1","FRG_M_t1","FRG_E_t1")]
library(NbClust)
NbClust(test.data, method = "ward.D", max.nc = 6)
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 6 proposed 2 as the best number of clusters
## * 9 proposed 3 as the best number of clusters
## * 1 proposed 5 as the best number of clusters
## * 7 proposed 6 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 3
##
##
## *******************************************************************## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW TraceW
## 2 3.9106 73.8923 56.8618 -3.8032 214.9066 15104339 27960.866 493.4919
## 3 0.5048 74.6275 27.2794 -6.3600 356.2574 17927139 17388.887 391.7713
## 4 6.4457 64.7720 32.0543 -10.6752 430.5491 22771698 12517.596 348.1994
## 5 0.5399 63.4746 32.9556 -10.2384 525.7075 23132171 9818.928 303.3847
## 6 99.5342 64.8169 23.3196 -9.2721 615.8861 22149608 8749.424 263.2240
## Friedman Rubin Cindex DB Silhouette Duda Pseudot2 Beale
## 2 1.3977 1.3374 0.3375 1.5880 0.2379 0.7172 56.3849 0.6666
## 3 2.3300 1.6847 0.3175 1.5066 0.2373 0.6977 37.2704 0.7293
## 4 2.8966 1.8955 0.3201 1.3688 0.2034 0.6064 35.6956 1.0852
## 5 3.8623 2.1755 0.3048 1.2213 0.2123 0.6998 31.7399 0.7205
## 6 4.9035 2.5074 0.3445 1.1717 0.2240 0.6922 26.6814 0.7446
## Ratkowsky Ball Ptbiserial Frey McClain Dunn Hubert SDindex
## 2 0.3116 246.7460 0.3268 0.1981 0.6330 0.0675 0.0023 1.8812
## 3 0.3637 130.5904 0.4203 0.5358 1.3055 0.0735 0.0028 1.6746
## 4 0.3431 87.0498 0.4163 0.1465 1.6207 0.0769 0.0029 1.5669
## 5 0.3279 60.6769 0.4319 0.1191 1.8356 0.0769 0.0031 1.4939
## 6 0.3160 43.8707 0.4514 0.4116 2.0962 0.0933 0.0035 1.4502
## Dindex SDbw
## 2 1.3702 1.5747
## 3 1.2170 1.4479
## 4 1.1381 0.9565
## 5 1.0621 0.8226
## 6 0.9977 0.5889
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 2 0.6024 94.3722 0.5729
## 3 0.5499 70.4054 0.5353
## 4 0.4921 56.7551 0.3570
## 5 0.5318 65.1614 0.5407
## 6 0.5043 58.9723 0.5268
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 6.0000 3.0000 3.0000 2.0000 3.0000 3 3.00
## Value_Index 99.5342 74.6275 29.5823 -3.8032 141.3508 2021758 10571.98
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 3.0000 6.0000 3.0000 5.0000 6.0000 2.0000 2.0000
## Value_Index 58.1487 1.0412 -0.1364 0.3048 1.1717 0.2379 0.7172
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 2.0000 2.0000 3.0000 3.0000 6.0000 1 2.000
## Value_Index 56.3849 0.6666 0.3637 116.1555 0.4514 NA 0.633
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 6.0000 0 6.0000 0 6.0000
## Value_Index 0.0933 0 1.4502 0 0.5889
##
## $Best.partition
## [1] 1 2 1 1 3 1 3 3 3 2 1 1 3 2 3 3 1 1 2 3 2 2 1 1 1 2 3 3 3 1 2 1 3 3 2
## [36] 3 1 3 1 2 2 1 3 1 3 2 2 3 2 3 3 1 1 1 2 1 3 3 2 3 1 2 1 3 1 1 2 3 3 1
## [71] 1 3 1 3 1 1 1 1 1 1 1 1 3 1 1 2 1 1 1 1 3 3 1 1 3 3 3 1 3 2 1 3 1 1 1
## [106] 1 1 3 3 1 1 2 1 2 3 3 2 2 1 3 1 2 2 1 1 1 2 3 3 1 1 2 2 2 2 1 1 1 1 3
## [141] 3 2 3 1 3 3 2 2 3 2 2 3 3 2 1 3 3 3 2 2 2 3 1 3 2 2 1 2 1 2 1 2 1 1 2
## [176] 2 2 3 2 2 1 1 1 1 3 1 3 3 3 3 3 1 1 1 1 3 3 2 2 3 3 3 1 3 1 2 1 3 2 1
## [211] 2 3 3 2 2 3 3 1 3 1 3solution <- NbClust(test.data, method = "ward.D", max.nc = 6)
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
##
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 6 proposed 2 as the best number of clusters
## * 9 proposed 3 as the best number of clusters
## * 1 proposed 5 as the best number of clusters
## * 7 proposed 6 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 3
##
##
## *******************************************************************data$group <- solution$Best.partition
mean(data$FRG_A_t1[data$group == 1])## [1] 0.4178485mean(data$FRG_M_t1[data$group == 1])## [1] 0.5807143mean(data$FRG_E_t1[data$group == 1])## [1] -0.5115429mean(data$FRG_A_t1[data$group == 2])## [1] 0.2514462mean(data$FRG_M_t1[data$group == 2])## [1] -1.125977mean(data$FRG_E_t1[data$group == 2])## [1] -0.5137296mean(data$FRG_A_t1[data$group == 3])## [1] -0.6724092mean(data$FRG_M_t1[data$group == 3])## [1] 0.1720765mean(data$FRG_E_t1[data$group == 3])## [1] 0.97761Multi Group Latent Difference Score Model
cov_model <- ' # Define latent difference Factor
delta_A =~ 1*FRG_A_t2
# Set autoregressive paths to 1
FRG_A_t2 ~ 1*FRG_A_t1
# Means and Intercept
delta_A ~ 1
FRG_A_t1 ~ 1
FRG_A_t2 ~ 0
# Exogenous (Co)Variances
delta_A ~ FRG_A_t1
delta_A ~~ delta_A
FRG_A_t1 ~~ FRG_A_t1
# Disturbances
FRG_A_t2 ~~ 0*FRG_A_t2
# Covariate
delta_M =~ 1*FRG_M_t2
# Set autoregressive paths to 1
FRG_M_t2 ~ 1*FRG_M_t1
# Means and Intercept
delta_M ~ 1
FRG_M_t1 ~ 1
FRG_M_t2 ~ 0
# Exogenous (Co)Variances
delta_M ~ FRG_M_t1
delta_M ~~ delta_M
FRG_M_t1 ~~ FRG_M_t1
# Disturbances
FRG_M_t2 ~~ 0*FRG_M_t2
# Covariate
delta_E =~ 1*FRG_E_t2
# Set autoregressive paths to 1
FRG_E_t2 ~ 1*FRG_E_t1
# Means and Intercept
delta_E ~ 1
FRG_E_t1 ~ 1
FRG_E_t2 ~ 0
# Exogenous (Co)Variances
delta_E ~ FRG_E_t1
delta_E ~~ delta_E
FRG_E_t1 ~~ FRG_E_t1
# Disturbances
FRG_E_t2 ~~ 0*FRG_E_t2
delta_E ~~ delta_M
delta_A ~~ delta_M
delta_A ~~ delta_E
delta_A ~ FRG_M_t1
delta_A ~ FRG_E_t1
delta_M ~ FRG_A_t1
delta_M ~ FRG_E_t1
delta_E ~ FRG_A_t1
delta_E ~ FRG_M_t1
FRG_A_t1 ~~ FRG_M_t1
FRG_A_t1 ~~ FRG_E_t1
FRG_E_t1 ~~ FRG_M_t1
'
fit_free <- sem(cov_model,
data = data,
group = "group")
fit_load <- sem(cov_model,
data = data,
group = "group", group.equal = c("loadings"))
fit_inter <- sem(cov_model,
data = data,
group = "group", group.equal = c("loadings","intercepts"))
anova(fit_free, fit_load, fit_inter)## Warning in lavTestLRT(object = new("lavaan", version = "0.6.4", call =
## lavaan::lavaan(model = cov_model, : lavaan WARNING: some models have the
## same degrees of freedom## Chi Square Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit_free 0 3265.1 3540.4 0.00
## fit_load 0 3265.1 3540.4 0.00 0.00 0
## fit_inter 6 3568.8 3823.6 315.63 315.63 6 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit_res <- sem(cov_model,
data = data,
group = "group", group.equal = c("loadings", "residuals"))
anova(fit_load, fit_res)## Chi Square Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit_load 0 3265.1 3540.4 0.000
## fit_res 6 3298.2 3553.0 45.001 45.001 6 4.677e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit_resc <- sem(cov_model,
data = data,
group = "group", group.equal = c("loadings", "residual.covariances"))
anova(fit_load, fit_resc)## Chi Square Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit_load 0 3265.1 3540.4 0.000
## fit_resc 6 3271.6 3526.4 18.435 18.435 6 0.005231 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit_var <- sem(cov_model,
data = data,
group = "group", group.equal = c("loadings", "lv.variances"))
fit_cov <- sem(cov_model,
data = data,
group = "group", group.equal = c("loadings","lv.variances","lv.covariances"))
fit_mean <- sem(cov_model,
data = data,
group = "group", group.equal = c("loadings", "lv.variances","lv.covariances","means"))
fit_reg <- sem(cov_model,
data = data,
group = "group", group.equal = c("loadings", "regressions", "lv.variances","lv.covariances","means"))
anova(fit_load, fit_var, fit_cov, fit_reg, fit_mean)## Chi Square Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit_load 0 3265.1 3540.4 0.0000
## fit_var 6 3255.6 3510.5 2.4668 2.4668 6 0.8722
## fit_cov 12 3253.7 3488.1 12.5161 10.0492 6 0.1226
## fit_mean 18 3243.7 3457.8 14.5207 2.0046 6 0.9193
## fit_reg 36 3227.6 3380.5 34.4492 19.9285 18 0.3369summary(fit_reg, standardized = T, rsquare = T)## lavaan 0.6-4 ended normally after 53 iterations
##
## Optimization method NLMINB
## Number of free parameters 81
## Number of equality constraints 36
## Row rank of the constraints matrix 36
##
## Number of observations per group
## 1 88
## 2 57
## 3 76
##
## Estimator ML
## Model Fit Test Statistic 34.449
## Degrees of freedom 36
## P-value (Chi-square) 0.542
##
## Chi-square for each group:
##
## 1 11.971
## 2 8.431
## 3 14.048
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Structured
## Standard Errors Standard
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## delta_A =~
## FRG_A_t2 1.000 0.985 0.961
## delta_M =~
## FRG_M_t2 1.000 0.994 0.944
## delta_E =~
## FRG_E_t2 1.000 0.848 0.963
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FRG_A_t2 ~
## FRG_A_1 1.000 1.000 0.902
## delta_A ~
## FRG_A_1 (.p6.) -0.420 0.061 -6.871 0.000 -0.426 -0.394
## FRG_M_t2 ~
## FRG_M_1 1.000 1.000 0.586
## delta_M ~
## FRG_M_1 (.15.) -0.346 0.065 -5.332 0.000 -0.348 -0.215
## FRG_E_t2 ~
## FRG_E_1 1.000 1.000 0.720
## delta_E ~
## FRG_E_1 (.24.) -0.491 0.055 -8.940 0.000 -0.579 -0.367
## delta_A ~
## FRG_M_1 (.31.) 0.015 0.059 0.253 0.800 0.015 0.009
## FRG_E_1 (.32.) -0.246 0.061 -4.019 0.000 -0.249 -0.158
## delta_M ~
## FRG_A_1 (.33.) 0.103 0.067 1.536 0.124 0.104 0.096
## FRG_E_1 (.34.) -0.159 0.067 -2.365 0.018 -0.160 -0.101
## delta_E ~
## FRG_A_1 (.35.) 0.138 0.055 2.510 0.012 0.163 0.150
## FRG_M_1 (.36.) -0.108 0.053 -2.032 0.042 -0.127 -0.079
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_M ~~
## .delta_E (.28.) 0.029 0.051 0.563 0.574 0.038 0.038
## .delta_A ~~
## .delta_M (.29.) 0.151 0.058 2.606 0.009 0.178 0.178
## .delta_E (.30.) -0.083 0.047 -1.778 0.075 -0.120 -0.120
## FRG_A_t1 ~~
## FRG_M_1 -0.128 0.062 -2.048 0.041 -0.128 -0.224
## FRG_E_1 0.108 0.064 1.702 0.089 0.108 0.185
## FRG_M_t1 ~~
## FRG_E_1 -0.093 0.043 -2.174 0.030 -0.093 -0.238
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_A (.p3.) -0.732 0.059 -12.388 0.000 -0.743 -0.743
## FRG_A_1 0.418 0.098 4.242 0.000 0.418 0.452
## .FRG_A_2 0.000 0.000 0.000
## .delta_M (.12.) -0.428 0.065 -6.599 0.000 -0.430 -0.430
## FRG_M_1 0.581 0.066 8.821 0.000 0.581 0.940
## .FRG_M_2 0.000 0.000 0.000
## .delta_E (.21.) 0.499 0.053 9.406 0.000 0.589 0.589
## FRG_E_1 -0.512 0.068 -7.564 0.000 -0.512 -0.806
## .FRG_E_2 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_A (.p7.) 0.771 0.073 10.512 0.000 0.794 0.794
## FRG_A_1 0.854 0.129 6.633 0.000 0.854 1.000
## .FRG_A_2 0.000 0.000 0.000
## .delta_M (.16.) 0.928 0.088 10.512 0.000 0.939 0.939
## FRG_M_1 0.381 0.058 6.633 0.000 0.381 1.000
## .FRG_M_2 0.000 0.000 0.000
## .delta_E (.25.) 0.623 0.059 10.512 0.000 0.865 0.865
## FRG_E_1 0.403 0.061 6.633 0.000 0.403 1.000
## .FRG_E_2 0.000 0.000 0.000
##
## R-Square:
## Estimate
## delta_A 0.206
## FRG_A_t2 1.000
## delta_M 0.061
## FRG_M_t2 1.000
## delta_E 0.135
## FRG_E_t2 1.000
##
##
## Group 2 [2]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## delta_A =~
## FRG_A_t2 1.000 0.989 0.969
## delta_M =~
## FRG_M_t2 1.000 0.986 0.917
## delta_E =~
## FRG_E_t2 1.000 0.907 0.946
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FRG_A_t2 ~
## FRG_A_1 1.000 1.000 0.834
## delta_A ~
## FRG_A_1 (.p6.) -0.420 0.061 -6.871 0.000 -0.425 -0.361
## FRG_M_t2 ~
## FRG_M_1 1.000 1.000 0.555
## delta_M ~
## FRG_M_1 (.15.) -0.346 0.065 -5.332 0.000 -0.351 -0.210
## FRG_E_t2 ~
## FRG_E_1 1.000 1.000 0.999
## delta_E ~
## FRG_E_1 (.24.) -0.491 0.055 -8.940 0.000 -0.542 -0.519
## delta_A ~
## FRG_M_1 (.31.) 0.015 0.059 0.253 0.800 0.015 0.009
## FRG_E_1 (.32.) -0.246 0.061 -4.019 0.000 -0.248 -0.238
## delta_M ~
## FRG_A_1 (.33.) 0.103 0.067 1.536 0.124 0.105 0.089
## FRG_E_1 (.34.) -0.159 0.067 -2.365 0.018 -0.161 -0.154
## delta_E ~
## FRG_A_1 (.35.) 0.138 0.055 2.510 0.012 0.152 0.129
## FRG_M_1 (.36.) -0.108 0.053 -2.032 0.042 -0.119 -0.071
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_M ~~
## .delta_E (.28.) 0.029 0.051 0.563 0.574 0.038 0.038
## .delta_A ~~
## .delta_M (.29.) 0.151 0.058 2.606 0.009 0.178 0.178
## .delta_E (.30.) -0.083 0.047 -1.778 0.075 -0.120 -0.120
## FRG_A_t1 ~~
## FRG_M_1 0.002 0.067 0.037 0.970 0.002 0.005
## FRG_E_1 0.108 0.109 0.995 0.320 0.108 0.133
## FRG_M_t1 ~~
## FRG_E_1 -0.236 0.082 -2.881 0.004 -0.236 -0.413
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_A (.p3.) -0.732 0.059 -12.388 0.000 -0.740 -0.740
## FRG_A_1 0.251 0.113 2.230 0.026 0.251 0.295
## .FRG_A_2 0.000 0.000 0.000
## .delta_M (.12.) -0.428 0.065 -6.599 0.000 -0.434 -0.434
## FRG_M_1 -1.126 0.079 -14.249 0.000 -1.126 -1.887
## .FRG_M_2 0.000 0.000 0.000
## .delta_E (.21.) 0.499 0.053 9.406 0.000 0.551 0.551
## FRG_E_1 -0.514 0.127 -4.050 0.000 -0.514 -0.536
## .FRG_E_2 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_A (.p7.) 0.771 0.073 10.512 0.000 0.788 0.788
## FRG_A_1 0.724 0.136 5.339 0.000 0.724 1.000
## .FRG_A_2 0.000 0.000 0.000
## .delta_M (.16.) 0.928 0.088 10.512 0.000 0.955 0.955
## FRG_M_1 0.356 0.067 5.339 0.000 0.356 1.000
## .FRG_M_2 0.000 0.000 0.000
## .delta_E (.25.) 0.623 0.059 10.512 0.000 0.757 0.757
## FRG_E_1 0.917 0.172 5.339 0.000 0.917 1.000
## .FRG_E_2 0.000 0.000 0.000
##
## R-Square:
## Estimate
## delta_A 0.212
## FRG_A_t2 1.000
## delta_M 0.045
## FRG_M_t2 1.000
## delta_E 0.243
## FRG_E_t2 1.000
##
##
## Group 3 [3]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## delta_A =~
## FRG_A_t2 1.000 0.958 0.961
## delta_M =~
## FRG_M_t2 1.000 1.013 0.886
## delta_E =~
## FRG_E_t2 1.000 0.837 0.988
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## FRG_A_t2 ~
## FRG_A_1 1.000 1.000 0.816
## delta_A ~
## FRG_A_1 (.p6.) -0.420 0.061 -6.871 0.000 -0.439 -0.357
## FRG_M_t2 ~
## FRG_M_1 1.000 1.000 0.789
## delta_M ~
## FRG_M_1 (.15.) -0.346 0.065 -5.332 0.000 -0.342 -0.309
## FRG_E_t2 ~
## FRG_E_1 1.000 1.000 0.629
## delta_E ~
## FRG_E_1 (.24.) -0.491 0.055 -8.940 0.000 -0.587 -0.313
## delta_A ~
## FRG_M_1 (.31.) 0.015 0.059 0.253 0.800 0.016 0.014
## FRG_E_1 (.32.) -0.246 0.061 -4.019 0.000 -0.257 -0.137
## delta_M ~
## FRG_A_1 (.33.) 0.103 0.067 1.536 0.124 0.102 0.083
## FRG_E_1 (.34.) -0.159 0.067 -2.365 0.018 -0.157 -0.083
## delta_E ~
## FRG_A_1 (.35.) 0.138 0.055 2.510 0.012 0.165 0.134
## FRG_M_1 (.36.) -0.108 0.053 -2.032 0.042 -0.129 -0.117
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_M ~~
## .delta_E (.28.) 0.029 0.051 0.563 0.574 0.038 0.038
## .delta_A ~~
## .delta_M (.29.) 0.151 0.058 2.606 0.009 0.178 0.178
## .delta_E (.30.) -0.083 0.047 -1.778 0.075 -0.120 -0.120
## FRG_A_t1 ~~
## FRG_M_1 0.210 0.088 2.396 0.017 0.210 0.286
## FRG_E_1 0.073 0.050 1.456 0.145 0.073 0.169
## FRG_M_t1 ~~
## FRG_E_1 0.038 0.055 0.684 0.494 0.038 0.079
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_A (.p3.) -0.732 0.059 -12.388 0.000 -0.764 -0.764
## FRG_A_1 -0.672 0.093 -7.209 0.000 -0.672 -0.827
## .FRG_A_2 0.000 0.000 0.000
## .delta_M (.12.) -0.428 0.065 -6.599 0.000 -0.422 -0.422
## FRG_M_1 0.172 0.104 1.661 0.097 0.172 0.191
## .FRG_M_2 0.000 0.000 0.000
## .delta_E (.21.) 0.499 0.053 9.406 0.000 0.596 0.596
## FRG_E_1 0.978 0.061 15.991 0.000 0.978 1.834
## .FRG_E_2 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .delta_A (.p7.) 0.771 0.073 10.512 0.000 0.841 0.841
## FRG_A_1 0.661 0.107 6.164 0.000 0.661 1.000
## .FRG_A_2 0.000 0.000 0.000
## .delta_M (.16.) 0.928 0.088 10.512 0.000 0.904 0.904
## FRG_M_1 0.815 0.132 6.164 0.000 0.815 1.000
## .FRG_M_2 0.000 0.000 0.000
## .delta_E (.25.) 0.623 0.059 10.512 0.000 0.888 0.888
## FRG_E_1 0.284 0.046 6.164 0.000 0.284 1.000
## .FRG_E_2 0.000 0.000 0.000
##
## R-Square:
## Estimate
## delta_A 0.159
## FRG_A_t2 1.000
## delta_M 0.096
## FRG_M_t2 1.000
## delta_E 0.112
## FRG_E_t2 1.000