step | purpose | model |
---|---|---|
1 | 観測変数の記述 | |
2 | 遷移パターンの検討 | LGM |
3 | 2の個人差予測 | 共変量+LGM |
4 | 変数間の因果的関連 | LCMS |
5 | 4のクラスタリング | GMM |
LGM=latent growth model, LCS=latent change score model, GMM=growth mixure model
McArdle, J. J., & Grimm, K. J. (2010). Five steps in latent curve and latent change score modeling with longitudinal data. In Longitudinal research with latent variables (pp. 245-273). Springer Berlin Heidelberg.
6日間ポジティブ気分を経時測定
X | 1 X | 2 X | 3 X | 4 X | 5 X | 6 |
---|---|---|---|---|---|---|
mean | 3.43 | 3.28 | 3.24 | 3.33 | 3.31 | 3.25 |
sd | 1.00 | 1.01 | 1.02 | 1.01 | 1.03 | 1.00 |
time | 0.00 | 1.00 | 2.00 | 3.00 | 4.00 | 5.00 |
Garland, E. L., Geschwind, N., Peeters, F., & Wichers, M. (2015). Mindfulness training promotes upward spirals of positive affect and cognition: multilevel and autoregressive latent trajectory modeling analyses. Frontiers in psychology, 6.
# 切片
level =~ 1* bmi1 +1* bmi2 +1* bmi3 +
1* bmi4 +1* bmi5 +1* bmi6
# 傾き
slope =~ 0 * bmi1 + 1 * bmi2 + 2 * bmi3 +
3 * bmi4 + 4 * bmi5 + 5 * bmi6
# 誤差分散
bmi1 ~~(vare)* bmi1 # 等値制約
bmi2 ~~(vare)* bmi2 # 等値制約
bmi3 ~~(vare)* bmi3 # 等値制約
bmi4 ~~(vare)* bmi4 # 等値制約
bmi5 ~~(vare)* bmi5 # 等値制約
bmi6 ~~(vare)* bmi6 # 等値制約
結構めんどい…
切片のみのモデル (model=‘no’)
線形モデル (model=‘linear’)
二次曲線モデル (model=‘quadratic’)
latent basisモデル (model = ‘latent’)
library(RAMpath)
fit.all<-ramLCM(data=data,outcome=1:6, model='all')
fit.no<-ramLCM(data=data,outcome=1:6, model='no')
fit.linear<-ramLCM(data=data,outcome=1:6, model='linear')
fit.quadratic<-ramLCM(data=data,outcome=1:6, model='quadratic')
fit.latent<-ramLCM(data=data,outcome=1:6, model='latent')
lavaanコード
cat(fit.all$model$no)
## level =~ 1* X1 +1* X2 +1* X3 +1* X4 +1* X5 +1* X6
## X1 ~~(vare)* X1
## X2 ~~(vare)* X2
## X3 ~~(vare)* X3
## X4 ~~(vare)* X4
## X5 ~~(vare)* X5
## X6 ~~(vare)* X6
lavaanコード
cat(fit.all$model$linear)
## level =~ 1* X1 +1* X2 +1* X3 +1* X4 +1* X5 +1* X6
## slope =~ 0 * X1 + 1 * X2 + 2 * X3 + 3 * X4 + 4 * X5 + 5 * X6
## X1 ~~(vare)* X1
## X2 ~~(vare)* X2
## X3 ~~(vare)* X3
## X4 ~~(vare)* X4
## X5 ~~(vare)* X5
## X6 ~~(vare)* X6
lavaanコード
cat(fit.all$model$quadratic)
## level =~ 1* X1 +1* X2 +1* X3 +1* X4 +1* X5 +1* X6
## slope =~ 0 * X1 + 1 * X2 + 2 * X3 + 3 * X4 + 4 * X5 + 5 * X6
## quadratic =~ 0 * X1 + 1 * X2 + 4 * X3 + 9 * X4 + 16 * X5 + 25 * X6
## X1 ~~(vare)* X1
## X2 ~~(vare)* X2
## X3 ~~(vare)* X3
## X4 ~~(vare)* X4
## X5 ~~(vare)* X5
## X6 ~~(vare)* X6
lavaanコード
cat(fit.all$model$latent)
## level =~ 1* X1 +1* X2 +1* X3 +1* X4 +1* X5 +1* X6
## slope =~ 0 * X1 +start( 1 )* X2 +start( 2 )* X3 +start( 3 )* X4 +start( 4 )* X5 + 5 * X6
## X1 ~~(vare)* X1
## X2 ~~(vare)* X2
## X3 ~~(vare)* X3
## X4 ~~(vare)* X4
## X5 ~~(vare)* X5
## X6 ~~(vare)* X6
fits<-round(fit.all$fit[
c("chisq","df","pvalue","cfi",
"srmr","rmsea","aic","bic"),],digits=2)
datatable(fits,option=list(dom='t'))
source("script/plot.growth.R")
a<-plot.growth(fit.all, type="no")+theme_bw()
b<-plot.growth(fit.all, type="lin")+theme_bw()
c<-plot.growth(fit.all, type="quad")+theme_bw()
d<-plot.growth(fit.all, type="latent")+theme_bw()
parm<-parameterEstimates(fit.all$lavaan$quadratic)
parm[,5:10]<-round(parm[,5:10],digits=3)
datatable(parm[c(37:39,28:30,25:27),],
extensions = 'Scroller',
options = list(dom= ' t',
deferRender = TRUE,
scrollY = 200,
scroller = TRUE))
model1 <-'
#切片因子の設定
i =~ 1*X1 + 1*X2 + 1*X3 +
1*X4 + 1*X5 + 1*X6
#傾き因子の設定
s1 =~ 0*X1 + 1*X2 + 2*X3 +
3*X4 + 3*X5 + 3*X6
s2 =~ 0*X1 + 0*X2 + 0*X3 +
0*X4 + 1*X5 + 2*X6
#切片と傾きの分散
i ~~ i ; s1 ~~ s1 ; s2 ~~ s2;
#因子間相関
i ~~ s1 + s2; s1 ~~ s2
#因子平均
i ~ 1 ; s1 ~ 1 ; s2 ~ 1
#誤差分散
X1 ~ 0; X2 ~ 0; X3 ~ 0
X4 ~ 0; X5 ~ 0; X6 ~ 0
'
#lavaan code
i =~ 1*t1+1*t2+1*t3+1*t4+1*t5
前半の傾き(s1)の因子負荷を
区分時点以降同値に固定
#lavaan model code
i=~0*t1+1*t2+2*t3+3*t4+3*t5+3*t6
後半の傾き(s1)の因子負荷を
区分時点まで0に固定
#lavaan model code
i=~0*t1+0*t2+0*t3+0*t4+1*t5+2*t6
#切片と傾きの分散
i ~~ i ; s1 ~~ s1 ; s2 ~~ s2
#因子間相関
i ~~ s1 + s2 ; s1 ~~ s2
#因子平均
i ~ 1 ; s1 ~ 1 ; s2 ~ 1
#誤差分散
bmi1 ~ 0; bmi2 ~ 0; bmi3 ~ 0
bmi4 ~ 0; bmi5 ~ 0; bmi6 ~ 0
library(lavaan)
model1.fit<-lavaan::growth(model1, data)
fit1.m<-round(fitMeasures(model1)[c("chisq","df","pvalue",
"cfi","srmr","rmsea")],digits=2)
fit1.m<-t(as.data.frame(fit1))
print(xtable(fit1.m),comment=F,type="html")
piecewise
quadratic
傾き因子の平均に等値制約を置いたモデルと比較
#傾き因子平均が等値
s1 ~ (a)*1 ; s2 ~ (a)*1
# model1.2fit = 等値制約のモデル
anova(model1.2fit, model1.fit)
## Chi Square Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## model1.fit 12 26592 26676 237.08
## model1.2fit 13 26590 26668 237.09 0.016421 1 0.898
今回のモデルでは期間による傾きの違いは認められない
model2 <-'
#切片因子の設定
i =~ 1*X1 + 1*X2 + 1*X3 + 1*X4 + 1*X5 + 1*X6
#傾き因子の設定
s1 =~ 0*X1 + 1*X2 + 2*X3 +3*X4 + 3*X5 + 3*X6
s2 =~ 0*X1 + 1*X2 + 4*X3 +9*X4 + 9*X5 + 9*X6
s3 =~ 0*X1 + 0*X2 + 0*X3 +0*X4 + 1*X5 + 2*X6
#切片と傾きの分散
i ~~ i ; s1 ~~ s1 ; s2 ~~ s2; s3 ~~ s3;
#因子間相関
i ~~ s1 + s2 + s3; s1 ~~ s2 + s3 ; s2 ~~ s3 ;
#因子平均
i ~ 1 ; s1 ~ 1 ; s2 ~ 1 ; s3 ~ 1
#誤差分散
X1 ~ 0; X2 ~ 0; X3 ~ 0; X4 ~ 0; X5 ~ 0; X6 ~ 0
'
model2.fit<-lavaan::growth(model2, data=data)
fit2.m<-round(fitMeasures(model2.fit)
[c("chisq","df","pvalue",
"cfi","srmr","rmsea")],digits=2)
fit2.m<-t(as.data.frame(fit2.m))
datatable(fit2.m,options=list(dom="t"))
model2.2 <-'
i1 =~ 1*X1 + 1*X2 + 1*X3 + 0*X4 + 0*X5 + 0*X6
i2 =~ 0*X1 + 0*X2 + 0*X3 + 1*X4 + 1*X5 + 1*X6
s1 =~ 0*X1 + 1*X2 + 2*X3 + 3*X4 + 3*X5 + 3*X6
s2 =~ 0*X1 + 0*X2 + 0*X3 + 0*X4 + 1*X5 + 2*X6
i1 ~~ i1
i2 ~~ i2
s1 ~~ s1
s2 ~~ s2
i1 ~~ i2 + s1 + s2
i2 ~~ s1 + s2
s1 ~~ s2
i1 ~ 1
i2 ~ 1
s1 ~ 1
s2 ~ 1
X1 ~ 0
X2 ~ 0
X3 ~ 0
X4 ~ 0
X5 ~ 0
X6 ~ 0 '
Garland, E. L., Geschwind, N., Peeters, F., & Wichers, M. (2015). Mindfulness training promotes upward spirals of positive affect and cognition: multilevel and autoregressive latent trajectory modeling analyses. Frontiers in psychology, 6.
parallel<-'
# posi感情のモデル (2次)
level.X =~ 1* X1 +1* X2 +1* X3 +1* X4 +1* X5 +1* X6
slope.X =~ 0 * X1 + 1 * X2 + 2 * X3 + 3 * X4 + 4 * X5 + 5 * X6
quadratic.X =~ 0 * X1 + 1 * X2 + 4 * X3 + 9 * X4 + 16 * X5 + 25 * X6
# posi認知のモデル (切片のみ)
level.Y =~ 1* Y1 +1* Y2 +1* Y3 +1* Y4 +1* Y5 +1* Y6
'
para<-lavaan::growth(parallel, data)
round(fitmeasures(para)[
c("chisq","df","pvalue","cfi",
"srmr","rmsea","aic","bic")],digits=2)
## chisq df pvalue cfi srmr rmsea aic bic
## 9867.75 64.00 0.00 0.57 0.10 0.28 55871.67 56017.29
parameterEstimates(para,standardized=T)[41:46,c(1:3,11,7)]
## lhs op rhs std.all pvalue
## 41 level.X ~~ slope.X -0.354 0
## 42 level.X ~~ quadratic.X 0.324 0
## 43 level.X ~~ level.Y 0.754 0
## 44 slope.X ~~ quadratic.X -0.983 0
## 45 slope.X ~~ level.Y 0.156 0
## 46 quadratic.X ~~ level.Y -0.125 0
parallel2<-'
# posi感情のモデル (2次)
level.X =~ 1* X1 +1* X2 +1* X3 +1* X4 +1* X5 +1* X6
# posi認知のモデル (切片のみ)
level.Y =~ 1* Y1 +1* Y2 +1* Y3 +1* Y4 +1* Y5 +1* Y6
X1 ~~ Y1
X2 ~~ Y2
X3 ~~ Y3
X4 ~~ Y4
X5 ~~ Y5
X6 ~~ Y6
'
para2<-lavaan::growth(parallel2, data)
round(fitmeasures(para2)[
c("chisq","df","pvalue","cfi",
"srmr","rmsea","aic","bic")],digits=2)
## chisq df pvalue cfi srmr rmsea aic bic
## 1849.42 67.00 0.00 0.92 0.07 0.12 47847.34 47976.16
summary(para2, standardized=T, fit.measures=T)
## lavaan (0.5-20) converged normally after 60 iterations
##
## Number of observations 2000
##
## Estimator ML
## Minimum Function Test Statistic 1849.421
## Degrees of freedom 67
## P-value (Chi-square) 0.000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 22631.255
## Degrees of freedom 66
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.921
## Tucker-Lewis Index (TLI) 0.922
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -23900.669
## Loglikelihood unrestricted model (H1) -22975.959
##
## Number of free parameters 23
## Akaike (AIC) 47847.338
## Bayesian (BIC) 47976.159
## Sample-size adjusted Bayesian (BIC) 47903.086
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.115
## 90 Percent Confidence Interval 0.111 0.120
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.072
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## level.X =~
## X1 1.000 0.821 0.766
## X2 1.000 0.821 0.786
## X3 1.000 0.821 0.822
## X4 1.000 0.821 0.820
## X5 1.000 0.821 0.845
## X6 1.000 0.821 0.787
## level.Y =~
## Y1 1.000 0.652 0.618
## Y2 1.000 0.652 0.653
## Y3 1.000 0.652 0.633
## Y4 1.000 0.652 0.659
## Y5 1.000 0.652 0.665
## Y6 1.000 0.652 0.640
##
## Covariances:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## X1 ~~
## Y1 0.413 0.018 23.226 0.000 0.413 0.722
## X2 ~~
## Y2 0.349 0.015 22.560 0.000 0.349 0.715
## X3 ~~
## Y3 0.332 0.015 22.634 0.000 0.332 0.734
## X4 ~~
## Y4 0.340 0.014 23.783 0.000 0.340 0.798
## X5 ~~
## Y5 0.281 0.013 21.981 0.000 0.281 0.738
## X6 ~~
## Y6 0.405 0.016 24.567 0.000 0.405 0.804
## level.X ~~
## level.Y 0.432 0.018 24.437 0.000 0.807 0.807
##
## Intercepts:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## X1 0.000 0.000 0.000
## X2 0.000 0.000 0.000
## X3 0.000 0.000 0.000
## X4 0.000 0.000 0.000
## X5 0.000 0.000 0.000
## X6 0.000 0.000 0.000
## Y1 0.000 0.000 0.000
## Y2 0.000 0.000 0.000
## Y3 0.000 0.000 0.000
## Y4 0.000 0.000 0.000
## Y5 0.000 0.000 0.000
## Y6 0.000 0.000 0.000
## level.X 3.300 0.019 172.275 0.000 4.018 4.018
## level.Y 3.308 0.016 204.535 0.000 5.074 5.074
##
## Variances:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## X1 0.474 0.017 28.067 0.000 0.474 0.413
## X2 0.418 0.015 27.585 0.000 0.418 0.383
## X3 0.323 0.012 26.358 0.000 0.323 0.324
## X4 0.329 0.012 26.450 0.000 0.329 0.328
## X5 0.270 0.011 25.312 0.000 0.270 0.286
## X6 0.414 0.015 27.536 0.000 0.414 0.380
## Y1 0.688 0.024 28.117 0.000 0.688 0.618
## Y2 0.570 0.021 27.384 0.000 0.570 0.573
## Y3 0.636 0.023 27.801 0.000 0.636 0.599
## Y4 0.554 0.020 27.253 0.000 0.554 0.566
## Y5 0.535 0.020 27.063 0.000 0.535 0.557
## Y6 0.613 0.022 27.681 0.000 0.613 0.591
## level.X 0.675 0.023 29.053 0.000 1.000 1.000
## level.Y 0.425 0.017 25.599 0.000 1.000 1.000
Bollen, K. A., & Curran, P. J. (2004). Autoregressive latent trajectory (ALT) models a synthesis of two traditions. Sociological Methods & Research, 32(3), 336-383.
例) T1の得点が高いとT2でも高い
例) T1のXが高いとT2のYが高くなる
source('script/bivALTM.R')
cat(ALTM)
##
## # posi感情のモデル
## level.X =~ 1* X1 +1* X2 +1* X3 +1* X4 +1* X5 +1* X6
## #slope.X =~ 0 * X1 + 1 * X2 + 2 * X3 + 3 * X4 + 4 * X5 + 5 * X6
## #quadratic.X =~ 0 * X1 + 1 * X2 + 4 * X3 + 9 * X4 + 16 * X5 + 25 * X6
##
##
## # posi認知のモデル
## level.Y =~ 1* Y1 +1* Y2 +1* Y3 +1* Y4 +1* Y5 +1* Y6
##
##
## # 自己回帰のモデル
## X2 ~ X1
## X3 ~ X2
## X4 ~ X3
## X5 ~ X4
## X6 ~ X5
##
## Y2 ~ Y1
## Y3 ~ Y2
## Y4 ~ Y3
## Y5 ~ Y4
## Y6 ~ Y5
##
## #交差遅延モデル
## Y2 ~ X1
## Y3 ~ X2
## Y4 ~ X3
## Y5 ~ X4
## Y6 ~ X5
##
## X2 ~ Y1
## X3 ~ Y2
## X4 ~ Y3
## X5 ~ Y4
## X6 ~ Y5
##
## # 同時点の残差相関
## X1 ~~ Y1
## X2 ~~ Y2
## X3 ~~ Y3
## X4 ~~ Y4
## X5 ~~ Y5
## X6 ~~ Y6
summary(AL<-growth(ALTM, data), standardized=T, fit.measures=T)
## lavaan (0.5-20) converged normally after 97 iterations
##
## Number of observations 2000
##
## Estimator ML
## Minimum Function Test Statistic 1630.385
## Degrees of freedom 47
## P-value (Chi-square) 0.000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 22631.255
## Degrees of freedom 66
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.930
## Tucker-Lewis Index (TLI) 0.901
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -23791.151
## Loglikelihood unrestricted model (H1) -22975.959
##
## Number of free parameters 43
## Akaike (AIC) 47668.302
## Bayesian (BIC) 47909.141
## Sample-size adjusted Bayesian (BIC) 47772.527
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.130
## 90 Percent Confidence Interval 0.124 0.135
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.061
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## level.X =~
## X1 1.000 0.823 0.768
## X2 1.000 0.823 0.773
## X3 1.000 0.823 0.830
## X4 1.000 0.823 0.834
## X5 1.000 0.823 0.826
## X6 1.000 0.823 0.808
## level.Y =~
## Y1 1.000 0.646 0.618
## Y2 1.000 0.646 0.650
## Y3 1.000 0.646 0.625
## Y4 1.000 0.646 0.651
## Y5 1.000 0.646 0.653
## Y6 1.000 0.646 0.636
##
## Regressions:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## X2 ~
## X1 0.096 0.021 4.502 0.000 0.096 0.097
## X3 ~
## X2 -0.009 0.020 -0.463 0.643 -0.009 -0.010
## X4 ~
## X3 -0.087 0.020 -4.258 0.000 -0.087 -0.087
## X5 ~
## X4 0.087 0.021 4.090 0.000 0.087 0.086
## X6 ~
## X5 -0.081 0.025 -3.293 0.001 -0.081 -0.079
## Y2 ~
## Y1 -0.107 0.026 -4.169 0.000 -0.107 -0.113
## Y3 ~
## Y2 0.017 0.028 0.613 0.540 0.017 0.017
## Y4 ~
## Y3 0.109 0.026 4.235 0.000 0.109 0.113
## Y5 ~
## Y4 -0.158 0.029 -5.554 0.000 -0.158 -0.159
## Y6 ~
## Y5 0.128 0.030 4.326 0.000 0.128 0.125
## Y2 ~
## X1 0.102 0.026 3.967 0.000 0.102 0.110
## Y3 ~
## X2 -0.016 0.028 -0.578 0.563 -0.016 -0.017
## Y4 ~
## X3 -0.074 0.026 -2.850 0.004 -0.074 -0.074
## Y5 ~
## X4 0.194 0.029 6.707 0.000 0.194 0.194
## Y6 ~
## X5 -0.128 0.030 -4.246 0.000 -0.128 -0.125
## X2 ~
## Y1 -0.106 0.021 -4.948 0.000 -0.106 -0.104
## X3 ~
## Y2 -0.005 0.020 -0.254 0.800 -0.005 -0.005
## X4 ~
## Y3 0.100 0.020 5.035 0.000 0.100 0.105
## X5 ~
## Y4 -0.076 0.021 -3.660 0.000 -0.076 -0.076
## X6 ~
## Y5 0.063 0.024 2.611 0.009 0.063 0.061
##
## Covariances:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## X1 ~~
## Y1 0.410 0.018 23.311 0.000 0.410 0.728
## X2 ~~
## Y2 0.342 0.015 22.348 0.000 0.342 0.709
## X3 ~~
## Y3 0.340 0.015 22.746 0.000 0.340 0.741
## X4 ~~
## Y4 0.330 0.014 23.562 0.000 0.330 0.796
## X5 ~~
## Y5 0.266 0.012 21.497 0.000 0.266 0.725
## X6 ~~
## Y6 0.401 0.016 24.582 0.000 0.401 0.804
## level.X ~~
## level.Y 0.424 0.018 23.099 0.000 0.799 0.799
##
## Intercepts:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## X1 0.000 0.000 0.000
## X2 0.000 0.000 0.000
## X3 0.000 0.000 0.000
## X4 0.000 0.000 0.000
## X5 0.000 0.000 0.000
## X6 0.000 0.000 0.000
## Y1 0.000 0.000 0.000
## Y2 0.000 0.000 0.000
## Y3 0.000 0.000 0.000
## Y4 0.000 0.000 0.000
## Y5 0.000 0.000 0.000
## Y6 0.000 0.000 0.000
## level.X 3.307 0.023 142.720 0.000 4.019 4.019
## level.Y 3.265 0.022 146.600 0.000 5.056 5.056
##
## Variances:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## X1 0.471 0.017 28.055 0.000 0.471 0.410
## X2 0.410 0.015 27.493 0.000 0.410 0.362
## X3 0.322 0.012 26.349 0.000 0.322 0.328
## X4 0.324 0.012 26.358 0.000 0.324 0.332
## X5 0.261 0.010 25.160 0.000 0.261 0.263
## X6 0.411 0.015 27.564 0.000 0.411 0.396
## Y1 0.674 0.024 27.914 0.000 0.674 0.618
## Y2 0.567 0.021 27.238 0.000 0.567 0.575
## Y3 0.651 0.024 27.690 0.000 0.651 0.609
## Y4 0.533 0.020 26.896 0.000 0.533 0.541
## Y5 0.517 0.019 26.697 0.000 0.517 0.528
## Y6 0.605 0.022 27.688 0.000 0.605 0.587
## level.X 0.677 0.024 27.666 0.000 1.000 1.000
## level.Y 0.417 0.017 24.511 0.000 1.000 1.000
cat(ALTM2)
##
## # posi感情のモデル
## level.X =~ 1* X1 +1* X2 +1* X3 +1* X4 +1* X5 +1* X6
## #slope.X =~ 0 * X1 + 1 * X2 + 2 * X3 + 3 * X4 + 4 * X5 + 5 * X6
## #quadratic.X =~ 0 * X1 + 1 * X2 + 4 * X3 + 9 * X4 + 16 * X5 + 25 * X6
##
##
## # posi認知のモデル
## level.Y =~ 1* Y1 +1* Y2 +1* Y3 +1* Y4 +1* Y5 +1* Y6
##
##
## # 自己回帰のモデル
## X2 ~ (a)*X1
## X3 ~ (a)*X2
## X4 ~ (a)*X3
## X5 ~ (a)*X4
## X6 ~ (a)*X5
##
## Y2 ~ (b)*Y1
## Y3 ~ (b)*Y2
## Y4 ~ (b)*Y3
## Y5 ~ (b)*Y4
## Y6 ~ (b)*Y5
##
## #交差遅延モデル
## Y2 ~ (c)*X1
## Y3 ~ (c)*X2
## Y4 ~ (c)*X3
## Y5 ~ (c)*X4
## Y6 ~ (c)*X5
##
## X2 ~ (d)*Y1
## X3 ~ (d)*Y2
## X4 ~ (d)*Y3
## X5 ~ (d)*Y4
## X6 ~ (d)*Y5
##
## # 同時点の残差相関
## X1 ~~ Y1
## X2 ~~ Y2
## X3 ~~ Y3
## X4 ~~ Y4
## X5 ~~ Y5
## X6 ~~ Y6
cat(ALTM3)
##
## # posi感情のモデル
## level.X =~ 1* X1 +1* X2 +1* X3 +1* X4 +1* X5 +1* X6
## #slope.X =~ 0 * X1 + 1 * X2 + 2 * X3 + 3 * X4 + 4 * X5 + 5 * X6
## #quadratic.X =~ 0 * X1 + 1 * X2 + 4 * X3 + 9 * X4 + 16 * X5 + 25 * X6
##
##
## # posi認知のモデル
## level.Y =~ 1* Y1 +1* Y2 +1* Y3 +1* Y4 +1* Y5 +1* Y6
##
##
## # 自己回帰のモデル
## X2 ~ (a)*X1
## X3 ~ (a)*X2
## X4 ~ (a)*X3
## X5 ~ (a)*X4
## X6 ~ (a)*X5
##
## Y2 ~ (b)*Y1
## Y3 ~ (b)*Y2
## Y4 ~ (b)*Y3
## Y5 ~ (b)*Y4
## Y6 ~ (b)*Y5
##
## #交差遅延モデル
## Y2 ~ X1
## Y3 ~ X2
## Y4 ~ X3
## Y5 ~ X4
## Y6 ~ X5
##
## X2 ~ Y1
## X3 ~ Y2
## X4 ~ Y3
## X5 ~ Y4
## X6 ~ Y5
##
## # 同時点の残差相関
## X1 ~~ Y1
## X2 ~~ Y2
## X3 ~~ Y3
## X4 ~~ Y4
## X5 ~~ Y5
## X6 ~~ Y6
cat(ALTM4)
##
## # posi感情のモデル
## level.X =~ 1* X1 +1* X2 +1* X3 +1* X4 +1* X5 +1* X6
## #slope.X =~ 0 * X1 + 1 * X2 + 2 * X3 + 3 * X4 + 4 * X5 + 5 * X6
## #quadratic.X =~ 0 * X1 + 1 * X2 + 4 * X3 + 9 * X4 + 16 * X5 + 25 * X6
##
##
## # posi認知のモデル
## level.Y =~ 1* Y1 +1* Y2 +1* Y3 +1* Y4 +1* Y5 +1* Y6
##
##
## # 自己回帰のモデル
## #X2 ~ (a)*X1
## #X3 ~ (a)*X2
## #X4 ~ (a)*X3
## #X5 ~ (a)*X4
## #X6 ~ (a)*X5
##
## #Y2 ~ (b)*Y1
## #Y3 ~ (b)*Y2
## #Y4 ~ (b)*Y3
## #Y5 ~ (b)*Y4
## #Y6 ~ (b)*Y5
##
## #交差遅延モデル
## Y2 ~ X1
## Y3 ~ X2
## Y4 ~ X3
## Y5 ~ X4
## Y6 ~ X5
##
## X2 ~ Y1
## X3 ~ Y2
## X4 ~ Y3
## X5 ~ Y4
## X6 ~ Y5
##
## # 同時点の残差相関
## X1 ~~ Y1
## X2 ~~ Y2
## X3 ~~ Y3
## X4 ~~ Y4
## X5 ~~ Y5
## X6 ~~ Y6
AL2<-growth(ALTM2, data); AL3<-growth(ALTM3, data); AL4<-growth(ALTM4, data)
library(semTools)
compareFit(para2,AL,AL2, AL3,AL4)
## ################### Nested Model Comparison #########################
## chi df p delta.cfi
## AL - AL3 106.48 8 <.001 0.0044
## AL3 - AL4 0.11 2 .946 -0.0001
## AL4 - AL2 92.65 6 <.001 0.0038
## AL2 - para2 19.80 4 <.001 0.0007
##
## #################### Fit Indices Summaries ##########################
## chisq df pvalue cfi tli aic bic rmsea
## para2 1849.421 67 .000† .921 .922† 47847.338 47976.159 .115†
## AL 1630.385 47 .000† .930† .901 47668.302† 47909.141† .130
## AL2 1829.620 63 .000† .922 .918 47835.537 47986.761 .118
## AL3 1736.865 55 .000† .925 .911 47758.782 47954.813 .124
## AL4 1736.975 57 .000† .926 .914 47754.892 47939.721 .121
## srmr
## para2 .072
## AL .061†
## AL2 .071
## AL3 .066
## AL4 .066
例) 1時点前の得点が高いor低いと次の時点では得点の変化が大きくなる(平均への回帰)
例) 1時点前の一方の変数の得点が高いor低いと、次の時点におけるもう一方の変数の得点の変化が大きくなる。
## lavaan (0.5-20) converged normally after 267 iterations
##
## Number of observations 500
##
## Estimator ML
## Minimum Function Test Statistic 64.600
## Degrees of freedom 70
## P-value (Chi-square) 0.660
##
## Model test baseline model:
##
## Minimum Function Test Statistic 3441.089
## Degrees of freedom 66
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.002
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -16562.752
## Loglikelihood unrestricted model (H1) -16530.452
##
## Number of free parameters 20
## Akaike (AIC) 33165.504
## Bayesian (BIC) 33249.796
## Sample-size adjusted Bayesian (BIC) 33186.315
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent Confidence Interval 0.000 0.022
## P-value RMSEA <= 0.05 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.027
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err Z-value P(>|z|)
## y0 =~
## y1 1.000
## dy2 =~
## y2 1.000
## dy3 =~
## y3 1.000
## dy4 =~
## y4 1.000
## dy5 =~
## y5 1.000
## dy6 =~
## y6 1.000
## ys =~
## dy2 1.000
## dy3 1.000
## dy4 1.000
## dy5 1.000
## dy6 1.000
## y1 =~
## Y7 1.000
## y2 =~
## Y8 1.000
## y3 =~
## Y9 1.000
## y4 =~
## Y10 1.000
## y5 =~
## Y11 1.000
## y6 =~
## Y12 1.000
## x0 =~
## x1 1.000
## dx2 =~
## x2 1.000
## dx3 =~
## x3 1.000
## dx4 =~
## x4 1.000
## dx5 =~
## x5 1.000
## dx6 =~
## x6 1.000
## xs =~
## dx2 1.000
## dx3 1.000
## dx4 1.000
## dx5 1.000
## dx6 1.000
## x1 =~
## X1 1.000
## x2 =~
## X2 1.000
## x3 =~
## X3 1.000
## x4 =~
## X4 1.000
## x5 =~
## X5 1.000
## x6 =~
## X6 1.000
##
## Regressions:
## Estimate Std.Err Z-value P(>|z|)
## y2 ~
## y1 1.000
## y3 ~
## y2 1.000
## y4 ~
## y3 1.000
## y5 ~
## y4 1.000
## y6 ~
## y5 1.000
## dy2 ~
## y1 (bety) -0.194 0.106 -1.824 0.068
## dy3 ~
## y2 (bety) -0.194 0.106 -1.824 0.068
## dy4 ~
## y3 (bety) -0.194 0.106 -1.824 0.068
## dy5 ~
## y4 (bety) -0.194 0.106 -1.824 0.068
## dy6 ~
## y5 (bety) -0.194 0.106 -1.824 0.068
## x2 ~
## x1 1.000
## x3 ~
## x2 1.000
## x4 ~
## x3 1.000
## x5 ~
## x4 1.000
## x6 ~
## x5 1.000
## dx2 ~
## x1 (betx) 0.226 0.047 4.769 0.000
## dx3 ~
## x2 (betx) 0.226 0.047 4.769 0.000
## dx4 ~
## x3 (betx) 0.226 0.047 4.769 0.000
## dx5 ~
## x4 (betx) 0.226 0.047 4.769 0.000
## dx6 ~
## x5 (betx) 0.226 0.047 4.769 0.000
## dy2 ~
## x1 (gmmx) 0.098 0.040 2.478 0.013
## dy3 ~
## x2 (gmmx) 0.098 0.040 2.478 0.013
## dy4 ~
## x3 (gmmx) 0.098 0.040 2.478 0.013
## dy5 ~
## x4 (gmmx) 0.098 0.040 2.478 0.013
## dy6 ~
## x5 (gmmx) 0.098 0.040 2.478 0.013
## dx2 ~
## y1 (gmmy) -0.139 0.127 -1.090 0.276
## dx3 ~
## y2 (gmmy) -0.139 0.127 -1.090 0.276
## dx4 ~
## y3 (gmmy) -0.139 0.127 -1.090 0.276
## dx5 ~
## y4 (gmmy) -0.139 0.127 -1.090 0.276
## dx6 ~
## y5 (gmmy) -0.139 0.127 -1.090 0.276
##
## Covariances:
## Estimate Std.Err Z-value P(>|z|)
## y0 ~~
## ys (vry0y) 0.893 0.346 2.582 0.010
## x0 ~~
## xs (vrx0x) 0.703 0.231 3.036 0.002
## y0 ~~
## x0 (vr00) 0.979 0.399 2.456 0.014
## ys ~~
## x0 (vrx0y) 0.222 0.206 1.078 0.281
## y0 ~~
## xs (vry0x) 0.475 0.489 0.972 0.331
## ys ~~
## xs (vrxs) 0.666 0.239 2.782 0.005
##
## Intercepts:
## Estimate Std.Err Z-value P(>|z|)
## ys (mys) 4.939 1.384 3.568 0.000
## y0 (my0) 19.934 0.153 130.588 0.000
## y1 0.000
## y2 0.000
## y3 0.000
## y4 0.000
## y5 0.000
## y6 0.000
## dy2 0.000
## dy3 0.000
## dy4 0.000
## dy5 0.000
## dy6 0.000
## Y7 0.000
## Y8 0.000
## Y9 0.000
## Y10 0.000
## Y11 0.000
## Y12 0.000
## xs (mxs) 5.090 1.657 3.072 0.002
## x0 (mx0) 20.193 0.149 135.178 0.000
## x1 0.000
## x2 0.000
## x3 0.000
## x4 0.000
## x5 0.000
## x6 0.000
## dx2 0.000
## dx3 0.000
## dx4 0.000
## dx5 0.000
## dx6 0.000
## X1 0.000
## X2 0.000
## X3 0.000
## X4 0.000
## X5 0.000
## X6 0.000
##
## Variances:
## Estimate Std.Err Z-value P(>|z|)
## dy2 0.000
## dy3 0.000
## dy4 0.000
## dy5 0.000
## dy6 0.000
## y1 0.000
## y2 0.000
## y3 0.000
## y4 0.000
## y5 0.000
## y6 0.000
## y0 (vry0) 3.459 0.630 5.493 0.000
## ys (vrys) 0.899 0.374 2.403 0.016
## Y7 (vary) 9.674 0.306 31.658 0.000
## Y8 (vary) 9.674 0.306 31.658 0.000
## Y9 (vary) 9.674 0.306 31.658 0.000
## Y10 (vary) 9.674 0.306 31.658 0.000
## Y11 (vary) 9.674 0.306 31.658 0.000
## Y12 (vary) 9.674 0.306 31.658 0.000
## dx2 0.000
## dx3 0.000
## dx4 0.000
## dx5 0.000
## dx6 0.000
## x1 0.000
## x2 0.000
## x3 0.000
## x4 0.000
## x5 0.000
## x6 0.000
## x0 (vrx0) 4.156 0.532 7.812 0.000
## xs (vrxs) 1.012 0.185 5.460 0.000
## X1 (varx) 9.088 0.287 31.614 0.000
## X2 (varx) 9.088 0.287 31.614 0.000
## X3 (varx) 9.088 0.287 31.614 0.000
## X4 (varx) 9.088 0.287 31.614 0.000
## X5 (varx) 9.088 0.287 31.614 0.000
## X6 (varx) 9.088 0.287 31.614 0.000
複雑なモデルを1行で済ませてくれる
## y0 =~ 1*y1
## y2~1*y1
## y3~1*y2
## y4~1*y3
## y5~1*y4
## y6~1*y5
## dy2=~1*y2
## dy3=~1*y3
## dy4=~1*y4
## dy5=~1*y5
## dy6=~1*y6
## dy2~betay*y1
## dy3~betay*y2
## dy4~betay*y3
## dy5~betay*y4
## dy6~betay*y5
## ys=~1*dy2
## ys=~1*dy3
## ys=~1*dy4
## ys=~1*dy5
## ys=~1*dy6
## dy2~~0*dy2
## dy3~~0*dy3
## dy4~~0*dy4
## dy5~~0*dy5
## dy6~~0*dy6
## y1~~0*y1
## y2~~0*y2
## y3~~0*y3
## y4~~0*y4
## y5~~0*y5
## y6~~0*y6
## ys~~vary0ys*y0
## y0~~vary0*y0
## ys~~varys*ys
## ys~mys*1
## y0~my0*1
## y1~0*1
## y2~0*1
## y3~0*1
## y4~0*1
## y5~0*1
## y6~0*1
## dy2~0*1
## dy3~0*1
## dy4~0*1
## dy5~0*1
## dy6~0*1
## y1=~1*Y7
## y2=~1*Y8
## y3=~1*Y9
## y4=~1*Y10
## y5=~1*Y11
## y6=~1*Y12
## Y7~0*1
## Y8~0*1
## Y9~0*1
## Y10~0*1
## Y11~0*1
## Y12~0*1
## Y7~~varey*Y7
## Y8~~varey*Y8
## Y9~~varey*Y9
## Y10~~varey*Y10
## Y11~~varey*Y11
## Y12~~varey*Y12
## x0 =~ 1*x1
## x2~1*x1
## x3~1*x2
## x4~1*x3
## x5~1*x4
## x6~1*x5
## dx2=~1*x2
## dx3=~1*x3
## dx4=~1*x4
## dx5=~1*x5
## dx6=~1*x6
## dx2~betax*x1
## dx3~betax*x2
## dx4~betax*x3
## dx5~betax*x4
## dx6~betax*x5
## xs=~1*dx2
## xs=~1*dx3
## xs=~1*dx4
## xs=~1*dx5
## xs=~1*dx6
## dx2~~0*dx2
## dx3~~0*dx3
## dx4~~0*dx4
## dx5~~0*dx5
## dx6~~0*dx6
## x1~~0*x1
## x2~~0*x2
## x3~~0*x3
## x4~~0*x4
## x5~~0*x5
## x6~~0*x6
## xs~~varx0xs*x0
## x0~~varx0*x0
## xs~~varxs*xs
## xs~mxs*1
## x0~mx0*1
## x1~0*1
## x2~0*1
## x3~0*1
## x4~0*1
## x5~0*1
## x6~0*1
## dx2~0*1
## dx3~0*1
## dx4~0*1
## dx5~0*1
## dx6~0*1
## x1=~1*X1
## x2=~1*X2
## x3=~1*X3
## x4=~1*X4
## x5=~1*X5
## x6=~1*X6
## X1~0*1
## X2~0*1
## X3~0*1
## X4~0*1
## X5~0*1
## X6~0*1
## X1~~varex*X1
## X2~~varex*X2
## X3~~varex*X3
## X4~~varex*X4
## X5~~varex*X5
## X6~~varex*X6
## dy2~gammax*x1
## dy3~gammax*x2
## dy4~gammax*x3
## dy5~gammax*x4
## dy6~gammax*x5
## dx2~gammay*y1
## dx3~gammay*y2
## dx4~gammay*y3
## dx5~gammay*y4
## dx6~gammay*y5
## x0~~varx0y0*y0
## x0~~varx0ys*ys
## y0~~vary0xs*xs
## xs~~varxsys*ys
##
-Yを指定を解説 -Xも同様の指定
# 切片をT1のファントム変数に負荷
y0 =~ 1*y1
# ファントム変数間の自己回帰
y2~1*y1
y3~1*y2
y4~1*y3
y5~1*y4
y6~1*y5
# 差得点から同時点のファントム変数へのパス
dy2=~1*y2
dy3=~1*y3
dy4=~1*y4
dy5=~1*y5
dy6=~1*y6
# betaパス 等値制約 (ファントムから差得点)
dy2~betay*y1
dy3~betay*y2
dy4~betay*y3
dy5~betay*y4
dy6~betay*y5
# 傾きから差得点への因子負荷1に固定
ys=~1*dy2
ys=~1*dy3
ys=~1*dy4
ys=~1*dy5
ys=~1*dy6
# 差得点とファントムの平均と分散は0に固定
#分散
dy2~~0*dy2
dy3~~0*dy3
dy4~~0*dy4
dy5~~0*dy5
dy6~~0*dy6
y1~~0*y1
y2~~0*y2
y3~~0*y3
y4~~0*y4
y5~~0*y5
y6~~0*y6
#平均
y1~0*1
y2~0*1
y3~0*1
y4~0*1
y5~0*1
y6~0*1
dy2~0*1
dy3~0*1
dy4~0*1
dy5~0*1
dy6~0*1
# 切片と傾きの平均と分散と共分散
ys~~vary0ys*y0
y0~~vary0*y0
ys~~varys*ys
ys~mys*1
y0~my0*1
#ファントム変数の作成
y1=~1*Y7
y2=~1*Y8
y3=~1*Y9
y4=~1*Y10
y5=~1*Y11
y6=~1*Y12
# 観測変数の平均を0に固定
Y7~0*1
Y8~0*1
Y9~0*1
Y10~0*1
Y11~0*1
Y12~0*1
# 観測変数の分散に等値制約
Y7~~varey*Y7
Y8~~varey*Y8
Y9~~varey*Y9
Y10~~varey*Y10
Y11~~varey*Y11
Y12~~varey*Y12
# gammaパス
dx2~gammay*y1
dx3~gammay*y2
dx4~gammay*y3
dx5~gammay*y4
dx6~gammay*y5
## lavaan (0.5-20) converged normally after 267 iterations
##
## Number of observations 500
##
## Estimator ML
## Minimum Function Test Statistic 64.600
## Degrees of freedom 70
## P-value (Chi-square) 0.660
##
## Model test baseline model:
##
## Minimum Function Test Statistic 3441.089
## Degrees of freedom 66
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.002
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -16562.752
## Loglikelihood unrestricted model (H1) -16530.452
##
## Number of free parameters 20
## Akaike (AIC) 33165.504
## Bayesian (BIC) 33249.796
## Sample-size adjusted Bayesian (BIC) 33186.315
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent Confidence Interval 0.000 0.022
## P-value RMSEA <= 0.05 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.027
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err Z-value P(>|z|)
## y0 =~
## y1 1.000
## dy2 =~
## y2 1.000
## dy3 =~
## y3 1.000
## dy4 =~
## y4 1.000
## dy5 =~
## y5 1.000
## dy6 =~
## y6 1.000
## ys =~
## dy2 1.000
## dy3 1.000
## dy4 1.000
## dy5 1.000
## dy6 1.000
## y1 =~
## Y7 1.000
## y2 =~
## Y8 1.000
## y3 =~
## Y9 1.000
## y4 =~
## Y10 1.000
## y5 =~
## Y11 1.000
## y6 =~
## Y12 1.000
## x0 =~
## x1 1.000
## dx2 =~
## x2 1.000
## dx3 =~
## x3 1.000
## dx4 =~
## x4 1.000
## dx5 =~
## x5 1.000
## dx6 =~
## x6 1.000
## xs =~
## dx2 1.000
## dx3 1.000
## dx4 1.000
## dx5 1.000
## dx6 1.000
## x1 =~
## X1 1.000
## x2 =~
## X2 1.000
## x3 =~
## X3 1.000
## x4 =~
## X4 1.000
## x5 =~
## X5 1.000
## x6 =~
## X6 1.000
##
## Regressions:
## Estimate Std.Err Z-value P(>|z|)
## y2 ~
## y1 1.000
## y3 ~
## y2 1.000
## y4 ~
## y3 1.000
## y5 ~
## y4 1.000
## y6 ~
## y5 1.000
## dy2 ~
## y1 (bety) -0.194 0.106 -1.824 0.068
## dy3 ~
## y2 (bety) -0.194 0.106 -1.824 0.068
## dy4 ~
## y3 (bety) -0.194 0.106 -1.824 0.068
## dy5 ~
## y4 (bety) -0.194 0.106 -1.824 0.068
## dy6 ~
## y5 (bety) -0.194 0.106 -1.824 0.068
## x2 ~
## x1 1.000
## x3 ~
## x2 1.000
## x4 ~
## x3 1.000
## x5 ~
## x4 1.000
## x6 ~
## x5 1.000
## dx2 ~
## x1 (betx) 0.226 0.047 4.769 0.000
## dx3 ~
## x2 (betx) 0.226 0.047 4.769 0.000
## dx4 ~
## x3 (betx) 0.226 0.047 4.769 0.000
## dx5 ~
## x4 (betx) 0.226 0.047 4.769 0.000
## dx6 ~
## x5 (betx) 0.226 0.047 4.769 0.000
## dy2 ~
## x1 (gmmx) 0.098 0.040 2.478 0.013
## dy3 ~
## x2 (gmmx) 0.098 0.040 2.478 0.013
## dy4 ~
## x3 (gmmx) 0.098 0.040 2.478 0.013
## dy5 ~
## x4 (gmmx) 0.098 0.040 2.478 0.013
## dy6 ~
## x5 (gmmx) 0.098 0.040 2.478 0.013
## dx2 ~
## y1 (gmmy) -0.139 0.127 -1.090 0.276
## dx3 ~
## y2 (gmmy) -0.139 0.127 -1.090 0.276
## dx4 ~
## y3 (gmmy) -0.139 0.127 -1.090 0.276
## dx5 ~
## y4 (gmmy) -0.139 0.127 -1.090 0.276
## dx6 ~
## y5 (gmmy) -0.139 0.127 -1.090 0.276
##
## Covariances:
## Estimate Std.Err Z-value P(>|z|)
## y0 ~~
## ys (vry0y) 0.893 0.346 2.582 0.010
## x0 ~~
## xs (vrx0x) 0.703 0.231 3.036 0.002
## y0 ~~
## x0 (vr00) 0.979 0.399 2.456 0.014
## ys ~~
## x0 (vrx0y) 0.222 0.206 1.078 0.281
## y0 ~~
## xs (vry0x) 0.475 0.489 0.972 0.331
## ys ~~
## xs (vrxs) 0.666 0.239 2.782 0.005
##
## Intercepts:
## Estimate Std.Err Z-value P(>|z|)
## ys (mys) 4.939 1.384 3.568 0.000
## y0 (my0) 19.934 0.153 130.588 0.000
## y1 0.000
## y2 0.000
## y3 0.000
## y4 0.000
## y5 0.000
## y6 0.000
## dy2 0.000
## dy3 0.000
## dy4 0.000
## dy5 0.000
## dy6 0.000
## Y7 0.000
## Y8 0.000
## Y9 0.000
## Y10 0.000
## Y11 0.000
## Y12 0.000
## xs (mxs) 5.090 1.657 3.072 0.002
## x0 (mx0) 20.193 0.149 135.178 0.000
## x1 0.000
## x2 0.000
## x3 0.000
## x4 0.000
## x5 0.000
## x6 0.000
## dx2 0.000
## dx3 0.000
## dx4 0.000
## dx5 0.000
## dx6 0.000
## X1 0.000
## X2 0.000
## X3 0.000
## X4 0.000
## X5 0.000
## X6 0.000
##
## Variances:
## Estimate Std.Err Z-value P(>|z|)
## dy2 0.000
## dy3 0.000
## dy4 0.000
## dy5 0.000
## dy6 0.000
## y1 0.000
## y2 0.000
## y3 0.000
## y4 0.000
## y5 0.000
## y6 0.000
## y0 (vry0) 3.459 0.630 5.493 0.000
## ys (vrys) 0.899 0.374 2.403 0.016
## Y7 (vary) 9.674 0.306 31.658 0.000
## Y8 (vary) 9.674 0.306 31.658 0.000
## Y9 (vary) 9.674 0.306 31.658 0.000
## Y10 (vary) 9.674 0.306 31.658 0.000
## Y11 (vary) 9.674 0.306 31.658 0.000
## Y12 (vary) 9.674 0.306 31.658 0.000
## dx2 0.000
## dx3 0.000
## dx4 0.000
## dx5 0.000
## dx6 0.000
## x1 0.000
## x2 0.000
## x3 0.000
## x4 0.000
## x5 0.000
## x6 0.000
## x0 (vrx0) 4.156 0.532 7.812 0.000
## xs (vrxs) 1.012 0.185 5.460 0.000
## X1 (varx) 9.088 0.287 31.614 0.000
## X2 (varx) 9.088 0.287 31.614 0.000
## X3 (varx) 9.088 0.287 31.614 0.000
## X4 (varx) 9.088 0.287 31.614 0.000
## X5 (varx) 9.088 0.287 31.614 0.000
## X6 (varx) 9.088 0.287 31.614 0.000
## lavaan (0.5-20) converged normally after 267 iterations
##
## Number of observations 500
##
## Estimator ML
## Minimum Function Test Statistic 64.600
## Degrees of freedom 70
## P-value (Chi-square) 0.660
##
## Model test baseline model:
##
## Minimum Function Test Statistic 3441.089
## Degrees of freedom 66
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.002
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -16562.752
## Loglikelihood unrestricted model (H1) -16530.452
##
## Number of free parameters 20
## Akaike (AIC) 33165.504
## Bayesian (BIC) 33249.796
## Sample-size adjusted Bayesian (BIC) 33186.315
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent Confidence Interval 0.000 0.022
## P-value RMSEA <= 0.05 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.027
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## y0 =~
## y1 1.000 1.000 1.000
## dy2 =~
## y2 1.000 0.389 0.389
## dy3 =~
## y3 1.000 0.286 0.286
## dy4 =~
## y4 1.000 0.223 0.223
## dy5 =~
## y5 1.000 0.186 0.186
## dy6 =~
## y6 1.000 0.165 0.165
## ys =~
## dy2 1.000 1.111 1.111
## dy3 1.000 1.227 1.227
## dy4 1.000 1.306 1.306
## dy5 1.000 1.326 1.326
## dy6 1.000 1.282 1.282
## y1 =~
## Y7 1.000 1.860 0.513
## y2 =~
## Y8 1.000 2.196 0.577
## y3 =~
## Y9 1.000 2.699 0.655
## y4 =~
## Y10 1.000 3.259 0.723
## y5 =~
## Y11 1.000 3.847 0.778
## y6 =~
## Y12 1.000 4.470 0.821
## x0 =~
## x1 1.000 1.000 1.000
## dx2 =~
## x2 1.000 0.406 0.406
## dx3 =~
## x3 1.000 0.331 0.331
## dx4 =~
## x4 1.000 0.284 0.284
## dx5 =~
## x5 1.000 0.252 0.252
## dx6 =~
## x6 1.000 0.230 0.230
## xs =~
## dx2 1.000 0.846 0.846
## dx3 1.000 0.729 0.729
## dx4 1.000 0.623 0.623
## dx5 1.000 0.529 0.529
## dx6 1.000 0.447 0.447
## x1 =~
## X1 1.000 2.039 0.560
## x2 =~
## X2 1.000 2.929 0.697
## x3 =~
## X3 1.000 4.163 0.810
## x4 =~
## X4 1.000 5.696 0.884
## x5 =~
## X5 1.000 7.546 0.929
## x6 =~
## X6 1.000 9.759 0.955
##
## Regressions:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## y2 ~
## y1 1.000 0.847 0.847
## y3 ~
## y2 1.000 0.814 0.814
## y4 ~
## y3 1.000 0.828 0.828
## y5 ~
## y4 1.000 0.847 0.847
## y6 ~
## y5 1.000 0.861 0.861
## dy2 ~
## y1 (bety) -0.194 0.106 -1.824 0.068 -0.423 -0.423
## dy3 ~
## y2 (bety) -0.194 0.106 -1.824 0.068 -0.552 -0.552
## dy4 ~
## y3 (bety) -0.194 0.106 -1.824 0.068 -0.722 -0.722
## dy5 ~
## y4 (bety) -0.194 0.106 -1.824 0.068 -0.885 -0.885
## dy6 ~
## y5 (bety) -0.194 0.106 -1.824 0.068 -1.010 -1.010
## x2 ~
## x1 1.000 0.696 0.696
## x3 ~
## x2 1.000 0.704 0.704
## x4 ~
## x3 1.000 0.731 0.731
## x5 ~
## x4 1.000 0.755 0.755
## x6 ~
## x5 1.000 0.773 0.773
## dx2 ~
## x1 (betx) 0.226 0.047 4.769 0.000 0.387 0.387
## dx3 ~
## x2 (betx) 0.226 0.047 4.769 0.000 0.480 0.480
## dx4 ~
## x3 (betx) 0.226 0.047 4.769 0.000 0.582 0.582
## dx5 ~
## x4 (betx) 0.226 0.047 4.769 0.000 0.676 0.676
## dx6 ~
## x5 (betx) 0.226 0.047 4.769 0.000 0.757 0.757
## dy2 ~
## x1 (gmmx) 0.098 0.040 2.478 0.013 0.234 0.234
## dy3 ~
## x2 (gmmx) 0.098 0.040 2.478 0.013 0.372 0.372
## dy4 ~
## x3 (gmmx) 0.098 0.040 2.478 0.013 0.562 0.562
## dy5 ~
## x4 (gmmx) 0.098 0.040 2.478 0.013 0.781 0.781
## dy6 ~
## x5 (gmmx) 0.098 0.040 2.478 0.013 1.000 1.000
## dx2 ~
## y1 (gmmy) -0.139 0.127 -1.090 0.276 -0.217 -0.217
## dx3 ~
## y2 (gmmy) -0.139 0.127 -1.090 0.276 -0.221 -0.221
## dx4 ~
## y3 (gmmy) -0.139 0.127 -1.090 0.276 -0.232 -0.232
## dx5 ~
## y4 (gmmy) -0.139 0.127 -1.090 0.276 -0.238 -0.238
## dx6 ~
## y5 (gmmy) -0.139 0.127 -1.090 0.276 -0.237 -0.237
##
## Covariances:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## y0 ~~
## ys (vry0y) 0.893 0.346 2.582 0.010 0.507 0.507
## x0 ~~
## xs (vrx0x) 0.703 0.231 3.036 0.002 0.343 0.343
## y0 ~~
## x0 (vr00) 0.979 0.399 2.456 0.014 0.258 0.258
## ys ~~
## x0 (vrx0y) 0.222 0.206 1.078 0.281 0.115 0.115
## y0 ~~
## xs (vry0x) 0.475 0.489 0.972 0.331 0.254 0.254
## ys ~~
## xs (vrxs) 0.666 0.239 2.782 0.005 0.698 0.698
##
## Intercepts:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## ys (mys) 4.939 1.384 3.568 0.000 5.210 5.210
## y0 (my0) 19.934 0.153 130.588 0.000 10.719 10.719
## y1 0.000 0.000 0.000
## y2 0.000 0.000 0.000
## y3 0.000 0.000 0.000
## y4 0.000 0.000 0.000
## y5 0.000 0.000 0.000
## y6 0.000 0.000 0.000
## dy2 0.000 0.000 0.000
## dy3 0.000 0.000 0.000
## dy4 0.000 0.000 0.000
## dy5 0.000 0.000 0.000
## dy6 0.000 0.000 0.000
## Y7 0.000 0.000 0.000
## Y8 0.000 0.000 0.000
## Y9 0.000 0.000 0.000
## Y10 0.000 0.000 0.000
## Y11 0.000 0.000 0.000
## Y12 0.000 0.000 0.000
## xs (mxs) 5.090 1.657 3.072 0.002 5.059 5.059
## x0 (mx0) 20.193 0.149 135.178 0.000 9.905 9.905
## x1 0.000 0.000 0.000
## x2 0.000 0.000 0.000
## x3 0.000 0.000 0.000
## x4 0.000 0.000 0.000
## x5 0.000 0.000 0.000
## x6 0.000 0.000 0.000
## dx2 0.000 0.000 0.000
## dx3 0.000 0.000 0.000
## dx4 0.000 0.000 0.000
## dx5 0.000 0.000 0.000
## dx6 0.000 0.000 0.000
## X1 0.000 0.000 0.000
## X2 0.000 0.000 0.000
## X3 0.000 0.000 0.000
## X4 0.000 0.000 0.000
## X5 0.000 0.000 0.000
## X6 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err Z-value P(>|z|) Std.lv Std.all
## dy2 0.000 0.000 0.000
## dy3 0.000 0.000 0.000
## dy4 0.000 0.000 0.000
## dy5 0.000 0.000 0.000
## dy6 0.000 0.000 0.000
## y1 0.000 0.000 0.000
## y2 0.000 0.000 0.000
## y3 0.000 0.000 0.000
## y4 0.000 0.000 0.000
## y5 0.000 0.000 0.000
## y6 0.000 0.000 0.000
## y0 (vry0) 3.459 0.630 5.493 0.000 1.000 1.000
## ys (vrys) 0.899 0.374 2.403 0.016 1.000 1.000
## Y7 (vary) 9.674 0.306 31.658 0.000 9.674 0.737
## Y8 (vary) 9.674 0.306 31.658 0.000 9.674 0.667
## Y9 (vary) 9.674 0.306 31.658 0.000 9.674 0.570
## Y10 (vary) 9.674 0.306 31.658 0.000 9.674 0.477
## Y11 (vary) 9.674 0.306 31.658 0.000 9.674 0.395
## Y12 (vary) 9.674 0.306 31.658 0.000 9.674 0.326
## dx2 0.000 0.000 0.000
## dx3 0.000 0.000 0.000
## dx4 0.000 0.000 0.000
## dx5 0.000 0.000 0.000
## dx6 0.000 0.000 0.000
## x1 0.000 0.000 0.000
## x2 0.000 0.000 0.000
## x3 0.000 0.000 0.000
## x4 0.000 0.000 0.000
## x5 0.000 0.000 0.000
## x6 0.000 0.000 0.000
## x0 (vrx0) 4.156 0.532 7.812 0.000 1.000 1.000
## xs (vrxs) 1.012 0.185 5.460 0.000 1.000 1.000
## X1 (varx) 9.088 0.287 31.614 0.000 9.088 0.686
## X2 (varx) 9.088 0.287 31.614 0.000 9.088 0.514
## X3 (varx) 9.088 0.287 31.614 0.000 9.088 0.344
## X4 (varx) 9.088 0.287 31.614 0.000 9.088 0.219
## X5 (varx) 9.088 0.287 31.614 0.000 9.088 0.138
## X6 (varx) 9.088 0.287 31.614 0.000 9.088 0.087