用 lavaan 功能分析
#product term, centered
dta$x1 <- dta$x1-mean( dta$x1)
dta$x2 <- dta$x2-mean( dta$x2)
dta$x3 <- dta$x3-mean( dta$x3)
dta$x4 <- dta$x4-mean( dta$x4)
x1x3 <- dta$x1* dta$x3
x1x4 <- dta$x1* dta$x4
x2x3 <- dta$x2* dta$x3
x2x4 <- dta$x2* dta$x4
dta <- data.frame(dta,x1x3,x1x4,x2x3,x2x4)
#Constrained approach
model1 <-'
f1 =~ 1*x1+a2*x2
f2 =~ 1*x3+a4*x4
f3 =~ 1*x1x3+a4*x1x4+a2*x2x3+a8*x2x4
f4 =~ y1+y2+y3
f4~f1+f2+f3
a8==a2*a4
f1~~c11*f1
f2~~c22*f2
f3~~c33*f3
f1+f2~~0*f3
f1~~c21*f2
c33 == c11*c22 + c21*c21
f1+f2~0*1
f3~c21*1
x1+x2+x3+x4~0*1
x1~~t11*x1
x2~~t22*x2
x3~~t33*x3
x4~~t44*x4
x1x3~~t55*x1x3
x1x4~~t66*x1x4
x2x3~~t77*x2x3
x2x4~~t88*x2x4
x1x3~~t65*x1x4
x2x3~~t75*x1x3
x2x4~~t86*x1x4
x2x3~~t87*x2x4
t55 == c11*t33+c22*t11+t11*t33
t65 ==a4*c22*t11
t66 ==c11*t44+a4^2*c22*t11+t11*t44
t75 ==a2*c11*t33
t77 ==a2^2*c11*t33+c22*t22+t22*t33
t86 ==a2*c11*t44
t87 ==a4*c22*t22
t88 ==a2^2*c11*t44+a4^2*c22*t22+t22*t44'
fit1 <- sem(model1,data=dta)
summary(fit1)
## lavaan 0.6.15 ended normally after 477 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 38
##
## Number of observations 1000
##
## Model Test User Model:
##
## Test statistic 58.460
## Degrees of freedom 52
## P-value (Chi-square) 0.250
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## f1 =~
## x1 1.000
## x2 (a2) 0.843 0.037 22.685 0.000
## f2 =~
## x3 1.000
## x4 (a4) 0.619 0.045 13.799 0.000
## f3 =~
## x1x3 1.000
## x1x4 (a4) 0.619 0.045 13.799 0.000
## x2x3 (a2) 0.843 0.037 22.685 0.000
## x2x4 (a8) 0.522 0.044 11.789 0.000
## f4 =~
## y1 1.000
## y2 0.927 0.071 13.132 0.000
## y3 0.988 0.075 13.207 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## f4 ~
## f1 0.225 0.022 10.287 0.000
## f2 0.151 0.022 6.770 0.000
## f3 0.146 0.020 7.155 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## f1 ~~
## f3 0.000
## f2 ~~
## f3 0.000
## f1 ~~
## f2 (c21) 0.357 0.034 10.504 0.000
## .x1x3 ~~
## .x1x4 (t65) 0.269 0.030 9.029 0.000
## .x2x3 (t75) 0.245 0.064 3.848 0.000
## .x1x4 ~~
## .x2x4 (t86) 0.426 0.029 14.836 0.000
## .x2x3 ~~
## .x2x4 (t87) 0.146 0.021 7.100 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## f1 0.000
## f2 0.000
## f3 (c21) 0.357 0.034 10.504 0.000
## .x1 0.000
## .x2 0.000
## .x3 0.000
## .x4 0.000
## .x1x3 0.029 0.056 0.524 0.601
## .x1x4 0.008 0.044 0.181 0.856
## .x2x3 0.000 0.046 0.005 0.996
## .x2x4 -0.006 0.036 -0.171 0.864
## .y1 0.005 0.024 0.227 0.821
## .y2 -0.024 0.023 -1.040 0.299
## .y3 -0.005 0.024 -0.210 0.834
## .f4 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## f1 (c11) 0.992 0.056 17.749 0.000
## f2 (c22) 1.042 0.083 12.555 0.000
## f3 (c33) 1.161 0.106 10.948 0.000
## .x1 (t11) 0.417 0.045 9.324 0.000
## .x2 (t22) 0.226 0.031 7.241 0.000
## .x3 (t33) 0.292 0.076 3.860 0.000
## .x4 (t44) 0.509 0.033 15.580 0.000
## .x1x3 (t55) 0.846 0.090 9.409 0.000
## .x1x4 (t66) 0.883 0.042 20.962 0.000
## .x2x3 (t77) 0.508 0.063 8.027 0.000
## .x2x4 (t88) 0.565 0.029 19.517 0.000
## .y1 0.361 0.022 16.678 0.000
## .y2 0.350 0.020 17.340 0.000
## .y3 0.385 0.022 17.169 0.000
## .f4 0.104 0.015 6.806 0.000
##
## Constraints:
## |Slack|
## a8 - (a2*a4) 0.000
## c33 - (c11*c22+c21*c21) 0.000
## t55 - (c11*t33+c22*t11+t11*t33) 0.000
## t65 - (a4*c22*t11) 0.000
## t66 - (c11*t44+a4^2*c22*t11+t11*t44) 0.000
## t75 - (a2*c11*t33) 0.000
## t77 - (a2^2*c11*t33+c22*t22+t22*t33) 0.000
## t86 - (a2*c11*t44) 0.000
## t87 - (a4*c22*t22) 0.000
## t88 - (a2^2*c11*t44+a4^2*c22*t22+t22*t44) 0.000
#unconstrained approach
model2 <-'
f1 =~ 1*x1+x2
f2 =~ 1*x3+x4
f3 =~ 1*x1x3+x1x4+x2x3+x2x4
f4 =~ y1+y2+y3
f4~f1+f2+f3
f1~~c21*f2
f1~0*1
f2~0*1
f3~c21*1
x1~0*1
x2~0*1
x3~0*1
x4~0*1
x1x3~~t65*x1x4
x2x3~~t75*x1x3
x2x4~~t86*x1x4
x2x3~~t87*x2x4
'
fit2 <- sem(model2,data=dta)
summary(fit2)
## lavaan 0.6.15 ended normally after 61 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 40
## Number of equality constraints 1
##
## Number of observations 1000
##
## Model Test User Model:
##
## Test statistic 33.673
## Degrees of freedom 38
## P-value (Chi-square) 0.670
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## f1 =~
## x1 1.000
## x2 0.831 0.043 19.259 0.000
## f2 =~
## x3 1.000
## x4 0.619 0.056 10.985 0.000
## f3 =~
## x1x3 1.000
## x1x4 0.635 0.077 8.224 0.000
## x2x3 0.859 0.075 11.430 0.000
## x2x4 0.541 0.082 6.639 0.000
## f4 =~
## y1 1.000
## y2 0.928 0.072 12.888 0.000
## y3 0.990 0.076 12.970 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## f4 ~
## f1 0.222 0.022 10.162 0.000
## f2 0.158 0.024 6.597 0.000
## f3 0.143 0.024 6.058 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## f1 ~~
## f2 (c21) 0.370 0.043 8.507 0.000
## .x1x3 ~~
## .x1x4 (t65) 0.254 0.069 3.671 0.000
## .x2x3 (t75) 0.150 0.122 1.231 0.218
## .x1x4 ~~
## .x2x4 (t86) 0.424 0.054 7.903 0.000
## .x2x3 ~~
## .x2x4 (t87) 0.133 0.050 2.649 0.008
## f1 ~~
## f3 -0.100 0.045 -2.211 0.027
## f2 ~~
## f3 -0.121 0.046 -2.636 0.008
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## f1 0.000
## f2 0.000
## f3 (c21) 0.370 0.043 8.507 0.000
## .x1 0.000
## .x2 0.000
## .x3 0.000
## .x4 0.000
## .x1x3 0.016 0.062 0.260 0.795
## .x1x4 -0.006 0.054 -0.118 0.906
## .x2x3 -0.017 0.059 -0.284 0.776
## .x2x4 -0.020 0.049 -0.414 0.679
## .y1 0.005 0.025 0.187 0.852
## .y2 -0.025 0.024 -1.034 0.301
## .y3 -0.006 0.025 -0.238 0.812
## .f4 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .x1 0.420 0.052 8.044 0.000
## .x2 0.219 0.035 6.244 0.000
## .x3 0.319 0.088 3.637 0.000
## .x4 0.517 0.040 12.816 0.000
## .x1x3 0.788 0.182 4.324 0.000
## .x1x4 0.829 0.079 10.429 0.000
## .x2x3 0.396 0.127 3.111 0.002
## .x2x4 0.577 0.059 9.757 0.000
## .y1 0.362 0.022 16.658 0.000
## .y2 0.350 0.020 17.309 0.000
## .y3 0.384 0.022 17.111 0.000
## f1 1.059 0.080 13.238 0.000
## f2 1.028 0.104 9.849 0.000
## f3 1.231 0.197 6.240 0.000
## .f4 0.104 0.015 6.781 0.000
#Coenders approach
model3 <-'
f1 =~ 1*x1+a2*x2
f2 =~ 1*x3+a4*x4
f3 =~ 1*x1x3+a4*x1x4+a2*x2x3+a8*x2x4
f4 =~ y1+y2+y3
f4~f1+f2+f3
a8==a2*a4
f1~~c11*f1
f2~~c22*f2
f3~~c33*f3
f1+f2~~0*f3
f1~~c21*f2
f1+f2~0*1
f3~c21*1
x1+x2+x3+x4~0*1
x1x3~~t65*x1x4
x2x3~~t75*x1x3
x2x4~~t86*x1x4
x2x3~~t87*x2x4
'
fit3 <- sem(model3,data=dta)
summary(fit3)
## lavaan 0.6.15 ended normally after 181 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 38
##
## Number of observations 1000
##
## Model Test User Model:
##
## Test statistic 43.006
## Degrees of freedom 43
## P-value (Chi-square) 0.471
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## f1 =~
## x1 1.000
## x2 (a2) 0.831 0.038 22.082 0.000
## f2 =~
## x3 1.000
## x4 (a4) 0.611 0.046 13.259 0.000
## f3 =~
## x1x3 1.000
## x1x4 (a4) 0.611 0.046 13.259 0.000
## x2x3 (a2) 0.831 0.038 22.082 0.000
## x2x4 (a8) 0.507 0.045 11.309 0.000
## f4 =~
## y1 1.000
## y2 0.929 0.070 13.260 0.000
## y3 0.990 0.074 13.336 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## f4 ~
## f1 0.220 0.021 10.324 0.000
## f2 0.152 0.023 6.748 0.000
## f3 0.132 0.019 6.840 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## f1 ~~
## f3 0.000
## f2 ~~
## f3 0.000
## f1 ~~
## f2 (c21) 0.371 0.043 8.610 0.000
## .x1x3 ~~
## .x1x4 (t65) 0.230 0.046 5.051 0.000
## .x2x3 (t75) 0.112 0.089 1.262 0.207
## .x1x4 ~~
## .x2x4 (t86) 0.439 0.040 10.877 0.000
## .x2x3 ~~
## .x2x4 (t87) 0.149 0.031 4.792 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## f1 0.000
## f2 0.000
## f3 (c21) 0.371 0.043 8.610 0.000
## .x1 0.000
## .x2 0.000
## .x3 0.000
## .x4 0.000
## .x1x3 0.015 0.062 0.243 0.808
## .x1x4 0.002 0.047 0.044 0.965
## .x2x3 -0.007 0.051 -0.139 0.889
## .x2x4 -0.008 0.039 -0.210 0.834
## .y1 0.009 0.024 0.356 0.722
## .y2 -0.021 0.023 -0.910 0.363
## .y3 -0.002 0.024 -0.085 0.932
## .f4 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## f1 (c11) 1.059 0.075 14.126 0.000
## f2 (c22) 1.041 0.095 10.982 0.000
## f3 (c33) 1.320 0.142 9.323 0.000
## .x1 0.420 0.048 8.686 0.000
## .x2 0.219 0.032 6.787 0.000
## .x3 0.305 0.078 3.907 0.000
## .x4 0.522 0.037 14.119 0.000
## .x1x3 0.699 0.130 5.401 0.000
## .x1x4 0.833 0.059 14.084 0.000
## .x2x3 0.394 0.087 4.524 0.000
## .x2x4 0.598 0.042 14.263 0.000
## .y1 0.362 0.022 16.728 0.000
## .y2 0.350 0.020 17.358 0.000
## .y3 0.385 0.022 17.186 0.000
## .f4 0.106 0.015 6.915 0.000
##
## Constraints:
## |Slack|
## a8 - (a2*a4) 0.000
#畫圖看模型與估計值
lavaanPlot::lavaanPlot(model = fit1,
edge_options = list(color = "grey"))
#畫圖
dtafactor <- lavPredict(fit1)
m1 <- lm(f4 ~ f1+f2+f1:f2, data = dtafactor)
interactions::interact_plot(m1, pred = f1, modx = f2, interval = TRUE,
int.type = "confidence", int.width = .8)
