library(lavaan)## Warning: 程辑包'lavaan'是用R版本4.3.1 来建造的## This is lavaan 0.6-15
## lavaan is FREE software! Please report any bugs.View(HolzingerSwineford1939)
#结构对应的代码放在引号中，每行末尾回车
HS.model <- '
visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
'
#cfa函数进行验证性因素分析，要指定模型和数据
fit <- cfa(HS.model, data = HolzingerSwineford1939)
#输出结果
summary(fit, fit.measures = TRUE, standardized = TRUE, modindices=TRUE)## lavaan 0.6.15 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Number of observations 301
##
## Model Test User Model:
##
## Test statistic 85.306
## Degrees of freedom 24
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 918.852
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.931
## Tucker-Lewis Index (TLI) 0.896
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3737.745
## Loglikelihood unrestricted model (H1) -3695.092
##
## Akaike (AIC) 7517.490
## Bayesian (BIC) 7595.339
## Sample-size adjusted Bayesian (SABIC) 7528.739
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.092
## 90 Percent confidence interval - lower 0.071
## 90 Percent confidence interval - upper 0.114
## P-value H_0: RMSEA <= 0.050 0.001
## P-value H_0: RMSEA >= 0.080 0.840
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.065
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## visual =~
## x1 1.000 0.900 0.772
## x2 0.554 0.100 5.554 0.000 0.498 0.424
## x3 0.729 0.109 6.685 0.000 0.656 0.581
## textual =~
## x4 1.000 0.990 0.852
## x5 1.113 0.065 17.014 0.000 1.102 0.855
## x6 0.926 0.055 16.703 0.000 0.917 0.838
## speed =~
## x7 1.000 0.619 0.570
## x8 1.180 0.165 7.152 0.000 0.731 0.723
## x9 1.082 0.151 7.155 0.000 0.670 0.665
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## visual ~~
## textual 0.408 0.074 5.552 0.000 0.459 0.459
## speed 0.262 0.056 4.660 0.000 0.471 0.471
## textual ~~
## speed 0.173 0.049 3.518 0.000 0.283 0.283
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x1 0.549 0.114 4.833 0.000 0.549 0.404
## .x2 1.134 0.102 11.146 0.000 1.134 0.821
## .x3 0.844 0.091 9.317 0.000 0.844 0.662
## .x4 0.371 0.048 7.779 0.000 0.371 0.275
## .x5 0.446 0.058 7.642 0.000 0.446 0.269
## .x6 0.356 0.043 8.277 0.000 0.356 0.298
## .x7 0.799 0.081 9.823 0.000 0.799 0.676
## .x8 0.488 0.074 6.573 0.000 0.488 0.477
## .x9 0.566 0.071 8.003 0.000 0.566 0.558
## visual 0.809 0.145 5.564 0.000 1.000 1.000
## textual 0.979 0.112 8.737 0.000 1.000 1.000
## speed 0.384 0.086 4.451 0.000 1.000 1.000
##
## Modification Indices:
##
## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 visual =~ x4 1.211 0.077 0.069 0.059 0.059
## 2 visual =~ x5 7.441 -0.210 -0.189 -0.147 -0.147
## 3 visual =~ x6 2.843 0.111 0.100 0.092 0.092
## 4 visual =~ x7 18.631 -0.422 -0.380 -0.349 -0.349
## 5 visual =~ x8 4.295 -0.210 -0.189 -0.187 -0.187
## 6 visual =~ x9 36.411 0.577 0.519 0.515 0.515
## 7 textual =~ x1 8.903 0.350 0.347 0.297 0.297
## 8 textual =~ x2 0.017 -0.011 -0.011 -0.010 -0.010
## 9 textual =~ x3 9.151 -0.272 -0.269 -0.238 -0.238
## 10 textual =~ x7 0.098 -0.021 -0.021 -0.019 -0.019
## 11 textual =~ x8 3.359 -0.121 -0.120 -0.118 -0.118
## 12 textual =~ x9 4.796 0.138 0.137 0.136 0.136
## 13 speed =~ x1 0.014 0.024 0.015 0.013 0.013
## 14 speed =~ x2 1.580 -0.198 -0.123 -0.105 -0.105
## 15 speed =~ x3 0.716 0.136 0.084 0.075 0.075
## 16 speed =~ x4 0.003 -0.005 -0.003 -0.003 -0.003
## 17 speed =~ x5 0.201 -0.044 -0.027 -0.021 -0.021
## 18 speed =~ x6 0.273 0.044 0.027 0.025 0.025
## 19 x1 ~~ x2 3.606 -0.184 -0.184 -0.233 -0.233
## 20 x1 ~~ x3 0.935 -0.139 -0.139 -0.203 -0.203
## 21 x1 ~~ x4 3.554 0.078 0.078 0.173 0.173
## 22 x1 ~~ x5 0.522 -0.033 -0.033 -0.067 -0.067
## 23 x1 ~~ x6 0.048 0.009 0.009 0.020 0.020
## 24 x1 ~~ x7 5.420 -0.129 -0.129 -0.195 -0.195
## 25 x1 ~~ x8 0.634 -0.041 -0.041 -0.079 -0.079
## 26 x1 ~~ x9 7.335 0.138 0.138 0.247 0.247
## 27 x2 ~~ x3 8.532 0.218 0.218 0.223 0.223
## 28 x2 ~~ x4 0.534 -0.034 -0.034 -0.052 -0.052
## 29 x2 ~~ x5 0.023 -0.008 -0.008 -0.011 -0.011
## 30 x2 ~~ x6 0.785 0.039 0.039 0.062 0.062
## 31 x2 ~~ x7 8.918 -0.183 -0.183 -0.192 -0.192
## 32 x2 ~~ x8 0.054 -0.012 -0.012 -0.017 -0.017
## 33 x2 ~~ x9 1.895 0.075 0.075 0.094 0.094
## 34 x3 ~~ x4 0.142 -0.016 -0.016 -0.028 -0.028
## 35 x3 ~~ x5 7.858 -0.130 -0.130 -0.212 -0.212
## 36 x3 ~~ x6 1.855 0.055 0.055 0.100 0.100
## 37 x3 ~~ x7 0.638 -0.044 -0.044 -0.054 -0.054
## 38 x3 ~~ x8 0.059 -0.012 -0.012 -0.019 -0.019
## 39 x3 ~~ x9 4.126 0.102 0.102 0.147 0.147
## 40 x4 ~~ x5 2.534 0.186 0.186 0.457 0.457
## 41 x4 ~~ x6 6.220 -0.235 -0.235 -0.646 -0.646
## 42 x4 ~~ x7 5.920 0.098 0.098 0.180 0.180
## 43 x4 ~~ x8 3.805 -0.069 -0.069 -0.162 -0.162
## 44 x4 ~~ x9 0.196 -0.016 -0.016 -0.035 -0.035
## 45 x5 ~~ x6 0.916 0.101 0.101 0.253 0.253
## 46 x5 ~~ x7 1.233 -0.049 -0.049 -0.083 -0.083
## 47 x5 ~~ x8 0.347 0.023 0.023 0.049 0.049
## 48 x5 ~~ x9 0.999 0.040 0.040 0.079 0.079
## 49 x6 ~~ x7 0.259 -0.020 -0.020 -0.037 -0.037
## 50 x6 ~~ x8 0.275 0.018 0.018 0.043 0.043
## 51 x6 ~~ x9 0.097 -0.011 -0.011 -0.024 -0.024
## 52 x7 ~~ x8 34.145 0.536 0.536 0.859 0.859
## 53 x7 ~~ x9 5.183 -0.187 -0.187 -0.278 -0.278
## 54 x8 ~~ x9 14.946 -0.423 -0.423 -0.805 -0.805#fit.measures = TRUE,输出拟合指数
#standardized = TRUE,输出标准化系数
#modindices=TRUE，输出修正指数HS.model <- '
visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
'
fit1 <- cfa(HS.model, group='sex',data = HolzingerSwineford1939)
fit2 <- cfa(HS.model, group='sex',data = HolzingerSwineford1939, group.equal = "loadings")
fit3 <- cfa(HS.model, group='sex',data = HolzingerSwineford1939, group.equal = c("intercepts", "loadings"))
fit4<- cfa(HS.model, group='sex',data = HolzingerSwineford1939, group.equal = c("intercepts","loadings" ,"residuals"))
# group.equal指定两组样本之间哪些参数等值
lavTestLRT(fit1, fit2, fit3,fit4)##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 54 7526.1 7726.2 126.23 20.431 0.126416 6 0.002320 **
## fit3 60 7532.8 7710.8 145.00 18.771 0.118926 6 0.004567 **
## fit4 69 7537.0 7681.5 167.11 22.115 0.098401 9 0.008521 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# 上述分析表明，男女样本只有结构等值，没有因子负荷等值，接下来寻找原因，究竟哪个因子不相等呢？
HS.model <- '
visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
'
# 结构等值模型
fit1 <- cfa(HS.model, group='sex',data = HolzingerSwineford1939)
# 限定某些因子相等/不相等，以确定哪些模型与结构等值模型没有显著差异
HS1.model <- '
visual =~ c(a1, a2)*x1 + b*x2 + c*x3
textual =~ d*x4 + e*x5 + f*x6
speed =~ g*x7 + h*x8 + i*x9
'
# 相等的因子负荷，使用一个字母即可；不相等的因子负荷，使用c(a1,a2)类的向量
# 受限制的因子负荷等值模型
fit2 <- cfa(HS1.model, group='sex',data = HolzingerSwineford1939)## Warning in lavaanify(model = FLAT, constraints = constraints, varTable = DataOV, : lavaan WARNING: using a single label per parameter in a multiple group
## setting implies imposing equality constraints across all the groups;
## If this is not intended, either remove the label(s), or use a vector
## of labels (one for each group);
## See the Multiple groups section in the man page of model.syntax.#检验模型1和2是否有差异，如果没有，说明新增加的限定模型2与结构等值模型1效果相同，因为1和2的差异只有a1和a2不相等，其他都相等。
lavTestLRT(fit1, fit2)##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 54 7526.1 7726.2 126.23 20.431 0.12642 6 0.00232 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# 依次检验b、c、d、e、f、g、h和i是否相等，最终找出不相等的因子负荷。
# 也有人建议采用如下方式，更方便地操作代码
HS1.model <- '
visual =~ c(a1,a2)*x1 + c(b,b)*x2 + c(c,c)*x3
textual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6
speed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9
'
HS2.model <- '
visual =~ c(a,a)*x1 + c(b1,b2)*x2 + c(c,c)*x3
textual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6
speed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9
'
HS3.model <- '
visual =~ c(a,a)*x1 + c(b,b)*x2 + c(c1,c2)*x3
textual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6
speed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9
'
HS4.model <- '
visual =~ c(a,a)*x1 + c(b,b)*x2 + c(c,c)*x3
textual =~ c(d1,d2)*x4 + c(e,e)*x5 + c(f,f)*x6
speed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9
'
HS5.model <- '
visual =~ c(a1,a2)*x1 + c(b,b)*x2 + c(c,c)*x3
textual =~ c(d,d)*x4 + c(e1,e1)*x5 + c(f,f)*x6
speed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9
'
HS6.model <- '
visual =~ c(a,a)*x1 + c(b,b)*x2 + c(c,c)*x3
textual =~ c(d,d)*x4 + c(e,e)*x5 + c(f1,f2)*x6
speed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9
'
HS7.model <- '
visual =~ c(a,a)*x1 + c(b,b)*x2 + c(c,c)*x3
textual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6
speed =~ c(g1,g2)*x7 + c(h,h)*x8 + c(i,i)*x9
'
HS8.model <- '
visual =~ c(a,a)*x1 + c(b,b)*x2 + c(c,c)*x3
textual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6
speed =~ c(g,g)*x7 + c(h1,h2)*x8 + c(i,i)*x9
'
HS9.model <- '
visual =~ c(a,a)*x1 + c(b,b)*x2 + c(c,c)*x3
textual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6
speed =~ c(g,g)*x7 + c(h,h)*x8 + c(i1,i2)*x9
'
HS<-c(HS1.model,HS2.model,HS3.model,HS4.model,HS5.model,HS6.model,HS7.model,HS8.model,HS9.model)
# 避免重复工作，可以使用循环
for(i in HS){
print(i)
fit2 <- cfa(i, group='sex',data = HolzingerSwineford1939)
print(lavTestLRT(fit1, fit2))
}## [1] "\nvisual =~ c(a1,a2)*x1 + c(b,b)*x2 + c(c,c)*x3\ntextual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6\nspeed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9\n"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 54 7526.1 7726.2 126.23 20.431 0.12642 6 0.00232 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "\nvisual =~ c(a,a)*x1 + c(b1,b2)*x2 + c(c,c)*x3\ntextual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6\nspeed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9\n"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 53 7527.0 7730.9 125.16 19.361 0.13815 5 0.001646 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "\nvisual =~ c(a,a)*x1 + c(b,b)*x2 + c(c1,c2)*x3\ntextual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6\nspeed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9\n"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 53 7525.0 7728.9 123.21 17.417 0.12846 5 0.003773 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "\nvisual =~ c(a,a)*x1 + c(b,b)*x2 + c(c,c)*x3\ntextual =~ c(d1,d2)*x4 + c(e,e)*x5 + c(f,f)*x6\nspeed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9\n"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 54 7526.1 7726.2 126.23 20.431 0.12642 6 0.00232 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "\nvisual =~ c(a1,a2)*x1 + c(b,b)*x2 + c(c,c)*x3\ntextual =~ c(d,d)*x4 + c(e1,e1)*x5 + c(f,f)*x6\nspeed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9\n"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 54 7526.1 7726.2 126.23 20.431 0.12642 6 0.00232 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "\nvisual =~ c(a,a)*x1 + c(b,b)*x2 + c(c,c)*x3\ntextual =~ c(d,d)*x4 + c(e,e)*x5 + c(f1,f2)*x6\nspeed =~ c(g,g)*x7 + c(h,h)*x8 + c(i,i)*x9\n"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.8
## fit2 53 7527.9 7731.8 126.1 20.306 0.14262 5 0.001095 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "\nvisual =~ c(a,a)*x1 + c(b,b)*x2 + c(c,c)*x3\ntextual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6\nspeed =~ c(g1,g2)*x7 + c(h,h)*x8 + c(i,i)*x9\n"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 54 7526.1 7726.2 126.23 20.431 0.12642 6 0.00232 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "\nvisual =~ c(a,a)*x1 + c(b,b)*x2 + c(c,c)*x3\ntextual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6\nspeed =~ c(g,g)*x7 + c(h1,h2)*x8 + c(i,i)*x9\n"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 53 7519.6 7723.5 117.79 11.999 0.096443 5 0.0348 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "\nvisual =~ c(a,a)*x1 + c(b,b)*x2 + c(c,c)*x3\ntextual =~ c(d,d)*x4 + c(e,e)*x5 + c(f,f)*x6\nspeed =~ c(g,g)*x7 + c(h,h)*x8 + c(i1,i2)*x9\n"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 53 7512.0 7715.9 110.12 4.3273 0 5 0.5033# 结果表明，当限定了x9系数不相等时，模型与结构等值模型没有差异。说明，男女生的x9在speed的负荷有显著差异，可以进一步讨论此题在放映因子时的男女生差异
#也可以采用group.partial逐一排除
HS.model <- '
visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
'
# 因子负荷相等，但是排除x1在visual上的因子负荷
fit2 <- cfa(HS.model, group='sex',data = HolzingerSwineford1939,group.equal = "loadings", group.partial="visual=~x1")
# 为了避免代码重复，可以建立一个向量，每次排除一个，然后循环执行
excluded<-c('visual=~x1','visual=~x2','visual=~x3','textual=~x4','textual=~x5','textual=~x6','speed=~x7','speed=~x8','speed=~x9')
for (i in excluded){
print(paste('排除',i))
fit1 <- cfa(HS.model, group='sex',data = HolzingerSwineford1939)
fit2<- cfa(HS.model, group='sex',data = HolzingerSwineford1939,group.equal = "loadings", group.partial=i)
print(lavTestLRT(fit1, fit2))
}## [1] "排除 visual=~x1"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 54 7526.1 7726.2 126.23 20.431 0.12642 6 0.00232 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "排除 visual=~x2"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 53 7527.0 7730.9 125.16 19.361 0.13815 5 0.001646 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "排除 visual=~x3"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 53 7525.0 7728.9 123.21 17.417 0.12846 5 0.003773 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "排除 textual=~x4"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 54 7526.1 7726.2 126.23 20.431 0.12642 6 0.00232 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "排除 textual=~x5"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 53 7527.5 7731.4 125.67 19.878 0.14061 5 0.001317 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "排除 textual=~x6"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.8
## fit2 53 7527.9 7731.8 126.1 20.306 0.14262 5 0.001095 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "排除 speed=~x7"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 54 7526.1 7726.2 126.23 20.431 0.12642 6 0.00232 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "排除 speed=~x8"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 53 7519.6 7723.5 117.79 11.999 0.096443 5 0.0348 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "排除 speed=~x9"
##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit1 48 7517.6 7740.1 105.80
## fit2 53 7512.0 7715.9 110.12 4.3273 0 5 0.5033model <- '
# measurement model
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8
# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
'
fit <- sem(model, data = PoliticalDemocracy)
summary(fit, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6.15 ended normally after 42 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 25
##
## Number of observations 75
##
## Model Test User Model:
##
## Test statistic 72.462
## Degrees of freedom 41
## P-value (Chi-square) 0.002
##
## Model Test Baseline Model:
##
## Test statistic 730.654
## Degrees of freedom 55
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.953
## Tucker-Lewis Index (TLI) 0.938
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1564.959
## Loglikelihood unrestricted model (H1) -1528.728
##
## Akaike (AIC) 3179.918
## Bayesian (BIC) 3237.855
## Sample-size adjusted Bayesian (SABIC) 3159.062
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.101
## 90 Percent confidence interval - lower 0.061
## 90 Percent confidence interval - upper 0.139
## P-value H_0: RMSEA <= 0.050 0.021
## P-value H_0: RMSEA >= 0.080 0.827
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.055
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ind60 =~
## x1 1.000 0.669 0.920
## x2 2.182 0.139 15.714 0.000 1.461 0.973
## x3 1.819 0.152 11.956 0.000 1.218 0.872
## dem60 =~
## y1 1.000 2.201 0.845
## y2 1.354 0.175 7.755 0.000 2.980 0.760
## y3 1.044 0.150 6.961 0.000 2.298 0.705
## y4 1.300 0.138 9.412 0.000 2.860 0.860
## dem65 =~
## y5 1.000 2.084 0.803
## y6 1.258 0.164 7.651 0.000 2.623 0.783
## y7 1.282 0.158 8.137 0.000 2.673 0.819
## y8 1.310 0.154 8.529 0.000 2.730 0.847
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dem60 ~
## ind60 1.474 0.392 3.763 0.000 0.448 0.448
## dem65 ~
## ind60 0.453 0.220 2.064 0.039 0.146 0.146
## dem60 0.864 0.113 7.671 0.000 0.913 0.913
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x1 0.082 0.020 4.180 0.000 0.082 0.154
## .x2 0.118 0.070 1.689 0.091 0.118 0.053
## .x3 0.467 0.090 5.174 0.000 0.467 0.240
## .y1 1.942 0.395 4.910 0.000 1.942 0.286
## .y2 6.490 1.185 5.479 0.000 6.490 0.422
## .y3 5.340 0.943 5.662 0.000 5.340 0.503
## .y4 2.887 0.610 4.731 0.000 2.887 0.261
## .y5 2.390 0.447 5.351 0.000 2.390 0.355
## .y6 4.343 0.796 5.456 0.000 4.343 0.387
## .y7 3.510 0.668 5.252 0.000 3.510 0.329
## .y8 2.940 0.586 5.019 0.000 2.940 0.283
## ind60 0.448 0.087 5.169 0.000 1.000 1.000
## .dem60 3.872 0.893 4.338 0.000 0.799 0.799
## .dem65 0.115 0.200 0.575 0.565 0.026 0.026# 查看修正指数
modindices(fit, minimum.value = 3.84, sort = TRUE)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 88 y2 ~~ y6 9.279 2.129 2.129 0.401 0.401
## 104 y6 ~~ y8 8.668 1.513 1.513 0.423 0.423
## 81 y1 ~~ y5 8.183 0.884 0.884 0.410 0.410
## 93 y3 ~~ y6 6.574 -1.590 -1.590 -0.330 -0.330
## 79 y1 ~~ y3 5.204 1.024 1.024 0.318 0.318
## 86 y2 ~~ y4 4.911 1.432 1.432 0.331 0.331
## 94 y3 ~~ y7 4.088 1.152 1.152 0.266 0.266
## 33 ind60 =~ y5 4.007 0.762 0.510 0.197 0.197# y1、y2、y3、y4分别与y5、y6、y7、y8重合，因此反映了共同成分，需要增加残差相关
model_r <- '
# measurement model
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8
# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
#residuals
y1~~y5
y2~~y6
y3~~y7
y4~~y8
'
fit_r <- sem(model_r, data = PoliticalDemocracy)
summary(fit_r, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6.15 ended normally after 58 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 29
##
## Number of observations 75
##
## Model Test User Model:
##
## Test statistic 50.835
## Degrees of freedom 37
## P-value (Chi-square) 0.064
##
## Model Test Baseline Model:
##
## Test statistic 730.654
## Degrees of freedom 55
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.980
## Tucker-Lewis Index (TLI) 0.970
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1554.146
## Loglikelihood unrestricted model (H1) -1528.728
##
## Akaike (AIC) 3166.292
## Bayesian (BIC) 3233.499
## Sample-size adjusted Bayesian (SABIC) 3142.099
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.071
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.115
## P-value H_0: RMSEA <= 0.050 0.234
## P-value H_0: RMSEA >= 0.080 0.396
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.050
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ind60 =~
## x1 1.000 0.670 0.920
## x2 2.181 0.139 15.720 0.000 1.460 0.973
## x3 1.819 0.152 11.966 0.000 1.218 0.872
## dem60 =~
## y1 1.000 2.145 0.824
## y2 1.388 0.188 7.401 0.000 2.977 0.760
## y3 1.053 0.161 6.552 0.000 2.259 0.694
## y4 1.368 0.153 8.928 0.000 2.933 0.881
## dem65 =~
## y5 1.000 2.014 0.777
## y6 1.317 0.180 7.314 0.000 2.654 0.790
## y7 1.326 0.174 7.618 0.000 2.672 0.817
## y8 1.391 0.171 8.118 0.000 2.803 0.870
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dem60 ~
## ind60 1.435 0.385 3.728 0.000 0.448 0.448
## dem65 ~
## ind60 0.507 0.209 2.425 0.015 0.168 0.168
## dem60 0.816 0.100 8.156 0.000 0.869 0.869
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .y1 ~~
## .y5 0.892 0.366 2.433 0.015 0.892 0.370
## .y2 ~~
## .y6 1.893 0.762 2.486 0.013 1.893 0.361
## .y3 ~~
## .y7 1.268 0.623 2.035 0.042 1.268 0.287
## .y4 ~~
## .y8 0.141 0.464 0.303 0.762 0.141 0.056
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x1 0.082 0.020 4.177 0.000 0.082 0.154
## .x2 0.120 0.070 1.708 0.088 0.120 0.053
## .x3 0.467 0.090 5.172 0.000 0.467 0.239
## .y1 2.181 0.456 4.779 0.000 2.181 0.322
## .y2 6.490 1.231 5.271 0.000 6.490 0.423
## .y3 5.490 0.991 5.538 0.000 5.490 0.518
## .y4 2.470 0.660 3.741 0.000 2.470 0.223
## .y5 2.662 0.506 5.260 0.000 2.662 0.396
## .y6 4.249 0.817 5.201 0.000 4.249 0.376
## .y7 3.560 0.712 4.999 0.000 3.560 0.333
## .y8 2.531 0.609 4.159 0.000 2.531 0.244
## ind60 0.448 0.087 5.171 0.000 1.000 1.000
## .dem60 3.678 0.885 4.154 0.000 0.799 0.799
## .dem65 0.350 0.187 1.865 0.062 0.086 0.086model_r <- '
# measurement model
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8
# regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
#residuals
y1~~y5
y2~~y6
y3~~y7
y4~~y8
'
fit_r <- sem(model_r, data = PoliticalDemocracy)
summary(fit_r, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6.15 ended normally after 58 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 29
##
## Number of observations 75
##
## Model Test User Model:
##
## Test statistic 50.835
## Degrees of freedom 37
## P-value (Chi-square) 0.064
##
## Model Test Baseline Model:
##
## Test statistic 730.654
## Degrees of freedom 55
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.980
## Tucker-Lewis Index (TLI) 0.970
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1554.146
## Loglikelihood unrestricted model (H1) -1528.728
##
## Akaike (AIC) 3166.292
## Bayesian (BIC) 3233.499
## Sample-size adjusted Bayesian (SABIC) 3142.099
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.071
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.115
## P-value H_0: RMSEA <= 0.050 0.234
## P-value H_0: RMSEA >= 0.080 0.396
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.050
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ind60 =~
## x1 1.000 0.670 0.920
## x2 2.181 0.139 15.720 0.000 1.460 0.973
## x3 1.819 0.152 11.966 0.000 1.218 0.872
## dem60 =~
## y1 1.000 2.145 0.824
## y2 1.388 0.188 7.401 0.000 2.977 0.760
## y3 1.053 0.161 6.552 0.000 2.259 0.694
## y4 1.368 0.153 8.928 0.000 2.933 0.881
## dem65 =~
## y5 1.000 2.014 0.777
## y6 1.317 0.180 7.314 0.000 2.654 0.790
## y7 1.326 0.174 7.618 0.000 2.672 0.817
## y8 1.391 0.171 8.118 0.000 2.803 0.870
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dem60 ~
## ind60 1.435 0.385 3.728 0.000 0.448 0.448
## dem65 ~
## ind60 0.507 0.209 2.425 0.015 0.168 0.168
## dem60 0.816 0.100 8.156 0.000 0.869 0.869
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .y1 ~~
## .y5 0.892 0.366 2.433 0.015 0.892 0.370
## .y2 ~~
## .y6 1.893 0.762 2.486 0.013 1.893 0.361
## .y3 ~~
## .y7 1.268 0.623 2.035 0.042 1.268 0.287
## .y4 ~~
## .y8 0.141 0.464 0.303 0.762 0.141 0.056
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x1 0.082 0.020 4.177 0.000 0.082 0.154
## .x2 0.120 0.070 1.708 0.088 0.120 0.053
## .x3 0.467 0.090 5.172 0.000 0.467 0.239
## .y1 2.181 0.456 4.779 0.000 2.181 0.322
## .y2 6.490 1.231 5.271 0.000 6.490 0.423
## .y3 5.490 0.991 5.538 0.000 5.490 0.518
## .y4 2.470 0.660 3.741 0.000 2.470 0.223
## .y5 2.662 0.506 5.260 0.000 2.662 0.396
## .y6 4.249 0.817 5.201 0.000 4.249 0.376
## .y7 3.560 0.712 4.999 0.000 3.560 0.333
## .y8 2.531 0.609 4.159 0.000 2.531 0.244
## ind60 0.448 0.087 5.171 0.000 1.000 1.000
## .dem60 3.678 0.885 4.154 0.000 0.799 0.799
## .dem65 0.350 0.187 1.865 0.062 0.086 0.086library(lavaanPlot)## Warning: 程辑包'lavaanPlot'是用R版本4.3.2 来建造的lavaanPlot(model = fit_r,coefs = TRUE, stand = TRUE,stars = c('regress','latent','covs','residual'))# 线性
model <- ' i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4
s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4 '
fit <- growth(model, data=Demo.growth)
summary(fit,fit.measures = TRUE, standardized = TRUE)## lavaan 0.6.15 ended normally after 29 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 9
##
## Number of observations 400
##
## Model Test User Model:
##
## Test statistic 8.069
## Degrees of freedom 5
## P-value (Chi-square) 0.152
##
## Model Test Baseline Model:
##
## Test statistic 1780.035
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.998
## Tucker-Lewis Index (TLI) 0.998
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2755.052
## Loglikelihood unrestricted model (H1) -2751.018
##
## Akaike (AIC) 5528.104
## Bayesian (BIC) 5564.027
## Sample-size adjusted Bayesian (SABIC) 5535.470
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.039
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.087
## P-value H_0: RMSEA <= 0.050 0.580
## P-value H_0: RMSEA >= 0.080 0.085
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.012
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i =~
## t1 1.000 1.390 0.874
## t2 1.000 1.390 0.660
## t3 1.000 1.390 0.511
## t4 1.000 1.390 0.411
## s =~
## t1 0.000 0.000 0.000
## t2 1.000 0.766 0.364
## t3 2.000 1.532 0.564
## t4 3.000 2.298 0.680
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i ~~
## s 0.618 0.071 8.686 0.000 0.580 0.580
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .t1 0.000 0.000 0.000
## .t2 0.000 0.000 0.000
## .t3 0.000 0.000 0.000
## .t4 0.000 0.000 0.000
## i 0.615 0.077 8.007 0.000 0.442 0.442
## s 1.006 0.042 24.076 0.000 1.314 1.314
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .t1 0.595 0.086 6.944 0.000 0.595 0.236
## .t2 0.676 0.061 11.061 0.000 0.676 0.153
## .t3 0.635 0.072 8.761 0.000 0.635 0.086
## .t4 0.508 0.124 4.090 0.000 0.508 0.044
## i 1.932 0.173 11.194 0.000 1.000 1.000
## s 0.587 0.052 11.336 0.000 1.000 1.000# 二次曲线
model <- ' i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4
s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4
q =~ 0*t1 + 1*t2 + 4*t3 + 9*t4 '
fit <- growth(model, data=Demo.growth)
summary(fit)## lavaan 0.6.15 ended normally after 79 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 13
##
## Number of observations 400
##
## Model Test User Model:
##
## Test statistic 2.717
## Degrees of freedom 1
## P-value (Chi-square) 0.099
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## i =~
## t1 1.000
## t2 1.000
## t3 1.000
## t4 1.000
## s =~
## t1 0.000
## t2 1.000
## t3 2.000
## t4 3.000
## q =~
## t1 0.000
## t2 1.000
## t3 4.000
## t4 9.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## i ~~
## s 0.217 0.312 0.696 0.486
## q 0.095 0.075 1.265 0.206
## s ~~
## q -0.155 0.066 -2.341 0.019
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .t1 0.000
## .t2 0.000
## .t3 0.000
## .t4 0.000
## i 0.600 0.079 7.606 0.000
## s 1.032 0.075 13.773 0.000
## q -0.008 0.020 -0.378 0.705
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .t1 0.226 0.273 0.827 0.408
## .t2 0.687 0.127 5.407 0.000
## .t3 0.560 0.159 3.516 0.000
## .t4 0.495 0.583 0.849 0.396
## i 2.268 0.316 7.171 0.000
## s 1.201 0.313 3.837 0.000
## q 0.039 0.028 1.387 0.166dat <- read.table("D:/Desktop/RICLPM.dat",
col.names = c(
"x1", "x2", "x3", "x4", "x5",
"y1", "y2", "y3", "y4", "y5")
)
# 传统的交叉滞后模型
CLPM<-'
#回归路径
x2+y2~x1+y1
x3+y3~x2+y2
x4+y4~x3+y3
x5+y5~x4+y4
#相关
x1~~y1
x2~~y2
x3~~y3
x4~~y4
x5~~y5'
CLPM.fit <- sem(CLPM,
data = dat)
summary(CLPM.fit, fit.measures = T,standardized = T)## lavaan 0.6.15 ended normally after 46 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 31
##
## Number of observations 1189
##
## Model Test User Model:
##
## Test statistic 202.225
## Degrees of freedom 24
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 3166.400
## Degrees of freedom 45
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.943
## Tucker-Lewis Index (TLI) 0.893
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) 443.540
## Loglikelihood unrestricted model (H1) 544.652
##
## Akaike (AIC) -825.080
## Bayesian (BIC) -667.573
## Sample-size adjusted Bayesian (SABIC) -766.041
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.079
## 90 Percent confidence interval - lower 0.069
## 90 Percent confidence interval - upper 0.089
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.451
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.074
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## x2 ~
## x1 0.321 0.023 13.743 0.000 0.321 0.392
## y1 0.061 0.019 3.269 0.001 0.061 0.093
## y2 ~
## x1 0.151 0.038 3.965 0.000 0.151 0.117
## y1 0.325 0.030 10.684 0.000 0.325 0.314
## x3 ~
## x2 0.388 0.028 13.991 0.000 0.388 0.389
## y2 0.055 0.017 3.135 0.002 0.055 0.087
## y3 ~
## x2 0.200 0.043 4.605 0.000 0.200 0.122
## y2 0.466 0.027 17.015 0.000 0.466 0.451
## x4 ~
## x3 0.414 0.029 14.368 0.000 0.414 0.403
## y3 0.047 0.018 2.666 0.008 0.047 0.075
## y4 ~
## x3 0.197 0.044 4.438 0.000 0.197 0.118
## y3 0.481 0.027 17.746 0.000 0.481 0.470
## x5 ~
## x4 0.423 0.028 15.120 0.000 0.423 0.425
## y4 0.025 0.017 1.450 0.147 0.025 0.041
## y5 ~
## x4 0.153 0.040 3.795 0.000 0.153 0.096
## y4 0.537 0.025 21.691 0.000 0.537 0.549
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## x1 ~~
## y1 0.031 0.002 13.022 0.000 0.031 0.408
## .x2 ~~
## .y2 0.013 0.002 8.128 0.000 0.013 0.243
## .x3 ~~
## .y3 0.014 0.002 9.163 0.000 0.014 0.276
## .x4 ~~
## .y4 0.016 0.002 9.802 0.000 0.016 0.296
## .x5 ~~
## .y5 0.009 0.001 6.326 0.000 0.009 0.187
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x2 0.033 0.001 24.382 0.000 0.033 0.808
## .y2 0.089 0.004 24.382 0.000 0.089 0.858
## .x3 0.034 0.001 24.382 0.000 0.034 0.819
## .y3 0.082 0.003 24.382 0.000 0.082 0.745
## .x4 0.035 0.001 24.382 0.000 0.035 0.810
## .y4 0.083 0.003 24.382 0.000 0.083 0.725
## .x5 0.034 0.001 24.382 0.000 0.034 0.804
## .y5 0.072 0.003 24.382 0.000 0.072 0.650
## x1 0.062 0.003 24.382 0.000 0.062 1.000
## y1 0.097 0.004 24.382 0.000 0.097 1.000# 随机截距的交叉滞后模型
RICLPM <- '
# Create between components (random intercepts)
RIx =~ 1*x1 + 1*x2 + 1*x3 + 1*x4 + 1*x5
RIy =~ 1*y1 + 1*y2 + 1*y3 + 1*y4 + 1*y5
# Create within-person centered variables
wx1 =~ 1*x1
wx2 =~ 1*x2
wx3 =~ 1*x3
wx4 =~ 1*x4
wx5 =~ 1*x5
wy1 =~ 1*y1
wy2 =~ 1*y2
wy3 =~ 1*y3
wy4 =~ 1*y4
wy5 =~ 1*y5
# Estimate lagged effects between within-person centered variables
wx2 + wy2 ~ wx1 + wy1
wx3 + wy3 ~ wx2 + wy2
wx4 + wy4 ~ wx3 + wy3
wx5 + wy5 ~ wx4 + wy4
# Estimate covariance between within-person centered variables at first wave
wx1 ~~ wy1 # Covariance
# Estimate covariances between residuals of within-person centered variables
# (i.e., innovations)
wx2 ~~ wy2
wx3 ~~ wy3
wx4 ~~ wy4
wx5 ~~ wy5
# Estimate variance and covariance of random intercepts
RIx ~~ RIx
RIy ~~ RIy
RIx ~~ RIy
# Estimate (residual) variance of within-person centered variables
wx1 ~~ wx1 # Variances
wy1 ~~ wy1
wx2 ~~ wx2 # Residual variances
wy2 ~~ wy2
wx3 ~~ wx3
wy3 ~~ wy3
wx4 ~~ wx4
wy4 ~~ wy4
wx5 ~~ wx5
wy5 ~~ wy5
'
RICLPM.fit <- lavaan(RICLPM,
data = dat,
missing = 'ML',
meanstructure = T,
int.ov.free = T
)
summary(RICLPM.fit,fit.measures = T, standardized = T)## lavaan 0.6.15 ended normally after 116 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 44
##
## Number of observations 1189
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 25.806
## Degrees of freedom 21
## P-value (Chi-square) 0.214
##
## Model Test Baseline Model:
##
## Test statistic 3166.400
## Degrees of freedom 45
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.998
## Tucker-Lewis Index (TLI) 0.997
##
## Robust Comparative Fit Index (CFI) 0.998
## Robust Tucker-Lewis Index (TLI) 0.997
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) 531.750
## Loglikelihood unrestricted model (H1) 544.652
##
## Akaike (AIC) -975.499
## Bayesian (BIC) -751.941
## Sample-size adjusted Bayesian (SABIC) -891.701
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.014
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.030
## P-value H_0: RMSEA <= 0.050 1.000
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.014
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.030
## P-value H_0: Robust RMSEA <= 0.050 1.000
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.014
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RIx =~
## x1 1.000 0.096 0.390
## x2 1.000 0.096 0.473
## x3 1.000 0.096 0.475
## x4 1.000 0.096 0.461
## x5 1.000 0.096 0.465
## RIy =~
## y1 1.000 0.178 0.569
## y2 1.000 0.178 0.558
## y3 1.000 0.178 0.535
## y4 1.000 0.178 0.525
## y5 1.000 0.178 0.533
## wx1 =~
## x1 1.000 0.227 0.921
## wx2 =~
## x2 1.000 0.179 0.881
## wx3 =~
## x3 1.000 0.178 0.880
## wx4 =~
## x4 1.000 0.185 0.887
## wx5 =~
## x5 1.000 0.183 0.885
## wy1 =~
## y1 1.000 0.257 0.822
## wy2 =~
## y2 1.000 0.265 0.830
## wy3 =~
## y3 1.000 0.281 0.845
## wy4 =~
## y4 1.000 0.288 0.851
## wy5 =~
## y5 1.000 0.282 0.846
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## wx2 ~
## wx1 0.232 0.028 8.314 0.000 0.294 0.294
## wy1 0.009 0.026 0.329 0.742 0.012 0.012
## wy2 ~
## wx1 0.174 0.045 3.888 0.000 0.149 0.149
## wy1 0.004 0.046 0.092 0.927 0.004 0.004
## wx3 ~
## wx2 0.241 0.037 6.509 0.000 0.242 0.242
## wy2 0.026 0.024 1.082 0.279 0.039 0.039
## wy3 ~
## wx2 0.156 0.054 2.871 0.004 0.099 0.099
## wy2 0.262 0.039 6.747 0.000 0.247 0.247
## wx4 ~
## wx3 0.279 0.038 7.267 0.000 0.269 0.269
## wy3 0.010 0.023 0.431 0.666 0.015 0.015
## wy4 ~
## wx3 0.185 0.055 3.367 0.001 0.114 0.114
## wy3 0.296 0.035 8.362 0.000 0.288 0.288
## wx5 ~
## wx4 0.290 0.035 8.244 0.000 0.293 0.293
## wy4 -0.004 0.022 -0.186 0.852 -0.006 -0.006
## wy5 ~
## wx4 0.124 0.048 2.612 0.009 0.082 0.082
## wy4 0.392 0.031 12.644 0.000 0.400 0.400
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## wx1 ~~
## wy1 0.021 0.002 9.372 0.000 0.364 0.364
## .wx2 ~~
## .wy2 0.009 0.002 5.168 0.000 0.196 0.196
## .wx3 ~~
## .wy3 0.013 0.002 7.837 0.000 0.274 0.274
## .wx4 ~~
## .wy4 0.013 0.002 8.177 0.000 0.277 0.277
## .wx5 ~~
## .wy5 0.007 0.001 4.916 0.000 0.160 0.160
## RIx ~~
## RIy 0.010 0.001 7.992 0.000 0.587 0.587
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x1 0.241 0.007 33.687 0.000 0.241 0.977
## .x2 0.173 0.006 29.331 0.000 0.173 0.851
## .x3 0.186 0.006 31.646 0.000 0.186 0.918
## .x4 0.117 0.006 19.288 0.000 0.117 0.559
## .x5 0.111 0.006 18.427 0.000 0.111 0.534
## .y1 0.336 0.009 37.099 0.000 0.336 1.076
## .y2 0.348 0.009 37.686 0.000 0.348 1.093
## .y3 0.319 0.010 33.098 0.000 0.319 0.960
## .y4 0.384 0.010 39.097 0.000 0.384 1.134
## .y5 0.388 0.010 40.056 0.000 0.388 1.162
## RIx 0.000 0.000 0.000
## RIy 0.000 0.000 0.000
## wx1 0.000 0.000 0.000
## .wx2 0.000 0.000 0.000
## .wx3 0.000 0.000 0.000
## .wx4 0.000 0.000 0.000
## .wx5 0.000 0.000 0.000
## wy1 0.000 0.000 0.000
## .wy2 0.000 0.000 0.000
## .wy3 0.000 0.000 0.000
## .wy4 0.000 0.000 0.000
## .wy5 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RIx 0.009 0.001 8.722 0.000 1.000 1.000
## RIy 0.032 0.003 12.351 0.000 1.000 1.000
## wx1 0.052 0.002 21.067 0.000 1.000 1.000
## wy1 0.066 0.004 17.985 0.000 1.000 1.000
## .wx2 0.029 0.001 20.793 0.000 0.911 0.911
## .wy2 0.068 0.004 17.503 0.000 0.977 0.977
## .wx3 0.030 0.001 20.467 0.000 0.935 0.935
## .wy3 0.072 0.003 21.324 0.000 0.918 0.918
## .wx4 0.032 0.001 21.445 0.000 0.925 0.925
## .wy4 0.074 0.003 21.876 0.000 0.884 0.884
## .wx5 0.031 0.001 21.680 0.000 0.915 0.915
## .wy5 0.065 0.003 22.446 0.000 0.813 0.813
## .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
## .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