### DATA PREPRATION ###
library(lavaan)This is lavaan 0.6-19
lavaan is FREE software! Please report any bugs.dat <- read.csv("https://stats.idre.ucla.edu/wp-content/uploads/2021/02/worland5.csv")SEM Notebook Assignment
#sample variance-covariance matrix
cov(dat) motiv harm stabi ppsych ses verbal read arith spell
motiv 100 77 59 -25 25 32 53 60 59
harm 77 100 58 -25 26 25 42 44 45
stabi 59 58 100 -16 18 27 36 38 38
ppsych -25 -25 -16 100 -42 -40 -39 -24 -31
ses 25 26 18 -42 100 40 43 37 33
verbal 32 25 27 -40 40 100 56 49 48
read 53 42 36 -39 43 56 100 73 87
arith 60 44 38 -24 37 49 73 100 72
spell 59 45 38 -31 33 48 87 72 100### MODEL 1: SIMPLE REGRESSION ###
#simple regression using lm()
m1a <- lm(read ~ motiv, data=dat)
(fit1a <-summary(m1a))
Call:
lm(formula = read ~ motiv, data = dat)
Residuals:
Min 1Q Median 3Q Max
-26.0995 -6.1109 0.2342 5.2237 24.0183
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.232e-07 3.796e-01 0.00 1
motiv 5.300e-01 3.800e-02 13.95 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 8.488 on 498 degrees of freedom
Multiple R-squared: 0.2809, Adjusted R-squared: 0.2795
F-statistic: 194.5 on 1 and 498 DF, p-value: < 2.2e-16### MODELS 1 AND 2: REGRESSION ###
#simple regression using lavaan
m1b <- '
# regressions
# regressions
read ~ 1 + motiv
# variance (optional)
motiv ~~ motiv
'
fit1b <- sem(m1b, data=dat)
summary(fit1b)lavaan 0.6-19 ended normally after 8 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 5
Number of observations 500
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
read ~
motiv 0.530 0.038 13.975 0.000
Intercepts:
Estimate Std.Err z-value P(>|z|)
.read -0.000 0.379 -0.000 1.000
motiv 0.000 0.447 0.000 1.000
Variances:
Estimate Std.Err z-value P(>|z|)
motiv 99.800 6.312 15.811 0.000
.read 71.766 4.539 15.811 0.000#obtain sample mean and variance
mean(dat$motiv)[1] 2.4e-07var(dat$motiv)[1] 100# 4. Multivariate Regression removing residual covariance (Model 3D)
m3d <- '
read ~ 1 + ppsych + motiv
arith ~ 1 + motiv
read ~~ 0*arith # fix residual covariance to zero
'
fit3d <- sem(m3d, data=dat)
summary(fit3d)lavaan 0.6-19 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 7
Number of observations 500
Model Test User Model:
Test statistic 234.960
Degrees of freedom 2
P-value (Chi-square) 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
read ~
ppsych -0.275 0.037 -7.385 0.000
motiv 0.461 0.037 12.404 0.000
arith ~
motiv 0.600 0.036 16.771 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
.read ~~
.arith 0.000
Intercepts:
Estimate Std.Err z-value P(>|z|)
.read -0.000 0.360 -0.000 1.000
.arith -0.000 0.357 -0.000 1.000
Variances:
Estimate Std.Err z-value P(>|z|)
.read 64.708 4.092 15.811 0.000
.arith 63.872 4.040 15.811 0.000#convert least squares to maximum likelihood
498/500*(fit1a$sigma)**2[1] 71.76618#multiple regression
m2 <- '
# regressions
read ~ 1 + ppsych + motiv
#covariance
#ppsych ~~ motiv
'
fit2 <- sem(m2, data=dat)
summary(fit2)lavaan 0.6-19 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 4
Number of observations 500
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
read ~
ppsych -0.275 0.037 -7.385 0.000
motiv 0.461 0.037 12.404 0.000
Intercepts:
Estimate Std.Err z-value P(>|z|)
.read -0.000 0.360 -0.000 1.000
Variances:
Estimate Std.Err z-value P(>|z|)
.read 64.708 4.092 15.811 0.000### MODEL 3: MULTIVARIATE REGRESSION ###
#multivariate regression (default)
m3a <- '
# regressions
read ~ ppsych + motiv
arith ~ motiv
'
fit3a <- sem(m3a, data=dat)
summary(fit3a)lavaan 0.6-19 ended normally after 17 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 6
Number of observations 500
Model Test User Model:
Test statistic 6.796
Degrees of freedom 1
P-value (Chi-square) 0.009
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
read ~
ppsych -0.216 0.030 -7.289 0.000
motiv 0.476 0.037 12.918 0.000
arith ~
motiv 0.600 0.036 16.771 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
.read ~~
.arith 39.179 3.373 11.615 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.read 65.032 4.113 15.811 0.000
.arith 63.872 4.040 15.811 0.000inspect(fit3a,"partable")$lambda
read arith ppsych motiv
read 0 0 0 0
arith 0 0 0 0
ppsych 0 0 0 0
motiv 0 0 0 0
$theta
read arith ppsych motiv
read 0
arith 0 0
ppsych 0 0 0
motiv 0 0 0 0
$psi
read arith ppsych motiv
read 4
arith 6 5
ppsych 0 0 7
motiv 0 0 8 9
$beta
read arith ppsych motiv
read 0 0 1 2
arith 0 0 0 3
ppsych 0 0 0 0
motiv 0 0 0 0#regression of read on psych and motiv
m3b <- lm(read ~ ppsych + motiv, data=dat)
(fit3b <- summary(m3b))
Call:
lm(formula = read ~ ppsych + motiv, data = dat)
Residuals:
Min 1Q Median 3Q Max
-21.7734 -5.5633 0.1389 5.3662 25.8209
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.336e-07 3.608e-01 0.000 1
ppsych -2.747e-01 3.730e-02 -7.363 7.51e-13 ***
motiv 4.613e-01 3.730e-02 12.367 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 8.068 on 497 degrees of freedom
Multiple R-squared: 0.3516, Adjusted R-squared: 0.349
F-statistic: 134.8 on 2 and 497 DF, p-value: < 2.2e-16#regression of arith on motiv
m3c <- lm(arith ~ motiv, data=dat)
(fit3c <- summary(m3c))
Call:
lm(formula = arith ~ motiv, data = dat)
Residuals:
Min 1Q Median 3Q Max
-23.633 -5.341 -0.214 5.106 21.271
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -5.400e-08 3.581e-01 0.00 1
motiv 6.000e-01 3.585e-02 16.74 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 8.008 on 498 degrees of freedom
Multiple R-squared: 0.36, Adjusted R-squared: 0.3587
F-statistic: 280.1 on 1 and 498 DF, p-value: < 2.2e-16#multivariate regression (set covariance to 0)
m3d <- '
# regressions
read ~ ppsych + motiv
arith ~ motiv
# covariance
read ~~ 0*arith
'
fit3d <- sem(m3d, data=dat)
summary(fit3d)lavaan 0.6-19 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 5
Number of observations 500
Model Test User Model:
Test statistic 234.960
Degrees of freedom 2
P-value (Chi-square) 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
read ~
ppsych -0.275 0.037 -7.385 0.000
motiv 0.461 0.037 12.404 0.000
arith ~
motiv 0.600 0.036 16.771 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
.read ~~
.arith 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.read 64.708 4.092 15.811 0.000
.arith 63.872 4.040 15.811 0.000#known values
cov(dat[,c("read","arith","ppsych","motiv")]) read arith ppsych motiv
read 100 73 -39 53
arith 73 100 -24 60
ppsych -39 -24 100 -25
motiv 53 60 -25 100#multivariate regression (saturated model)
m3e <- '
# regressions
read ~ ppsych + motiv
arith ~ ppsych + motiv
#covariance
ppsych ~~ motiv
ppsych ~~ ppsych
motiv ~~ motiv
'
fit3e <- sem(m3e, data=dat)
summary(fit3e)lavaan 0.6-19 ended normally after 41 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 10
Number of observations 500
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
read ~
ppsych -0.275 0.037 -7.385 0.000
motiv 0.461 0.037 12.404 0.000
arith ~
ppsych -0.096 0.037 -2.616 0.009
motiv 0.576 0.037 15.695 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
ppsych ~~
motiv -24.950 4.601 -5.423 0.000
.read ~~
.arith 38.651 3.338 11.579 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
ppsych 99.800 6.312 15.811 0.000
motiv 99.800 6.312 15.811 0.000
.read 64.708 4.092 15.811 0.000
.arith 63.010 3.985 15.811 0.000#inspect(fit3e,"partable")### MODEL 4: PATH ANALYSIS ###
#path analysis model
m4a <- '
# regressions
read ~ ppsych + motiv
arith ~ motiv + read
# covariance
# read ~~ 0*arith
'
fit4a <- sem(m4a, data=dat)
summary(fit4a)lavaan 0.6-19 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 6
Number of observations 500
Model Test User Model:
Test statistic 4.870
Degrees of freedom 1
P-value (Chi-square) 0.027
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
read ~
ppsych -0.275 0.037 -7.385 0.000
motiv 0.461 0.037 12.404 0.000
arith ~
motiv 0.296 0.034 8.841 0.000
read 0.573 0.034 17.093 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.read 64.708 4.092 15.811 0.000
.arith 40.314 2.550 15.811 0.000#re-run with fit indexes
summary(fit4a, fit.measures=TRUE)lavaan 0.6-19 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 6
Number of observations 500
Model Test User Model:
Test statistic 4.870
Degrees of freedom 1
P-value (Chi-square) 0.027
Model Test Baseline Model:
Test statistic 674.748
Degrees of freedom 5
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.994
Tucker-Lewis Index (TLI) 0.971
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -3385.584
Loglikelihood unrestricted model (H1) -3383.149
Akaike (AIC) 6783.168
Bayesian (BIC) 6808.456
Sample-size adjusted Bayesian (SABIC) 6789.411
Root Mean Square Error of Approximation:
RMSEA 0.088
90 Percent confidence interval - lower 0.024
90 Percent confidence interval - upper 0.172
P-value H_0: RMSEA <= 0.050 0.139
P-value H_0: RMSEA >= 0.080 0.662
Standardized Root Mean Square Residual:
SRMR 0.018
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
read ~
ppsych -0.275 0.037 -7.385 0.000
motiv 0.461 0.037 12.404 0.000
arith ~
motiv 0.296 0.034 8.841 0.000
read 0.573 0.034 17.093 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.read 64.708 4.092 15.811 0.000
.arith 40.314 2.550 15.811 0.000#model chi-square
pchisq(q=4.870,df=1,lower.tail=FALSE)[1] 0.0273275#modification index
modindices(fit4a,sort=TRUE) lhs op rhs mi epc sepc.lv sepc.all sepc.nox
17 motiv ~ arith 68.073 8.874 8.874 8.874 8.874
10 read ~~ arith 4.847 16.034 16.034 0.314 0.314
12 arith ~ ppsych 4.847 0.068 0.068 0.068 0.007
11 read ~ arith 4.847 0.398 0.398 0.398 0.398
14 ppsych ~ arith 2.188 0.071 0.071 0.071 0.071
16 motiv ~ read 0.000 0.000 0.000 0.000 0.000
18 motiv ~ ppsych 0.000 0.000 0.000 0.000 0.000
13 ppsych ~ read 0.000 0.000 0.000 0.000 0.000
8 ppsych ~~ motiv 0.000 0.000 0.000 NA 0.000
15 ppsych ~ motiv 0.000 0.000 0.000 0.000 0.000## model4a customized for degrees of freedom
m4aa <- '
# regressions
read ~ 1 + ppsych + motiv
motiv ~ 1 + arith + read
# covariance
# read ~~ 0*arith
'
fit4aa <- sem(m4aa, data=dat)
summary(fit4aa)lavaan 0.6-19 ended normally after 26 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 8
Number of observations 500
Model Test User Model:
Test statistic 55.114
Degrees of freedom 1
P-value (Chi-square) 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
read ~
ppsych -0.108 0.047 -2.322 0.020
motiv 1.127 0.075 15.035 0.000
motiv ~
arith 1.864 0.197 9.483 0.000
read -1.732 0.256 -6.775 0.000
Intercepts:
Estimate Std.Err z-value P(>|z|)
.read -0.000 0.461 -0.000 1.000
.motiv 0.000 0.686 0.000 1.000
Variances:
Estimate Std.Err z-value P(>|z|)
.read 106.183 11.504 9.230 0.000
.motiv 235.494 48.319 4.874 0.000#path analysis model after modification
m4b <- '
# regressions
read ~ ppsych + motiv
arith ~ motiv + read + ppsych
'
fit4b <- sem(m4b, data=dat)
summary(fit4b)lavaan 0.6-19 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 7
Number of observations 500
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
read ~
ppsych -0.275 0.037 -7.385 0.000
motiv 0.461 0.037 12.404 0.000
arith ~
motiv 0.300 0.033 8.993 0.000
read 0.597 0.035 17.004 0.000
ppsych 0.068 0.031 2.212 0.027
Variances:
Estimate Std.Err z-value P(>|z|)
.read 64.708 4.092 15.811 0.000
.arith 39.923 2.525 15.811 0.000modindices(fit4b,sort=TRUE)[1] lhs op rhs mi epc sepc.lv sepc.all sepc.nox
<0 rows> (or 0-length row.names)#baseline model
m4c <- '
# variances only
read ~~ read
ppsych ~~ ppsych
motiv ~~ motiv
arith ~~ arith
'
fit4c <- sem(m4c, data=dat)
summary(fit4c, fit.measures=TRUE)lavaan 0.6-19 ended normally after 8 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 4
Number of observations 500
Model Test User Model:
Test statistic 707.017
Degrees of freedom 6
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 707.017
Degrees of freedom 6
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.000
Tucker-Lewis Index (TLI) 0.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -7441.045
Loglikelihood unrestricted model (H1) -7087.537
Akaike (AIC) 14890.091
Bayesian (BIC) 14906.949
Sample-size adjusted Bayesian (SABIC) 14894.253
Root Mean Square Error of Approximation:
RMSEA 0.483
90 Percent confidence interval - lower 0.454
90 Percent confidence interval - upper 0.514
P-value H_0: RMSEA <= 0.050 0.000
P-value H_0: RMSEA >= 0.080 1.000
Standardized Root Mean Square Residual:
SRMR 0.380
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Variances:
Estimate Std.Err z-value P(>|z|)
read 99.800 6.312 15.811 0.000
ppsych 99.800 6.312 15.811 0.000
motiv 99.800 6.312 15.811 0.000
arith 99.800 6.312 15.811 0.000### MODEL 5: MEASUREMENT MODEL ###
#exogenous factor analysis for adjust
m5a <- 'risk =~ verbal + ses + ppsych
#intercepts (nu = tau)
verbal ~ 1
ses ~ 1
ppsych ~ 1'
fit5a <- sem(m5a, data=dat)
summary(fit5a, standardized=TRUE)lavaan 0.6-19 ended normally after 37 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 9
Number of observations 500
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
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
risk =~
verbal 1.000 6.166 0.617
ses 1.050 0.126 8.358 0.000 6.474 0.648
ppsych -1.050 0.126 -8.358 0.000 -6.474 -0.648
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.verbal 0.000 0.447 0.000 1.000 0.000 0.000
.ses -0.000 0.447 -0.000 1.000 -0.000 -0.000
.ppsych -0.000 0.447 -0.000 1.000 -0.000 -0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.verbal 61.781 5.810 10.634 0.000 61.781 0.619
.ses 57.884 5.989 9.664 0.000 57.884 0.580
.ppsych 57.884 5.989 9.664 0.000 57.884 0.580
risk 38.019 6.562 5.794 0.000 1.000 1.000### MODEL 6: STRUCTURAL REGRESSION ###
#structural regression (one endogenous variable)
m6a <- '
# measurement model
adjust =~ motiv + harm + stabi
risk =~ verbal + ppsych + ses
achieve =~ read + arith + spell
# regressions
achieve ~ adjust + risk
'
fit6a <- sem(m6a, data=dat)
summary(fit6a, standardized=TRUE, fit.measures=TRUE)lavaan 0.6-19 ended normally after 130 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 21
Number of observations 500
Model Test User Model:
Test statistic 148.982
Degrees of freedom 24
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 2597.972
Degrees of freedom 36
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.951
Tucker-Lewis Index (TLI) 0.927
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -15517.857
Loglikelihood unrestricted model (H1) -15443.366
Akaike (AIC) 31077.713
Bayesian (BIC) 31166.220
Sample-size adjusted Bayesian (SABIC) 31099.565
Root Mean Square Error of Approximation:
RMSEA 0.102
90 Percent confidence interval - lower 0.087
90 Percent confidence interval - upper 0.118
P-value H_0: RMSEA <= 0.050 0.000
P-value H_0: RMSEA >= 0.080 0.990
Standardized Root Mean Square Residual:
SRMR 0.041
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
adjust =~
motiv 1.000 9.324 0.933
harm 0.884 0.041 21.774 0.000 8.246 0.825
stabi 0.695 0.043 15.987 0.000 6.478 0.648
risk =~
verbal 1.000 7.319 0.733
ppsych -0.770 0.075 -10.223 0.000 -5.636 -0.564
ses 0.807 0.076 10.607 0.000 5.906 0.591
achieve =~
read 1.000 9.404 0.941
arith 0.837 0.034 24.437 0.000 7.873 0.788
spell 0.976 0.028 34.338 0.000 9.178 0.919
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
achieve ~
adjust 0.375 0.046 8.085 0.000 0.372 0.372
risk 0.724 0.078 9.253 0.000 0.564 0.564
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
adjust ~~
risk 32.098 4.320 7.431 0.000 0.470 0.470
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.motiv 12.870 2.852 4.512 0.000 12.870 0.129
.harm 31.805 2.973 10.698 0.000 31.805 0.319
.stabi 57.836 3.990 14.494 0.000 57.836 0.580
.verbal 46.239 4.788 9.658 0.000 46.239 0.463
.ppsych 68.033 5.068 13.425 0.000 68.033 0.682
.ses 64.916 4.975 13.048 0.000 64.916 0.650
.read 11.372 1.608 7.074 0.000 11.372 0.114
.arith 37.818 2.680 14.109 0.000 37.818 0.379
.spell 15.560 1.699 9.160 0.000 15.560 0.156
adjust 86.930 6.830 12.727 0.000 1.000 1.000
risk 53.561 6.757 7.927 0.000 1.000 1.000
.achieve 30.685 3.449 8.896 0.000 0.347 0.347#structural regression (two endogenous variables)
m6b <- '
# measurement model
adjust =~ motiv + harm + stabi
risk =~ verbal + ses + ppsych
achieve =~ read + arith + spell
# regressions
adjust ~ risk
achieve ~ adjust + risk
'
fit6b <- sem(m6b, data=dat)
summary(fit6b, standardized=TRUE, fit.measures=TRUE)lavaan 0.6-19 ended normally after 112 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 21
Number of observations 500
Model Test User Model:
Test statistic 148.982
Degrees of freedom 24
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 2597.972
Degrees of freedom 36
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.951
Tucker-Lewis Index (TLI) 0.927
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -15517.857
Loglikelihood unrestricted model (H1) -15443.366
Akaike (AIC) 31077.713
Bayesian (BIC) 31166.220
Sample-size adjusted Bayesian (SABIC) 31099.565
Root Mean Square Error of Approximation:
RMSEA 0.102
90 Percent confidence interval - lower 0.087
90 Percent confidence interval - upper 0.118
P-value H_0: RMSEA <= 0.050 0.000
P-value H_0: RMSEA >= 0.080 0.990
Standardized Root Mean Square Residual:
SRMR 0.041
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
adjust =~
motiv 1.000 9.324 0.933
harm 0.884 0.041 21.774 0.000 8.246 0.825
stabi 0.695 0.043 15.987 0.000 6.478 0.648
risk =~
verbal 1.000 7.319 0.733
ses 0.807 0.076 10.607 0.000 5.906 0.591
ppsych -0.770 0.075 -10.223 0.000 -5.636 -0.564
achieve =~
read 1.000 9.404 0.941
arith 0.837 0.034 24.437 0.000 7.873 0.788
spell 0.976 0.028 34.338 0.000 9.178 0.919
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
adjust ~
risk 0.599 0.076 7.837 0.000 0.470 0.470
achieve ~
adjust 0.375 0.046 8.085 0.000 0.372 0.372
risk 0.724 0.078 9.253 0.000 0.564 0.564
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.motiv 12.870 2.852 4.512 0.000 12.870 0.129
.harm 31.805 2.973 10.698 0.000 31.805 0.319
.stabi 57.836 3.990 14.494 0.000 57.836 0.580
.verbal 46.239 4.788 9.658 0.000 46.239 0.463
.ses 64.916 4.975 13.048 0.000 64.916 0.650
.ppsych 68.033 5.068 13.425 0.000 68.033 0.682
.read 11.372 1.608 7.074 0.000 11.372 0.114
.arith 37.818 2.680 14.109 0.000 37.818 0.379
.spell 15.560 1.699 9.160 0.000 15.560 0.156
.adjust 67.694 6.066 11.160 0.000 0.779 0.779
risk 53.561 6.757 7.927 0.000 1.000 1.000
.achieve 30.685 3.449 8.896 0.000 0.347 0.347#structural regression (observed endogenous variable)
m6c <- '
# measurement model
adjust =~ motiv + harm + stabi
risk =~ verbal + ses + ppsych
# regressions
adjust ~ risk
read ~ adjust + risk
'
fit6c <- sem(m6c, data=dat)
summary(fit6c, standardized=TRUE, fit.measures=TRUE)lavaan 0.6-19 ended normally after 105 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 16
Number of observations 500
Model Test User Model:
Test statistic 35.555
Degrees of freedom 12
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 1339.008
Degrees of freedom 21
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.982
Tucker-Lewis Index (TLI) 0.969
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -12370.103
Loglikelihood unrestricted model (H1) -12352.325
Akaike (AIC) 24772.206
Bayesian (BIC) 24839.640
Sample-size adjusted Bayesian (SABIC) 24788.855
Root Mean Square Error of Approximation:
RMSEA 0.063
90 Percent confidence interval - lower 0.039
90 Percent confidence interval - upper 0.087
P-value H_0: RMSEA <= 0.050 0.170
P-value H_0: RMSEA >= 0.080 0.127
Standardized Root Mean Square Residual:
SRMR 0.025
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
adjust =~
motiv 1.000 9.172 0.918
harm 0.914 0.043 21.334 0.000 8.379 0.839
stabi 0.716 0.045 16.025 0.000 6.569 0.658
risk =~
verbal 1.000 7.208 0.722
ses 0.829 0.076 10.848 0.000 5.973 0.598
ppsych -0.794 0.076 -10.486 0.000 -5.726 -0.573
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
adjust ~
risk 0.604 0.077 7.834 0.000 0.474 0.474
read ~
adjust 0.285 0.050 5.658 0.000 2.610 0.261
risk 0.853 0.087 9.824 0.000 6.147 0.615
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.motiv 15.676 2.982 5.257 0.000 15.676 0.157
.harm 29.595 3.030 9.767 0.000 29.595 0.297
.stabi 56.650 3.960 14.307 0.000 56.650 0.568
.verbal 47.846 4.666 10.254 0.000 47.846 0.479
.ses 64.125 4.903 13.078 0.000 64.125 0.643
.ppsych 67.008 4.993 13.421 0.000 67.008 0.671
.read 39.974 3.823 10.456 0.000 39.974 0.401
.adjust 65.185 6.022 10.824 0.000 0.775 0.775
risk 51.954 6.580 7.895 0.000 1.000 1.000#inspect(fit6c,"partable")#model6c (manual specification)
m6cc <- '
# measurement model
adjust =~ motiv + harm + stabi
risk =~ verbal + ses + ppsych
#single indicator factor
readf =~ 1*read
#residuel variance to zero
read ~~ 0*read
# regressions
adjust ~ risk
readf ~ adjust + risk
'
fit6cc <- sem(m6cc, data=dat, optim.method=list("BFGS"))
summary(fit6cc)lavaan 0.6-19 ended normally after 2153 iterations
Estimator ML
Optimization method BFGS
Number of model parameters 16
Number of observations 500
Model Test User Model:
Test statistic 35.585
Degrees of freedom 12
P-value (Chi-square) 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
adjust =~
motiv 1.000
harm 0.914 0.043 21.345 0.000
stabi 0.717 0.045 16.043 0.000
risk =~
verbal 1.000
ses 0.834 0.077 10.876 0.000
ppsych -0.799 0.076 -10.518 0.000
readf =~
read 1.000
Regressions:
Estimate Std.Err z-value P(>|z|)
adjust ~
risk 0.605 0.077 7.832 0.000
readf ~
adjust 0.285 0.050 5.671 0.000
risk 0.854 0.087 9.822 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.read 0.000
.motiv 15.752 2.980 5.286 0.000
.harm 29.529 3.028 9.752 0.000
.stabi 56.536 3.953 14.301 0.000
.verbal 48.246 4.669 10.334 0.000
.ses 63.580 4.879 13.032 0.000
.ppsych 66.414 4.964 13.380 0.000
.adjust 65.143 6.019 10.822 0.000
risk 51.680 6.566 7.871 0.000
.readf 40.060 3.820 10.486 0.000#inspect(fit6cc,"partable")