SEM Analysis Project
Roxanne Felig
10/23/2020
Project overview
This data was used to conduct a structural equation model of academic performance. Latent variables of attention, relevance, confidence, and satisfaction were created, and then satisfaction was predicted from attention, relevance, and confidence.
my_data <- read.table("~/Downloads/motivate2.txt", quote="\"", comment.char="")
names(my_data)[names(my_data) == "V1"] <- "att1"
names(my_data)[names(my_data) == "V2"] <- "att2"
names(my_data)[names(my_data) == "V3"] <- "att3"
names(my_data)[names(my_data) == "V4"] <- "rel1"
names(my_data)[names(my_data) == "V5"] <- "rel2"
names(my_data)[names(my_data) == "V6"] <- "rel3"
names(my_data)[names(my_data) == "V7"] <- "con1"
names(my_data)[names(my_data) == "V8"] <- "con2"
names(my_data)[names(my_data) == "V9"] <- "con3"
names(my_data)[names(my_data) == "V10"] <- "sat1"
names(my_data)[names(my_data) == "V11"] <- "sat2"
names(my_data)[names(my_data) == "V12"] <- "sat3"
colnames(my_data)## [1] "att1" "att2" "att3" "rel1" "rel2" "rel3" "con1" "con2" "con3" "sat1"
## [11] "sat2" "sat3"Model specificication
mod<-'ATT=~1*att1+att2+att3
REL=~1*rel1+rel2+rel3
CON=~1*con1+con2+con3
SAT=~1*sat1+sat2+sat3
ATT~g1*REL+G2*CON+g3*SAT
#covariances between exo variables
REL~~CON+SAT
#variance of exo variables
REL~~REL
CON~~CON
SAT~~SAT
'Fit and summarize model
fit.mod <- sem(model = mod,
missing = "ML",
data = my_data)
summary(fit.mod,
fit.measures= TRUE,
standardized = TRUE,
cov=TRUE,
rsquare=TRUE
#if you want fit measures like AIC, BIC, etc, use
#fit.measures = TRUE
)## lavaan 0.6-7 ended normally after 56 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 42
##
## Number of observations 193
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 90.820
## Degrees of freedom 48
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1565.675
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.971
## Tucker-Lewis Index (TLI) 0.961
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1553.397
## Loglikelihood unrestricted model (H1) -1507.988
##
## Akaike (AIC) 3190.795
## Bayesian (BIC) 3327.828
## Sample-size adjusted Bayesian (BIC) 3194.783
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.068
## 90 Percent confidence interval - lower 0.046
## 90 Percent confidence interval - upper 0.089
## P-value RMSEA <= 0.05 0.083
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.046
##
## 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
## ATT =~
## att1 1.000 0.441 0.672
## att2 1.176 0.133 8.849 0.000 0.518 0.765
## att3 1.261 0.138 9.143 0.000 0.555 0.843
## REL =~
## rel1 1.000 0.515 0.869
## rel2 1.202 0.075 15.924 0.000 0.619 0.911
## rel3 1.011 0.084 12.013 0.000 0.521 0.746
## CON =~
## con1 1.000 0.551 0.881
## con2 1.081 0.063 17.071 0.000 0.595 0.895
## con3 1.044 0.061 17.113 0.000 0.575 0.893
## SAT =~
## sat1 1.000 0.483 0.817
## sat2 1.201 0.100 12.002 0.000 0.580 0.791
## sat3 1.008 0.081 12.464 0.000 0.487 0.806
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ATT ~
## REL (g1) 0.187 0.077 2.440 0.015 0.219 0.219
## CON (G2) -0.217 0.095 -2.291 0.022 -0.271 -0.271
## SAT (g3) 0.788 0.152 5.180 0.000 0.863 0.863
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REL ~~
## CON 0.100 0.024 4.155 0.000 0.354 0.354
## SAT 0.143 0.025 5.825 0.000 0.575 0.575
## CON ~~
## SAT 0.200 0.028 7.054 0.000 0.752 0.752
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .att1 2.914 0.047 61.722 0.000 2.914 4.443
## .att2 3.157 0.049 64.787 0.000 3.157 4.663
## .att3 3.147 0.047 66.349 0.000 3.147 4.776
## .rel1 3.449 0.043 80.860 0.000 3.449 5.820
## .rel2 3.349 0.049 68.451 0.000 3.349 4.927
## .rel3 3.389 0.050 67.415 0.000 3.389 4.853
## .con1 3.145 0.045 69.934 0.000 3.145 5.034
## .con2 3.221 0.048 67.327 0.000 3.221 4.846
## .con3 3.216 0.046 69.383 0.000 3.216 4.994
## .sat1 3.169 0.043 74.487 0.000 3.169 5.362
## .sat2 3.090 0.053 58.536 0.000 3.090 4.214
## .sat3 3.249 0.043 74.795 0.000 3.249 5.384
## .ATT 0.000 0.000 0.000
## REL 0.000 0.000 0.000
## CON 0.000 0.000 0.000
## SAT 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## REL 0.265 0.036 7.323 0.000 1.000 1.000
## CON 0.303 0.040 7.603 0.000 1.000 1.000
## SAT 0.233 0.035 6.612 0.000 1.000 1.000
## .att1 0.236 0.028 8.298 0.000 0.236 0.549
## .att2 0.190 0.026 7.387 0.000 0.190 0.414
## .att3 0.126 0.023 5.532 0.000 0.126 0.289
## .rel1 0.086 0.014 6.266 0.000 0.086 0.244
## .rel2 0.079 0.017 4.522 0.000 0.079 0.171
## .rel3 0.216 0.026 8.393 0.000 0.216 0.443
## .con1 0.087 0.013 6.697 0.000 0.087 0.223
## .con2 0.088 0.014 6.357 0.000 0.088 0.198
## .con3 0.084 0.013 6.498 0.000 0.084 0.202
## .sat1 0.116 0.016 7.220 0.000 0.116 0.332
## .sat2 0.202 0.026 7.809 0.000 0.202 0.375
## .sat3 0.127 0.017 7.500 0.000 0.127 0.350
## .ATT 0.060 0.016 3.684 0.000 0.311 0.311
##
## R-Square:
## Estimate
## att1 0.451
## att2 0.586
## att3 0.711
## rel1 0.756
## rel2 0.829
## rel3 0.557
## con1 0.777
## con2 0.802
## con3 0.798
## sat1 0.668
## sat2 0.625
## sat3 0.650
## ATT 0.689View path diagram
semPaths(fit.mod,
whatLabels = "std",
what="std",
layout='tree',
curve=TRUE,
edge.label.cex = .5,
edge.label.color = "black",
edge.width = 0.3,
normalize=TRUE,
covAtResiduals = TRUE
)