Chapter 10 Week8_2: Lavaan Lab 7 Two-factor SR Model
10.1 Data Prep
Again, we use cfaInClassData.csv in this lab
Let’s read this dataset in:
cfaData<- read.csv("cfaInclassData.csv", header = T)Load up the lavaan library:
library(lavaan)10.2 PART I: Two-Factor SR, Fixed Loading
10.2.1 Fixed Loading, AKA Marker Variable method.
Let’s write up the model syntax for the structural regression (SR) model with two factors:
srSyntax <- "
#Factor Specification
posAffect =~ glad + cheerful + happy
satisfaction =~ satisfied + content + comfortable
#Structural Regression!
satisfaction ~ posAffect
"Here we named the fitted object ‘srRun’ to see our output:
srRun = lavaan::sem(model = srSyntax,
data = cfaData,
fixed.x=FALSE)Get a summary using summary() function, add standardized=T to request standardized parameter estimates:
summary(srRun, standardized = T)## lavaan 0.6-12 ended normally after 22 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 13
##
## Number of observations 1000
##
## Model Test User Model:
##
## Test statistic 2.957
## Degrees of freedom 8
## P-value (Chi-square) 0.937
##
## 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
## posAffect =~
## glad 1.000 0.694 0.706
## cheerful 1.112 0.057 19.458 0.000 0.772 0.785
## happy 1.067 0.055 19.294 0.000 0.740 0.758
## satisfaction =~
## satisfied 1.000 0.773 0.767
## content 1.068 0.052 20.525 0.000 0.826 0.762
## comfortable 0.918 0.045 20.336 0.000 0.709 0.746
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## satisfaction ~
## posAffect 0.544 0.047 11.490 0.000 0.488 0.488
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .glad 0.484 0.029 16.647 0.000 0.484 0.501
## .cheerful 0.371 0.029 13.004 0.000 0.371 0.384
## .happy 0.405 0.028 14.389 0.000 0.405 0.425
## .satisfied 0.419 0.029 14.326 0.000 0.419 0.412
## .content 0.491 0.034 14.542 0.000 0.491 0.419
## .comfortable 0.400 0.026 15.315 0.000 0.400 0.443
## posAffect 0.482 0.042 11.439 0.000 1.000 1.000
## .satisfaction 0.455 0.038 11.869 0.000 0.762 0.762The above syntax reproduces the SR analysis from the class slides.
- CFA part under “Latent Variables” remains unchanged
- “Covariances” section no longer exists
- satisfaction is also removed under “Variances”
Instead, in the Regressions section:
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
satisfaction ~
posAffect 0.544 0.047 11.490 0.000 0.488 0.488returns the regression slope of posAffect (b = 0.544). One-unit change in posAffect is leading to one-unit change in satisfaction.
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.satisfaction 0.455 0.038 11.869 0.000 0.762 0.762returns the disturbance variance of satisfaction (sigma_(d_2)^2, not psi_2!)
10.3 PART II: Two-Factor SR, Fixed Factor Variance
10.3.1 Fixed Factor Method
Here we named the fitted object ‘srRun2’.
We add std.lv=T to fix all latent factor variances to 1:
srRun2 = lavaan::sem(model = srSyntax,
data = cfaData,
fixed.x=FALSE,
std.lv=T)
summary(srRun2, standardized = T)## lavaan 0.6-12 ended normally after 17 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 13
##
## Number of observations 1000
##
## Model Test User Model:
##
## Test statistic 2.957
## Degrees of freedom 8
## P-value (Chi-square) 0.937
##
## 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
## posAffect =~
## glad 0.694 0.030 22.878 0.000 0.694 0.706
## cheerful 0.772 0.030 25.798 0.000 0.772 0.785
## happy 0.740 0.030 24.806 0.000 0.740 0.758
## satisfaction =~
## satisfied 0.675 0.028 23.737 0.000 0.773 0.767
## content 0.721 0.031 23.611 0.000 0.826 0.762
## comfortable 0.619 0.027 23.124 0.000 0.709 0.746
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## satisfaction ~
## posAffect 0.559 0.049 11.501 0.000 0.488 0.488
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .glad 0.484 0.029 16.647 0.000 0.484 0.501
## .cheerful 0.371 0.029 13.004 0.000 0.371 0.384
## .happy 0.405 0.028 14.389 0.000 0.405 0.425
## .satisfied 0.419 0.029 14.326 0.000 0.419 0.412
## .content 0.491 0.034 14.542 0.000 0.491 0.419
## .comfortable 0.400 0.026 15.315 0.000 0.400 0.443
## posAffect 1.000 1.000 1.000
## .satisfaction 1.000 0.762 0.762This doesn’t work as expected, why?
Therefore, for SR models, we should always go with fixed loading scaling approach.
10.4 PART III: Exercise (what fun!): 3-Factor SR Model
Suppose that in a 3-factor SR model:
- Positive Affect is measured by Happy and Cheerful
- Satisfaction is measured by Satisfied and Content
- Pleasure is measured by Glad and Comfortable
- Satisfaction is predicted by both Positive Affect and Pleasure
Can you use cfaData to fit such a model?