Model Structure

Structural Equation Modeling with lavaan in R

Erin Buchanan

Professor

Multifactor Model Estimation

twofactor.model <- 'visual =~ x1 + x2 + x3
    speed =~ x7 + x8 + x9'

Your Expected Two-Factor Model

Multifactor Model Estimation

twofactor.model <- 'visual =~ x1 + x2 + x3
    speed =~ x7 + x8 + x9'

The Real Two-Factor Model with Correlation

Summary Output

Latent Variables:
           Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  visual =~                                                             
    x1       1.000                               0.777    0.667
    x2       0.690    0.124    5.585    0.000    0.536    0.456
    x3       0.985    0.160    6.157    0.000    0.766    0.678
  speed =~                                                              
    x7       1.000                               0.622    0.572
    x8       1.204    0.170    7.090    0.000    0.749    0.741
    x9       1.052    0.147    7.142    0.000    0.654    0.649

Summary Output (2)

Covariances:
            Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  visual ~~                                                             
    speed    0.223    0.052    4.290    0.000    0.460    0.460

Model Specification Syntax

Covariances:
            Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  visual ~~                                                             
    speed    0.223    0.052    4.290    0.000    0.460    0.460

=~ creates latent variables
~~ creates covariance between variables
~ creates direct prediction between variables
- Remember, y ~ x to specify direction

Edit the Model

twofactor.model <- 'visual =~ x1 + x2 + x3
    speed =~ x7 + x8 + x9
    speed ~~ 0*visual'

Covariances:
            Estimate  Std.Err  z-value  P(>|z|)  Std.lv  Std.all
  speed ~~                                                             
    visual     0.000                              0.000    0.000

Edit the Model (2)

twofactor.model <- 'visual =~ x1 + x2 + x3
    speed =~ x7 + x8 + x9
    speed~visual'

Regressions:
          Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  speed ~                                                               
    visual  0.368    0.083    4.439    0.000    0.460    0.460

Let's practice!

Structural Equation Modeling with lavaan in R