A Hierarchical Model of IQ

Structural Equation Modeling with lavaan in R

Erin Buchanan

Professor

Hierarchical Three-Factor Model of the WAIS-III

Model Specification

#updated model with correlated error from exercise
wais.model2 <- 'verbalcomp =~ vocab + simil + inform + compreh 
    workingmemory =~ arith + digspan + lnseq
    perceptorg =~ piccomp + block + matrixreason + digsym + symbolsearch
    simil ~~ inform'

#updated model with hierarchy added
wais.model3 <- 'verbalcomp =~ vocab + simil + inform + compreh 
    workingmemory =~ arith + digspan + lnseq
    perceptorg =~ piccomp + block + matrixreason + digsym + symbolsearch
    simil ~~ inform
    general =~ verbalcomp + workingmemory + perceptorg'

No Change in Model Fit

#regular model 
fitmeasures(wais.fit2, c("cfi", "tli"))

  cfi   tli 
0.833 0.780

#hierarchical model
fitmeasures(wais.fit3, c("cfi", "tli"))

  cfi   tli 
0.833 0.780

Why Use Hierarchical Models

Covariances:
                Estimate Std.Err z-value P(>|z|)  Std.lv Std.all
  verbalcomp ~~                                                         
    workingmemory  6.278   1.181   5.315   0.000   0.416   0.416
    perceptorg     5.654   0.859   6.583   0.000   0.634   0.634
  workingmemory ~~                                                      
    perceptorg     2.237   0.363   6.172   0.000   0.576   0.576

  Latent Variables:
               Estimate Std.Err z-value P(>|z|)  Std.lv Std.all
  general =~                                                            
    verbalcomp    1.000                           0.676   0.676
    workingmemory 0.396   0.060   6.635   0.000   0.615   0.615
    perceptorg    0.356   0.062   5.713   0.000   0.937   0.937

Let's practice!

Structural Equation Modeling with lavaan in R