Modification Indices

Structural Equation Modeling with lavaan in R

Erin Buchanan

Professor

Updating Poor Models

User model versus baseline model:
  Comparative Fit Index (CFI)                    0.879
  Tucker-Lewis Index (TLI)                       0.774

Root Mean Square Error of Approximation:
  RMSEA                                          0.128
  90 Percent Confidence Interval          0.094  0.164
  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:
  SRMR                                           0.079

Updating Poor Models (2)

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

Updating Poor Models (3)

Variances:
          Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .x1      0.754    0.110    6.838    0.000    0.754    0.555
   .x2      1.094    0.103   10.661    0.000    1.094    0.792
   .x3      0.688    0.105    6.557    0.000    0.688    0.540
   .x7      0.796    0.082    9.756    0.000    0.796    0.673
   .x8      0.461    0.077    6.002    0.000    0.461    0.451
   .x9      0.587    0.071    8.273    0.000    0.587    0.578

var(HolzingerSwineford1939$x1)

1.362898

Modification Indices

modificationindices(twofactor.fit, sort = TRUE)

      lhs op rhs     mi    epc sepc.lv sepc.all sepc.nox
34     x7 ~~  x8 35.521  0.624   0.624    0.568    0.568
18 visual =~  x9 35.521  0.659   0.512    0.508    0.508
36     x8 ~~  x9 19.041 -0.527  -0.527   -0.517   -0.517
16 visual =~  x7 19.041 -0.503  -0.391   -0.359   -0.359
26     x1 ~~  x9 11.428  0.177   0.177    0.151    0.151

Add one at a time
Add parameters that make sense

Updating the Model

34     x7 ~~  x8 35.521  0.624   0.624    0.568    0.568

twofactor.model <- 'visual =~ x1 + x2 + x3 
                        speed =~ x7 + x8 + x9 
                        x7 ~~ x8'
twofactor.fit <- cfa(model = twofactor.model,
                     data = HolzingerSwineford1939)
summary(twofactor.fit, standardized = TRUE, 
        fit.measures = TRUE)

User model versus baseline model:
  Comparative Fit Index (CFI)                    0.976
  Tucker-Lewis Index (TLI)                       0.949

Let's practice!

Structural Equation Modeling with lavaan in R