Bayes finally reached Mplus

In 2007, “Structural Equation Modelling: A Bayesian Approach” was published by Sik-Yum Lee. This monograph gave the first full account on Bayesian SEM. However, interested readers may struggle with the WinBUGS software introduced in the monograph. The good news is now: Four new documents describing Bayesian analysis in Mplus are now available! I especially recommend this article: Muthén, B. (2010). Bayesian analysis in Mplus: A brief introduction. Technical Report. Version 3.

Invariance testing using lavaan

Today, Michael showed me the lavaan function <measurement.invariance>. I instantly was delirious with joy: While in AMOS one struggles through several chi-square difference test tables, lavaan provides an easy to read output – no more, no less.

Measurement invariance tests:

Model 1: configural invariance
chisq      df  pvalue    cfi    tli  rmsea       bic
18.570 26.000   0.854  1.000  1.010  0.000  9979.522

Model 2: weak invariance (equal loadings):
chisq      df  pvalue    cfi    tli  rmsea       bic
25.096 31.000   0.763  1.000  1.007  0.000  9956.090

[Model 1 versus model 2]
delta.chisq  df  p.value  delta.cfi
6.53   5  0.25838     0.0000

Model 3: strong invariance (equal loadings + equal intercepts):
chisq       df  pvalue    cfi    tli  rmsea        bic
28.078  36.000   0.824  1.000  1.008  0.000  10012.996

[Model 1 versus model 3]
delta.chisq  df  p.value  delta.cfi
9.51  10  0.48469     0.0000

[Model 2 versus model 3]
delta.chisq  df  p.value  delta.cfi
2.98   5  0.70275     0.0000

Model 4: equal loadings + intercepts + means:
chisq      df  pvalue     cfi    tli  rmsea        bic
31.045  38.000    0.781  1.000  1.008  0.000  10003.979

[Model 1 versus model 4]
delta.chisq  df  p.value  delta.cfi
12.47 12  0.40837     0.0000

[Model 3 versus model 4]
delta.chisq  df  p.value  delta.cfi
2.97   2  0.22687     0.0000