Updated 11-20-02

Multi-group analysis (257-265 in Maruyama, 6.10 and 7.8 in Kline)

1.

In Path analysis

(a)

To test for interaction effect of the groups, hold paths constant across groups and test if there is a significant difference compared to when paths were not held constant across groups.

(b)

To test for mean difference in outcome for the groups, estimate intercepts and compare chi-square when they are held constant to when they are left freely estimated across groups.

2.

In CFA

(a)

We want to test if the latent variables defined the same way in each group

(b)

Recall that to make a CFA identified, we either had to fix a loading to 1 or the variance of the factor to 1.

• For multiple group comparisons, it makes sense to fix the loading to 1 so that way the variance can be different in each group
• Kline tries to make an issue of concern about the fact that the loading fixed to 1 cannot be tested across groups, I'm not sure this is important because we should be testing all the indicators of a particular factor at once.

3.

In SEM or Hybrid Models, just the same as above

Handout of two multi-group examples from Kline 1. Lynam et.al (1993) - delinquency. 2. Kaufman Assessment Battery for Children.

• Must analyze covariance matrices because there may be differences in variability across groups and if a correlation matrix is used (all variables are standardized) this info about differences in variances is lost.
• To make comparison about causal paths across groups it is recommended that the latent variables are being "measured" in the same way. That is, the CFA loadings should be equal across groups.

WE WILL WORK THROUGH A MULTI-GROUP SEM IN LAB