3
$\begingroup$

A Chi-square (p-value) of a single group SEM is easy to interpret. It is a measure of exact fit.

When one runs a multiple group, say grouping the data by gender or by the presence of a condition like a disease, lavaan outputs a chi-square, together with the chi-square of the particular groups.

How to interpret that general multigroup chi-square? I have applied a same model to two groups, one with and the other without the diagnosis of schizophrenia. In that case the single non-significant chi-square allows me to say that schizophrenia mediates whatever relation I am evaluating in the path?

I am aware that I have to run invariance tests after the multigroup analysis, but I am curious about the particular interpretation of that Chi-square.

$\endgroup$

1 Answer 1

4
$\begingroup$

Ideally, invariance tests would culminate in a model that constrained the path between the "mediating" factor and the outcome factor to equality across groups. Global $\chi^2$ values are used to evaluate relative fit between models representing different levels of invariance.$^1$ Assuming measurement invariance has been established,$^2$ testing for mediation would be accomplished by constraining the relevant structural paths to equality across groups and conducting $\Delta\chi^2$ tests.

$^1$ Cheung and Rensvold (2002) recommend using $\Delta$CFI when testing invariance across groups. $\Delta$CFI values above .01 represent non-trivial group differences.

$^2$ People have different opinions about this. Most would agree that you need to provide evidence of weak (or metric) invariance (same factors and loadings constrained to equality across groups).

$\endgroup$
2
  • $\begingroup$ Lovely, Mike. I am so grateful for your answer. Now it is clear to me. One other thing, can I report metric invariance without having reported configural invariance, for example? Or they have to be all reported in all cases? $\endgroup$
    – lf_araujo
    Commented Oct 27, 2015 at 20:04
  • $\begingroup$ A lot paper have tables that include fit statistics for each model. Some papers make it a footnote. And others just reference that they checked it. I suppose it depends on how important those line of tests are and what the reviewers think. $\endgroup$
    – mkearney
    Commented Oct 29, 2015 at 16:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.