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.


1 Answer 1


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).

  • $\begingroup$ 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

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