# Measurement invariance Chisquare difference test statistic - ordinal variables

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### Ignazio Craparo

Feb 27, 2020, 6:35:17 PM2/27/20
to lavaan
Hi everyone,

I'm working on testing measurement invariance in 3 groups using cfa() with 54 ordinal variables (5 points Likert type) and 8 latent factors.
My question regards on whether the Chisquare statistic with method="satorra.bentler.2010" is reliable or affected by sample size, complexity of the estimated.
Regarding the Difference in CFI, TLI and RMSEA I'm not sure on what cut-off values should I choose, someone suggests to use the .01 for delta.CFI and 0.015 for delta.RMSEA, others 0.001 for CFI.
Is there also a function I could use to "automatically" check for constraints to free for partial invariance? Having so many variables and thresholds make things complex.

Thank you in advance!!

Best regards

### Terrence Jorgensen

Mar 21, 2020, 9:39:16 AM3/21/20
to lavaan
My question regards on whether the Chisquare statistic with method="satorra.bentler.2010" is reliable or affected by sample size, complexity of the estimated.

The test statistic is always affected by these things. You could test invariance of 1 factor at a time to reduce the size of the model relative to N.

Regarding the Difference in CFI, TLI and RMSEA I'm not sure on what cut-off values should I choose, someone suggests to use the .01 for delta.CFI and 0.015 for delta.RMSEA, others 0.001 for CFI.

None, a fixed cutoff for the change in a fit index is never consistent.  If you are going to use a critical value, it should be one from a known distribution for the statistic, so that sampling variability is properly accounted for.

Is there also a function I could use to "automatically" check for constraints to free for partial invariance? Having so many variables and thresholds make things complex.

The semTools package has a function partialInvarianceCat() that might be useful.

Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam