Testing measurement invariance and latent mean differences in lavaan

[Sara]

Hello everyone,

 I have been testing for measurement invariance following the instructions of Svetina et al. 

I compared the configural model with the threshold invariance model, and then tested loading invariance (both item thresholds and factor loadings are constrained to equality)  against threshold invariance. The results support loading invariance, so I proceeded to compare the latent means across over time.

As usual, I set the latent mean of the first year (the reference group) to 0. The estimated latent means for the other years are reported in the attached table.

Now, instead of only comparing each group mean against the reference year, I would also like to obtain pairwise comparisons of consecutive years ( 2002–2000, 2004–2002, etc.). My idea was to compute these differences and then apply a Wald test to evaluate their statistical significance. Is this approach correct? 

Thanks in advanced 

[Jeremy Miles]

First I would test equality of all means (as a general rule, looking at your  estimates this test is going to be statistically significant).

I don't see any reason not to do this (looking at your table, I'm going to guess that these will all be statistically significant, so I'm not sure it's necessary though.)

Jeremy

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[Alex Schoemann]

If you want you can also apply a Tukey test to pairwise comparisons latent means. There's a function TukeySEM in the SEM tools package (for each pairwise comparison you provide the mean, variance and sample size for each group. There's nothing magically "SEM-y" about the function, it just applies a Tukey test with unequal variances and sample sizes but it should work in your case.

Alex

[Terrence Jorgensen]

The results support [threshold and] loading invariance, so I proceeded to compare the latent means across over time.

Comparing latent means additionally requires equivalence of intercepts (unless you are using the project method, which I don't think has been developed for treating ordinal indicators as discretized normal latent responses).

 

I would also like to obtain pairwise comparisons of consecutive years ( 2002–2000, 2004–2002, etc.). My idea was to compute these differences and then apply a Wald test to evaluate their statistical significance. Is this approach correct? 

Yes, that's one way.  If your means are labeled, you can either define new parameters to represent each difference (so their Wald z tests appear in your summary() output, or specify equality constraintss= using the lavWaldTest() function to obtain an equivalent 1-df Wald chi-squared statistic.

Terrence D. Jorgensen    (he, him, his)
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
http://www.uva.nl/profile/t.d.jorgensen