Comparing Latent Means from Different Latent Factors across Groups and Time

[rpc...@psu.edu]

Hello,

I am currently working on an analysis where I am interested in looking at latent mean differences among four groups at three timepoints with a two-factor latent variable model specified at each timepoint. I've used the measEq.syntax() function from semTools to help get the necessary syntax for lavaan to estimate the configural, metric, and scalar models. Everything seems to be working as it should, and by setting the latent means for both factors to zero at the first timepoint in one of my groups, I am able to look at latent mean differences within the multiple group CFA context. It is my understanding, however, that the latent mean differences are within a factor (e.g., group 1 vs group 2 on Factor A) as opposed to between factors (e.g., group 1 on Factor A vs group 2 on Factor B). I can think of two ways to try to compare latent means between groups and factors:

1. Adjust the syntax so that only one factor in one group is constrained to 0 and re-estimate the model. I believe this should make the estimated latent means on the other factor for the other groups be the latent mean difference for those groups on that factor and the reference group/factor.

2. Use the ':=' operator to define a new parameter in the originally estimated model, which would be the difference between two groups on the model estimated latent means for each factor (e.g., NewParameter := Group1FactorAMean - Group2FactorBMean).

Are either, or both, of these approaches an appropriate way to go about estimating latent mean differences between groups and factors in lavaan?

Thank you,

Ryan

[Ingo Man]

Dear Ryan,

this is an interesting question. Technically, this should be possible as long as the indicators of the respective factor were asked on exactly the same response scale. However, the question certainly remains open as to what extent measurement invariance can be used for such a comparison of (latent) mean values that are not identical in content; I do not have an answer to this at the moment. Please let us know if you find an answer to that.
Testing, whether the latent mean values do differ statistically different from each other can be done via := - constraints. If your indicators per factor all have the same scaling, I would always work with the effects-coding approach, here the mean values are displayed directly for all groups (use the unstandardized solution), no factor loading has to be fixed to one or the factor variance. Hope that helps a bit.

Kindly,

marcus