High SRMR in complex model due to residual measurement invariance?

[Anja Morstatt]

Hi all, 

I would like to get some crowd intelligence on a more conceptual issue that I encountered with a model of mine. 

In my final model, I have three time points, where I would like to assess an indirect effect of X to Y via M. For Y and M, I control for the stability. Therefore, I investigated measurement invariance prior to setting up the complex model. I did so per construct individually - and from these analyses, residual measurement invariance (MI) assumptions fit the models well (all indicators within recommended ranges). So in my complex model, I used this model, but fit decreased (but still acceptable) and the SRMR value was almost 1 (no joke!). I compared observed and implied model covariance matrix and saw that most misfit was within the cluster of items that are modelled with the residual MI. I took that out and only modelled metric MI (minimum required, as far as I know), and fit is as expected all within range. 

What I do not fully understand and would appreciate some expert weighing in here, is how the longitudinal measurement model can be fine when individually assessed, but causing so severe problems in the complex model? I was so far under the assumption that relationships with other constructs are explained via latent variable associations, so why does adding the other variables "create" misfit in the measurement model? 

I would appreciate ideas and potential explanations -  and if further information from my side is needed, I'd be happy to provide that. 

Thanks a lot and BR

Anja

[Prof. Gavin Brown]

Perhaps the problem lies in that over time only metric equivalence is required. After all change over time is likely to appear in the intercept values.

this chapter argues for just metric equivalence in longitudinal analysis.

McArdle, J. J. (2007). Five steps in the structural factor analysis of longitudinal data. In R. Cudeck & R. C. MacCallum (Eds.), Factor analysis at 100: Historical developments and future directions (pp. 99-130). LEA.