I'd like to conduct a test of measurement invariance for daily diary data based on mood assessments. I have roughly 30 time points (although some individuals have missing data at various time points), and 200-300 participants.
Iíve seen discussion of longitudinal measurement invariance here and elsewhere. But those examples typically focus on a much smaller number of time points. I'm wondering if the following is the most appropriate approach?
*Treat each time point as a factor, allowing the factors to correlate. *Test configural invariance first, before evaluating the change in model fit once factor loadings etc. are constrained to be equal across time points.
My concern is that as a single level analysis, I will have a lot of factors to correlate - will the model encounter problems if my sample is 200-300 participants?
Is there another way to do this analysis (e.g., MLM with time points at level 2 and a clustering effect for individuals as well?)
So you have 6 x 30 = 180 variables if you do it as a wide analysis with a longitudinal factor model. That will be heavy and won't work well with your smallish sample.
You can do it as a twolevel model, so 6 variables, 30 "cluster members", and subject as the level 2 unit, that is, using cluster=id. But then you don't get a test of measurement invariance across time as you would in a wide analysis.
So maybe you can take a wide approach and choose a few critical time points such as beginning, middle, and end in order to have fewer variables. Testing the longitudinal invariance that way.