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.
In the same vein as the questions above, I am evaluating a longitudinal measurement invariance model. In short, the model is a 2-factor model with 4 indicators each across 4 time points. N = 280. When I set up the configural model, it runs fine except for the warning noted above that there may be a linear dependency etc. and to check Tech 4. None of the latent variable corrs are > .85 and the variances across time are set = 1 so there is not a negative latent variance. I have tried constraining factor covars across time to equality but this doesn't work.
Two queries: what are the implications of ignoring this warning and
is it possible that my sample size is simply too small for this longitudinal configuration?
Thank you. I had been running this longitudinal invariance setup on a subset (validation sample) of a larger sample. When I run this setup on the full sample, the warning disappears. My inclination is this points to sample size issues.
A query: if I do an EFA on a calibration sample, confirm CFA on a validation sample (other half of the sample) and then do longitudinal invariance on the full sample, does this go against the grain of best practice in confirming a measurement model in an independent sample? In short, I confirm with the other half (validation sample) but would be demonstrating long. invar. with the full sample. I want to make use of the available data as best as possible while maintaining best practices.