Having a repeated survey of four waves, we want to test measurement invariance over time of our instruments. Due to the dependent nature of our measures, we built a single group model with four latent variables (each for each wave).
However, the sample sizes of each wave differ remarkably: We started with 3000 participants in wave 1, but took only 400 specifically chosen participants for the following waves 2, 3, and 4. Now, we are quite unsure of how to deal with this "attrition", which is the best way to handle this design?
1) Shall we compute measurement invariance over time only for the 400 persons who participated in all waves and apply a ML estimator, which is robust against non-normality of outcomes and non-independence of observations (such as MLM, MLR)? 2) Or are we allowed to apply the default ML estimator and include the 2600 remaining persons into our analysis? Does FIML still deliver robust estimates although we deliberately lost 80% of our sample after the first wave? 3) Or shall we regard our data as a specific form of a nested design and hence have to use the "TYPE=COMPLEX" command and its estimators?
Which of these options would be preferable? Or are we still missing anything?
Any feedback you can provide will be most appreciated! Thank you!
The question is how you selected the participant for the later waves. If it was random or if it was based on the values of the outcomes in wave 1 you are fine when using the default ML MAR approach of Mplus. This approach considers the outcomes for all waves and uses all available observed data.
Nesting is handled by analyzing all your time points together and letting them correlate according to a model such as growth modeling.