I got a question regarding the kind of data I have and suitable analysis methods. What I did is that I collected data over 5 points in time. Subjects could sign up for the study (~1100 did) and then I sent out 5 survey (3 weeks in between every survey) to these 1100 students, and got different numbers of responses each time. My goal is to evaluate differences in the strength of path coefficients in a structural model.
So what I did was to take all the data I have for each t (ranges from 613 to 335), and compared the structural models using multi-group analysis. Now I was told that there are better ways to do that since my models do not control for several biases (such as auto-correlation).
Now, I took a deeper look to identify which kind of data I have, but I start wondering whether I would use this data in that way at all. Since I do not have longitudinal data, since I currently do not ensure that I have data from the same individuals. Furthermore, pooled cross sectional data seems to require to randomly draw from the same population, but I only draw from the people that signed up for the study.
So I wonder if anyone can recommend me what to do. In particular I wonder about the following things:
Does ist make sense at all to use the data this way (kind of cross-sectional over time, but from different individuals)? If yes, which method(s) would be suitable for data analysis?
Another option is that I rely on longitudinal data (I have 284 data sets from the same individuals across all 5 time periods). Would you recommend this? If yes, which method would you use (I know some basics of LGM in Mplus)?