I’m currently revisiting some prior analytical work in light of decisions I made in the past (e.g., dealing with missing data, examining measurement invariance). I’m basically examining whether psychological tests that have been administered under different methodological conditions (e.g., randomized items vs. non-randomized items) satisfy constraints for invariance. The datasets are small (N ~ 150) and contain missing data, so I'm trying to make every captured datapoint count.
I'm not entirely sure were I should begin. The various semTools functions, specifically the measurementInvarianceCat() and cfa.mi() functions, seem to be helpful but I have not gotten very far. While the former can deal with missing data using pairwise deletion, I would much prefer to impute missing data and then analyze that dataset. The latter does not seem to test measurement invariance.
Additionally, the data that I’ve collected are highly skewed. In fact, when I fit a model to my data using DWLS estimation, lavaan notifies me that certain categories of variables are empty in a certain group. Often, it is the case that these are response categories toward the low end of the scale (e.g., "strongly disagree" and "disagree"). I’ve decided to collapse responses for low base-rate response categories (e.g., “strongly disagree” and “strongly agree”), which addresses the error. Admittedly, I’m unsure of exactly what this implies for my model or if there are better ways of handling such skewed data.
What advice would you have to give on this? I’ve been working at this for several hours now and am at a loss as to where to begin.
Thanks in advance,