I'm trying to find the optimal number of exploratory dimensions to explain covariance in a data set with 20 psychopathology items and (highly skewed) 4-point ordered categorical responses to each.
Though I have over 30 000 response sets, I don't want to lose any information, and missingness seems to be random, so I'm using MLR of all available categorical responses under EFA.
I've tried up to a seven-dimensional model, which is still interpretable, though memory constraints (16 GB) limit the adaptive integration to 3 integration points per dimension (3^7=2187). I seem to get a better fit with the Monte Carlo integration of the same number of points, so my question is this:
If I want to compare e.g. the 6- and 7-dimensional models with the BIC, how many integration points should I use for the adaptive MC integration? Always as many as available RAM allows, or scale it by the number of dimensions, for instance to 3^6 and 3^7 points?
I would recommend using the same number of integration points for the two runs you are comparing. Also I would recommend using the WLSMV estimator just for comparison (that estimator assumes missing completely at random)