I am working with three factor models predicting various outcomes (one at a time), and I would like to compare these models in terms of the observed r-squares for the outcomes (e.g., does one model produce a higher r-square than another in the same outcome variable). However, my three factor models have different numbers of latent factors, so I would like to make r-square comparisons among these models using adjusted r-squares. I know that mplus does not provide these values, and I also know that in regression I could convert my r-square values into adjusted r-square values using: adjusted r-square = 1 - ( (1-R-sq)(N-1 / N - k - 1) ). My question is: can I use this same formula for my SEM models even though my "k" are latent factors (indicated by many observed categorical variables). So, for example, if my model has 3 latent factors, indicated by 14 observed categorical variables, and my 3 latent factors are all predicting a single categorical outcome variable, does "k" = 3 for the adjusted r-square formula above? Or is this formula altogether inappropriate for my situation?
Neither Bengt nor I are familiar with the adjusted r-square. I don't think the issue is whether the variables are latent versus observed. I think the issue would be if you meet the assumptions of this test.
Can you think of any alternative method (other than comparing adjusted r-square values) that I could use to compare r-square values from various dependent variables predicted by multiple factor models? Specifically, say I have two measurement (i.e., factor) models, and I construct several SEM models such that each factor model predicts multiple outcomes one at a time (i.e., so if there are two measurement models and 25 outcomes of interest; there would be 50 SEM models total, each factor model predicting each outcome one at a time). I would like to be able to report which measurement model did a better job of predicting outcomes (i.e., on average, across outcomes), but I can't think of a way to do so. Any guidance would be appreciated.