I am fitting a bifactor IRT model using MLR with 4 latent factors (one primary, three group factors) onto 42 items of categorical data (three categories). Mplus provides a loglikelihood that I have used to test fit against a unidimensional IRT model (-2ll, using scaled X^2). Is there any other way I might judge the fit of the bifactor model with information Mplus provides?
Thank you. A loglikelihood test suggest superior fit for the bifactor model over the unidimensional model. The bifactor model does have many significant bivariate residuals, however. I wonder if from this I would conclude that, although my data is multidimensional, the bifactor structure may not account for its multidimensionality adequately. Would this be correct? I know I have provided little in terms of context, but I wonder if you see any other interpretations of these findings?
I noticed that BVRs are given per category for categorical items. In the data I am using the category response distributions (3 categories) show substantial positive skew. Might this have any bearing on the many significant BVRs?