I have 2 latent variable predictors (X & Z) and 1 DV that is categorical (Y). Running the model separately for each IV, X predicts Y & Z predicts Y. However, when I have both X & Z predicting Y, neither is statistically significant. My DV is categorical, so Mplus doesn't give me the residual variance for it. However, in the Brown (2006) book, it says that the residual variance for categorical indicators is 1 minus the squared standardized solution. Thus, I assume that the square of the standardized solution for each predictor is the amount of variance accounted for in the categorical DV. When I have X & Z predicting Y, the sum of their squared standardized loadings is less than what I get for each of them individually. It seems to me like I'm not accounting for the shared effects of X & Z on Y. Is that correct? If so, how can I get this information?
I created factor scores for my latent variables (X & Z), and ran a logistic regression. In the logistic regression, when I have both X & Z predicting Y, neither is individually statistically significant, but that step is statistically significant. I'm just not sure how to show that in an SEM (i.e., that both things together are predicting). It seems to me that whatever is common between X & Z is driving the relationship that I find in the regression. Any information you have would be very helpful. Thanks!