I am doing a multinomial logistic regression in R for an outcome variable with four categories, and 9 categorical independent variables. My dataset contains 1408 observations. When I run the model with all variables, the GVIF (1/2*df) values are good. However, when I compare the odds ratios of the multivariable model with univariable models for each predictor, the direction of the odds ratio changes for the variable gender, and for the intercept of one group. When I leave the variable gender out of the model this still happens to the intercept of that group. I am not sure how to interpret is. I also tested interactions between gender and the other predictor variables, and those are non-significant. I know that changes in odds ratios/regression signs can be a case of multicollinearity, but can there be other explanations as this does not seem to be the case here?
1 Answer
I would not worry about the intercept terms unless there is some reason to do so. In general, they aren't too informative or interesting as you are usually interested in the independent variables and the dependent variable.
The fact that the sign for the parameter for sex changes when you add other variables means that, controlling for those variables, the shape of the relationship between sex and the DV changes. This can only happen if the variables are not completely orthogonal, but it doesn't have to involve a problematic level of collinearity.
One way this can happen is if two of the IVs (sex and another) are mediators (in one direction or another). Interactions (which you looked at) are about moderation rather than mediation -- it is easy to get these two confused.
There is a tag for mediation, which might be useful to look at.
