Comparing logistic regression coefficients between different datasets I have multiple datasets coming from different distributions but having the same dependent and independent variables. I am running a logistic regression on each of the datasets and I would like to somehow compare the regression coefficients between the models, eg. test if they are the same across all models, since I am using backward elemination the variable kept in the models differ in some cases. Is there a way to do this? I though about using a F-test, but I am not sure if this applicable since the underlying data differs between the models.
Thank you in advance!
 A: Append the two datasets and create a new variable denoting which dataset each observation belongs to. Fit a logistic regression that includes the predictors, the dataset variable, and the interaction between the dataset variable and each of the predictors. The coefficient on each interaction term corresponds to the difference between each coefficient in the two datasets. For an omnibus test of whether the models differ at all, fit a model without the dataset variable and compare it to the full model using a likelihood ratio test.
A: If you have different variables in the models, then the coefficients are automatically different for that reason alone, and it is not an interesting comparison to make. But if you have the same variables it becomes more interesting. In this case you can test the differences simultaneously using a likelihood ratio test, and you can compare individual coefficients using Wald intervals for the differences.  You can do all this in the context of a model that uses dummy variables to model different "distributions," although if I understand correctly, a better term would be "groups" rather than "distributions."
