# Help with question comparing logistic regression analyses

I have accounted a problem when trying to finish my analyses. So, I want to compare the beta weights between two logistic regression analyses from independent samples (same IV and DV in both regression analyses). As far as I know, there are not any established tests to test the significance in differences between beta weights. So I have standardized the beta weights and applied the method of comparing the confidence overlap described in the article of G. Cumming from 2009 (Inference by eye: reading the overlap of independent confidence intervals. Stat Med, 28(2), 205-220.). My question: is it accurate to compare the beta weights from two logistic regression models in this way? Appreciated if not trying to overcomplicate the answer. I do not want to be more confused.

• What exactly is different about the beta weights you are mentioning? Does one model have more predictors than another? Commented Oct 22, 2023 at 10:45
• there is nothing different about the models. They have the same predictors. Commented Oct 22, 2023 at 11:20
• How are the beta weights different then? I think there is something missing in your question. Commented Oct 22, 2023 at 11:42
• @ShawnHemelstrand I think the OP has two distinct samples so the coefficients could differ. Commented Oct 22, 2023 at 14:02

Confidence interval overlap is never appropriate, as this disagrees with what you get when you compute the proper confidence limits for differences. Your problem is appropriately and easily addressed by combining the two samples, having an indicator variable say $$s$$ for which sample an observation comes from, and later interacting $$s$$ with all the model variables. Suppose there are $$p$$ model variables and after expanding them to include originally specified nonlinearities and interactions among the Xs there are $$q$$ ($$q \geq p)$$ parameters. Get the likelihood ratio $$\chi^2$$ test statistic for all $$q + 1$$ parameters, with $$q + 1$$ degrees of freedom. Now add all $$q$$ interaction terms between predictor terms and $$s$$ and compute the model likelihood ratio $$\chi^2$$ with $$q + 1 + q$$ degrees of freedom. Subtract the two $$\chi^2$$ to get a $$q$$ degree of freedom test statistic for interaction. This tests whether any of the $$q$$ coefficients differ between the first and second samples. It contains a perfect multiplicity adjustment.