Comparing logistic regressions

What is an appropriate way to test whether two logistic regressions are significantly different from one another?

Essentially, I have two similar logistic regressions made from two different sets of data, and one made from the two data sets combined. I'd like to be able to perform further analyses on the whole data set using the regression made from combining the data sets, but first I have to be sure that the relationship is not significantly different from either of the two original regressions. I'd also like to know if the two separate original regressions are different from one another. Is there a straightforward way to do this?

Thanks!!

• Welcome to this site. A search at the upper right for "compare logistic" comes up with multiple threads that should help you. But I'd also like to ask what you have tried so far. Commented Jan 22, 2012 at 22:33

For example if you had one predictor $X_1$, you would fit the following model:
$$logit(p_i) = \beta_0 + \beta_1 \cdot Pop + \beta_2 \cdot X_1 + \beta_3 \cdot Pop \cdot X_1$$
Then you can test whether constraining $\beta_1$ and $\beta_3$ to zero significantly worsens the fit of the model using a likelihood ratio test (LRT). These two variables give the difference in the intercept and slope coefficients in the linear prediction equation when Pop is one versus zero; if you can set them to zero and not significantly worsen the fit of your model, it suggests you can use the same regression model for both data sets.