A generalized-moments specification test for the logistic link

Abstract

The authors consider the problem of testing the validity of the logistic regression model using a random sample. Given the values of the response variable, they observe that the sample actually consists of two independent subsets of observations whose density ratio has a known parametric form when the model is true. They are thus led to propose a generalized-moments specification test in detail. In addition, they show that this test can be derived using Neyman's smooth tests for goodness of fit. They present simulation results and apply the methodology to the analysis of two real data sets.