A Chi-Square Goodness-of-Fit Test for Autoregressive Logistic Regression Models with Applications to Patient Screening

We propose a chi-square goodness-of-fit test for autoregressive logistic regression models. General guidelines for a two-dimensional binning strategy are provided, which make use of two types of maximum likelihood parameter estimates. For smaller sample sizes, a bootstrap p-value procedure is discussed. Simulation studies indicate that the test procedure satisfactorily approximates the correct size and has good power for detecting model misspecification. In particular, the test is very good at detecting the need for an additional lag. An application to a dataset relating to screening patients for late-onset Alzheimer’s disease is provided.