Statistica Sinica 11(2001), 199-211
Abstract: Logistic regression is a widely applied tool for the analysis of binary response variables. Several test statistics have been proposed for the purpose of assessing the goodness of fit of the logistic regression model. Unfortunately, analysis based on these test statistics requires a moderately large sample size so that the chi-square approximation can be applied. When the sample size is small or the data structure is sparse, the asymptotic approximation becomes unreliable. In this article, an exact conditional goodness-of-fit test for the logistic regression model with grouped binomial response data is proposed. Two efficient algorithms are presented for carrying out the exact conditional goodness-of-fit test in small sample studies. Two data sets from an animal carcinogenesis experiment and a study on self-esteem are analyzed to demonstrate the methods.
Key words and phrases: Exact inference, goodness-of-fit test, grouped binomial response data, recursive algorithm.