Exact goodness-of-fit test for binary logistic model

Logistic regression is a widely applied tool for the analysis of binary res ponse variables. Several test statistics have been proposed for the purpose of assessing the goodness of fit of the logistic regression model. Unfortu nately, 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 approx imation becomes unreliable. In this article, an exact conditional goodness- of-fit test for the logistic regression model with grouped binomial respons e data is proposed. Two efficient algorithms are presented for carrying out the exact conditional goodness-of-fit test in small sample studies. Two da ta sets from an animal carcinogenesis experiment and a study on self-esteem are analyzed to demonstrate the methods.