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\noindent Statistica Sinica {\bf 11}(2001), 199-211
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\centerline{\large\bf EXACT GOODNESS-OF-FIT TEST FOR}
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\centerline{\large\bf BINARY LOGISTIC MODEL}
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\centerline{Man-Lai Tang}
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\centerline{\it The Chinese University of Hong Kong}
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\begin{quotation}
\noindent {\it Abstract:}
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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.\par
\vspace{9pt} \noindent {\it Key words and phrases:}
Exact inference, goodness-of-fit test, grouped binomial response data,
recursive algorithm.                \par
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