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Goodness of fit of generalized linear models to sparse data

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We derive approximations to the first three moments of the conditional distribution of the deviance statistic, for testing the goodness of fit of generalized linear models with non-canonical links, by using an estimating equations approach, for data that are extensive but sparse. A supplementary estimating equation is proposed from which the modified deviance statistic is obtained. An application of a modified deviance statistic is shown to binomial and Poisson data. We also conduct a performance study of the modified Pearson statistic derived by Farrington and the modified deviance statistic derived in this paper, in terms of size and power, through a small scale simulation experiment. Both statistics are shown to perform well in terms of size. The deviance statistic, however, shows an advantage of power. Two examples are given.
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Keywords: Binomial and Poisson linear model; Deviance statistic; Generalized linear model; Power; Size; Sparse data

Document Type: Research Article

Affiliations: University of Windsor, Canada

Publication date: February 1, 2000

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