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Score test for goodness of fit of generalized linear models to sparse data. (English) Zbl 1192.62175
Summary: We develop a score test statistic based on quasi-score functions for goodness of fit of generalized linear models with sparse data. A modified score test statistic is also obtained. The modified score test statistic has a simple form and is closely related to the test statistic based on the modified Pearson statistic developed by C.P. Farrrington [J. R. Stat. Soc., Ser. B 58, No. 2, 349–360 (1996; Zbl 0866.62040)]. The modified score test statistic is greater than or equal to the standardized modified Pearson statistic. For Poisson data the modified score test statistic is identical to the standardized modified Pearson statistic. For binomial data the modified score test statistic is, in general, more powerful than the test based on the modified Pearson statistic. The gain in power of the modified Pearson statistic and the modified score statistic over the score statistic may be substantial.

MSC:
62J12 Generalized linear models (logistic models)
62G10 Nonparametric hypothesis testing
62F03 Parametric hypothesis testing
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