Transformed goodness-of-fit statistics for a generalized linear model of binary data

Nobuhiro Taneichi, Yuri Sekiya and Jun Toyama

Journal of Multivariate Analysis, 2014, vol. 123, issue C, 311-329

Abstract: In a generalized linear model of binary data, we consider models based on a general link function including a logistic regression model and a probit model as special cases. For testing the null hypothesis H0 that the considered model is correct, we consider a family of ϕ-divergence goodness-of-fit test statistics Cϕ that includes a power divergence family of statistics Ra. We propose a transformed Cϕ statistics that improves the speed of convergence to a chi-square limiting distribution and show numerically that the transformed Ra statistic performs well. We also give a real data example of the transformed Ra statistic being more reliable than the original Ra statistic for testing H0.

Keywords: Asymptotic expansion; Binary data; ϕ-divergence statistics; Generalized linear model; Improved transformation (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.jmva.2013.09.014

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