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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:123

Article

Taneichi, Nobuhiro¹  Sekiya, Yuri²  Toyama, Jun³ 

[1] Kagoshima Univ, Grad Sch Sci & Engn, Dept Math & Comp Sci, Kagoshima 89000065, Japan

[2] Hokkaido Univ, Kushiro, Hokkaido 0858580, Japan

[3] Inst Use Math, Sapporo, Hokkaido 0630001, Japan

关键词: Asymptotic expansion;    Binary data;    phi-divergence statistics;    Generalized linear model;    Improved transformation;   

DOI  :  10.1016/j.jmva.2013.09.014

来源: Elsevier

【 摘 要 】

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 H-0 that the considered model is correct, we consider a family of phi-divergence goodness-of-fit test statistics C-phi that includes a power divergence family of statistics R-a. We propose a transformed C-phi statistics that improves the speed of convergence to a chi-square limiting distribution and show numerically that the transformed R-a statistic performs well. We also give a real data example of the transformed R-a statistic being more reliable than the original R-a statistic for testing H-0. (C) 2013 Elsevier Inc. All rights reserved.

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