Goodness of fit for the logistic regression model using relative belief

Luai Al-Labadi; Zeynep Baskurt; Michael Evans

doi:10.1186/s40488-017-0070-7

Goodness of fit for the logistic regression model using relative belief

J Stat Distrib Appl. 2017;4(1):17. doi: 10.1186/s40488-017-0070-7. Epub 2017 Aug 31.

Authors

Luai Al-Labadi¹, Zeynep Baskurt², Michael Evans¹

Affiliations

¹ 1Department of Statistical Sciences, University of Toronto, 100 St. George St., Toronto, M5S 3G3 Canada.
² 2Genetics and Genome Biology, Hospital for Sick Children, 686 Bay Street, Toronto, M5G 0A4 Canada.

Abstract

A logistic regression model is a specialized model for product-binomial data. When a proper, noninformative prior is placed on the unrestricted model for the product-binomial model, the hypothesis H ₀ of a logistic regression model holding can then be assessed by comparing the concentration of the posterior distribution about H ₀ with the concentration of the prior about H ₀. This comparison is effected via a relative belief ratio, a measure of the evidence that H ₀ is true, together with a measure of the strength of the evidence that H ₀ is either true or false. This gives an effective goodness of fit test for logistic regression.

Keywords: Concentration; Model checking; Relative belief ratio.