A comparison of the Hosmer–Lemeshow, Pigeon–Heyse, and Tsiatis goodness-of-fit tests for binary logistic regression under two grouping methods. Issue 3 (16th March 2017)

• Record Type: Journal Article
• Authors: Canary, Jana D.; Blizzard, Leigh; Barry, Ronald P.; Hosmer, David W.; Quinn, Stephen J.
• Is Part Of: Communications in statistics. Volume 46:Issue 3(2017)
• Page Start: 1871
• Page End: 1894
• Publication Date: 2017-03-16
• Subjects: Binary logistic regression -- Deciles-of-risk -- Goodness-of-fit -- Hosmer–Lemeshow -- Partition the covariate space -- Pigeon–Heyse -- Tsiatis; 62H10; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2015.1017583
• Languages: English
• ISSNs: 0361-0918

Abstract

ABSTRACT: Algebraic relationships between Hosmer–Lemeshow ( HL ), Pigeon–Heyse ( J 2 ), and Tsiatis ( T ) goodness-of-fit statistics for binary logistic regression models with continuous covariates were investigated, and their distributional properties and performances studied using simulations. Groups were formed under deciles-of-risk (DOR) and partition-covariate-space (PCS) methods. Under DOR, HL and T followed reported null distributions, while J 2 did not. Under PCS, only T followed its reported null distribution, with HL and J 2 dependent on model covariate number and partitioning. Generally, all had similar power. Of the three, T performed best, maintaining Type-I error rates and having a distribution invariant to covariate characteristics, number, and partitioning.