A Comparison of the Hosmer-Lemeshow, Pigeon-Heyse, and Tsiatis Goodness-of-fit Tests for Binary Logistic Regression Under Two Grouping Methods

Jana Canary, Leigh Blizzard, Ronald Barry, David Hosmer, Stephen Quinn

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    Algebraic relationships between Hosmer–Lemeshow (HL), Pigeon–Heyse (J2), 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 J2 did not. Under PCS, only T followed its reported null distribution, with HL and J2 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.

    Original languageEnglish
    Pages (from-to)1871-1894
    Number of pages24
    JournalCOMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
    Volume46
    Issue number3
    Early online date2017
    DOIs
    Publication statusPublished - 16 Mar 2017

    Keywords

    • Binary logistic regression
    • Deciles-of-risk
    • Goodness-of-fit
    • Hosmer–Lemeshow
    • Partition the covariate space
    • Pigeon–Heyse
    • Tsiatis

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