Improving the Hosmer-Lemeshow Goodness-of-Fit Test in Large Models with\n Replicated Trials

2021/02/25 by Nikola Surjanovic, Surjanovic, Nikola, Thomas M. Loughin +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Advanced Causal Inference Techniques #Applications (stat.AP) #Economic and Environmental Valuation #FOS: Computer and information sciences #Forecasting Techniques and Applications #Methodology (stat.ME) #Multi-Criteria Decision Making

paper · pdf · doi:10.48550/arxiv.2102.12698

openalex publication_date 2021/02/25 · openalex created_date 2023/11/01 · openalex updated_date 2026/07/28

Abstract

The Hosmer-Lemeshow (HL) test is a commonly used global goodness-of-fit (GOF)\ntest that assesses the quality of the overall fit of a logistic regression\nmodel. In this paper, we give results from simulations showing that the type 1\nerror rate (and hence power) of the HL test decreases as model complexity\ngrows, provided that the sample size remains fixed and binary replicates are\npresent in the data. We demonstrate that the generalized version of the HL test\nby Surjanovic et al. (2020) can offer some protection against this power loss.\nWe conclude with a brief discussion explaining the behaviour of the HL test,\nalong with some guidance on how to choose between the two tests.\n

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