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An omnibus lack of fit test in logistic regression with sparse data

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  • Ying Liu
  • Paul Nelson
  • Shie-Shien Yang

Abstract

The usefulness of logistic regression depends to a great extent on the correct specification of the relation between a binary response and characteristics of the unit on which the response is recoded. Currently used methods for testing for misspecification (lack of fit) of a proposed logistic regression model do not perform well when a data set contains almost as many distinct covariate vectors as experimental units, a condition referred to as sparsity. A new algorithm for grouping sparse data to create pseudo replicates and using them to test for lack of fit is developed. A simulation study illustrates settings in which the new test is superior to existing ones. Analysis of a dataset consisting of the ages of menarche of Warsaw girls is also used to compare the new and existing lack of fit tests. Copyright Springer-Verlag 2012

Suggested Citation

  • Ying Liu & Paul Nelson & Shie-Shien Yang, 2012. "An omnibus lack of fit test in logistic regression with sparse data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 437-452, November.
    • Handle: RePEc:spr:stmapp:v:21:y:2012:i:4:p:437-452
    DOI: 10.1007/s10260-012-0197-0
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    References listed on IDEAS

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    1. Joseph Pigeon & Joseph Heyse, 1999. "A cautionary note about assessing the fit of logistic regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 847-853.
    2. Xie, Xian-Jin & Pendergast, Jane & Clarke, William, 2008. "Increasing the power: A practical approach to goodness-of-fit test for logistic regression models with continuous predictors," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2703-2713, January.
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