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Cited by 514Statistical Methods and Bayesian InferenceStatistical Methods in EpidemiologyStatistical Methods and Applications

Modelling multivariate binary data with alternating logistic regressions

CAREY, VINCENT, ZEGER, SCOTT L., DIGGLE, PETER·1993·Biometrika
DOI 10.1093/biomet/80.3.517
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Abstract

Marginal models for multivariate binary data permit separate modelling of the relationship of the response with explanatory variables, and the association between pairs of responses. When the former is the scientific focus, a first-order generalized estimating equation method (Liang & Zeger, 1986) is easy to implement and gives efficient estimates of regression coefficients, although estimates of the association among the binary outcomes can be inefficient. When the association model is a focus, simultaneous modelling of the responses and all pairwise products (Prentice, 1988) using second-order estimating equations gives more efficient estimates of association parameters as well. However, this procedure can become computationally infeasible as the cluster size gets large. This paper proposes an alternative approach, alternating logistic regressions, for simultaneously regressing the response on explanatory variables as well as modelling the association among responses in terms of pairwise odds ratios. This algorithm iterates between a logistic regression using first-order generalized estimating equations to estimate regression coefficients and a logistic regression of each response on others from the same cluster using an appropriate offset to update the odds ratio parameters. For clusters of size n, alternating logistic regression involves evaluation and inversion of matrices of order n2 rather than n4 as required for second-order generalized estimating equations. The alternating logistic regression estimates are shown to be reasonably efficient relative to solutions of second-order equations in a few problems. The new method is illustrated with an analysis of neuropsychological tests on patients with epileptic seizures.

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Authors
CAREY, V., ZEGER, S. L., & DIGGLE, P.
Affiliations
  • Johns Hopkins University (US)
  • Lancaster University (GB)
ORCID
Venue
Biometrika
Publisher
Oxford University Press (OUP)
Published
1993
Volume
80
Issue
3
Pages
517-526
ISSN
  • 0006-3444 (ISSN-L)
  • 1464-3510
DOI
10.1093/biomet/80.3.517
OpenAlex
W1969672258
Cited by
514
References
17
Citations by year
2026: 5 · 2025: 3 · 2024: 7 · 2023: 12 · 2022: 5 · 2021: 12 · 2020: 20 · 2019: 13 · 2018: 13 · 2017: 15 · 2016: 10 · 2015: 14 · 2014: 14 · 2013: 26 · 2012: 44
FWCI
8.60
Type
journal article
Language
en
Open access
closed
Locations
  • Biometrika (publishedVersion)
  • Lancaster EPrints (Lancaster University) (submittedVersion)
Funders
  • National Institutes of Health
  • Merck Sharp and Dohme
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords
multivariate binary data, marginal models, generalized estimating equations, computational efficiency, cluster size, neuropsychological assessment, epileptic seizures

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