Permutation invariance of alternating logistic regression for multivariate binary data

Author: Kuk, Anthony Y. C.

Source: Biometrika, Volume 91, Number 3, September 2004 , pp. 758-761(4)

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Abstract:

A practically important but not so obvious result is that alternating logistic regression is invariant to permutations of the response variables within clusters. In this note, we give a short proof of the invariance result using a pairwise likelihood argument. The same proof can be used to establish invariance for a more general class of estimating equations based on conditional residuals. As it stands, the invariance theory is incomplete because existing standard error estimates are not invariant to permutations. To solve this problem we present a symmetrised version of the estimating equation and use it to obtain permutation-invariant standard errors.

Keywords: Clustered data; Conditional residual; Generalised estimating equation; Longitudinal data; Pairwise likelihood

Document Type: Research article

Affiliations: 1: Department of Statistics & Applied Probability, National University of Singapore, 6 Science Drive 2, Singapore 117546, Email: stakuka@nus.edu.sg

Publication date: 2004-09-01