Permutation invariance of alternating logistic regression for multivariate binary data

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.