Canadian Journal of Statistics

Conditions for consistent estimation in mixed‐effects models for binary matched‐pairs data

Journal Article

Abstract

Parametric mixed‐effects logistic models can provide effective analysis of binary matched‐pairs data. Responses are assumed to follow a logistic model within pairs, with an intercept which varies across pairs according to a specified family of probability distributions G. In this paper we give necessary and sufficient conditions for consistent covariate effect estimation and present a geometric view of estimation which shows that when the assumed family of mixture distributions is rich enough, estimates of the effect of the binary covariate are typically consistent. The geometric view also shows that under the conditions for consistent estimation, the mixed‐model estimator is identical to the familar conditional‐likelihood estimator for matched pairs. We illustrate the findings with some examples.

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