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On the use of between-within models to adjust for confounding due to unmeasured cluster-level covariates. (English) Zbl 1372.62025
Summary: Between-within models are generalized linear mixed models (GLMMs) for clustered data that incorporate a random intercept together with fixed effects for within-cluster and between-cluster covariates; the between-cluster covariates represent the cluster means of the within-cluster covariates. One popular use of these models is to adjust for confounding of the effect of within-cluster covariates due to unmeasured between-cluster covariates. Previous research has shown via simulations that using this approach can yield inconsistent estimators. We present theory and simulations as evidence that a primary cause of the inconsistency is heteroscedasticity of the linearized version of the GLMM used for estimation.
62J12 Generalized linear models (logistic models)
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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