Mean and median bias reduction in generalized linear models
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This paper presents an integrated framework for estimation and inference from generalized linear models using adjusted score functions for mean and median bias reduction. General expressions for the mean and median bias-reducing adjusted score functions are derived in terms of quantities that are readily available in standard software for fitting generalized linear models. The adjusted score equations are solved using a quasi-Fisher scoring algorithm that is shown to be equivalent to iteratively re-weighted least squares with appropriately adjusted working variates. Inference about the model parameters, including procedures for model comparison, can be done in a plug-in manner using Wald statistics based on the resulting estimators. We further discuss how reduced-bias estimation of multinomial logistic regression can be achieved within this framework via the corresponding Poisson log-linear model, and present a mixed adjustment strategy when the estimation of a dispersion parameter is necessary that relies on core invariance properties that are desirable when using generalized linear models.
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