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Abstract:
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I am very pleased to participate in this session in honor and memory of Professor Donald A S Fraser. I first met Don in 1968 when I was a graduate student working on various derived likelihoods motivated by Don’s work on marginal likelihood. Later, when I was Chair at Waterloo, Don gave gave frequent seminars on his current research. On one visit, Nancy Reid happened also to be visiting, and the rest is history. Mixed models are used in many applications, including profiling medical providers based on some quality measurement on patients they serve. It is often assumed that the provider effects are random, and the aim is to identify providers whose patients have extreme results. In order to make fair assessments, it is important to adjust for patient characteristics that are related to the response of interest. In the simplest case, we have a linear model for the response with a normally distributed provider effect and regression on measured covariates. The usual likelihood from this model is based on an often unrecognized assumption that the covariates and the facility effects are independent. This simple and common error can result in substantial bias in estimation.
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