Detecting stage-wise outliers in hierarchical Bayesian linear models of repeated measures data

Abstract

We propose numerical and graphical methods for outlier detection in hierarchical Bayes modeling and analyses of repeated measures regression data from multiple subjects; data from a single subject are generically called a "curve." The first-stage of our model has curve-specific regression coefficients with possibly autoregressive errors of a prespecified order. The first-stage regression vectors for different curves are linked in a second-stage modeling step, possibly involving additional regression variables. Detection of the stage at which the curve appears to be an outlier and the magnitude and specific component of the violation at that stage is accomplished by embedding the null model into a larger parametric model that can accommodate such unusual observations.As a first diagnostic, we examine the posterior probabilities of first-stage and second-stage anomalies relative to the modeling assumptions for each curve. For curves where there is evidence of a model violation at either stage, we propose additional numerical and graphical diagnostics. For first-stage violations, the diagnostics identify the specific measurements within a curve that are anomalous. For second-stage violations, the diagnostics identify the curve parameters that are unusual relative to the pattern of parameter values for the majority of the curves. We give two examples to illustrate the diagnostics, develop a BUGS program to compute them using MCMC techniques, and examine the sensitivity of the conclusions to the prior modeling assumptions.2

Outlier detection in a repeated measure design

“…and Lim et al 18 19 Weiss 20 and Peruggia 21 ). However, to the best of our knowledge, no work has been done in the literature on detection of outliers in RMDs using the Liu and Weng's Residual and Estimate Distance tests.…”

“…Therefore, it will be necessary for outliers to be checked before conducting data analysis. Several works exist in the literature on the detection of outliers in the design of experiments (see Lim et al, 12 Chow and Tse, 14 Liu and Weng, 15 Wang and Chow, 16 Nawama et al 17 and Lim et al 18 ) with little works focusing on repeated measure experiments (see Huggins, 19 Weiss 20 and Peruggia 21 ). However, to the best of our knowledge, no work has been done in the literature on detection of outliers in RMDs using the Liu and Weng's Residual and Estimate Distance tests.…”

A Bayesian Computer Model Analysis of Robust Bayesian Analyses

“…While not all choices can be parameterised directly, as we will discuss, often the major sources of concern can be addressed in this way. We note that Peruggia et al (2004) employed GPs to explore prior robustness issues, but were limited to a small number of prior quantities. Here, we argue for a general analysis which examines both prior and (the more analytically challenging) likelihood quantities, and their various interactions, simultaneously in a comprehensive global approach.…”