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Effect of individual observations on the Box–Cox transformation

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In this paper, we consider the influence of individual observations on inferences about the Box–Cox power transformation parameter from a Bayesian point of view. We compare Bayesian diagnostic measures with the ‘forward’ method of analysis due to Riani and Atkinson. In particular, we look at the effect of omitting observations on the inference by comparing particular choices of transformation using the conditional predictive ordinate and the k d measure of Pettit and Young. We illustrate the methods using a designed experiment. We show that a group of masked outliers can be detected using these single deletion diagnostics. Also, we show that Bayesian diagnostic measures are simpler to use to investigate the effect of observations on transformations than the forward search method.
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Keywords: Bayesian methods; deletion diagnostics; influential observations; masking; outliers

Document Type: Research Article

Affiliations: School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK

Publication date: July 1, 2013

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