Influential observations in transformations: A bayesian approach

Abstract

This paper presents a bayesian approach to the problem of detecting influential observations when estimating the Box-Cox transformation. The influence of a group I={i₁, …,i_n} of observations is measured by means of the Kullback-Leibler distance between the marginal posterior; distributions for the transformation parameter which are computed, respectively, without and with the cases indexed by I. A measure is proposed and its properties and relationship to other diagnostic methods are studied.

Keywords:

• Box-Cox transformation
• Constructed variables
• Cook and Wang diagnostic
• Kullback-Leibler distance
• Laplace's method
• Score statistic