Bayesian Local Influence

Abstract

This chapter is devoted to the discussion of local influence procedures in growth curve models (GCMs) with Rao’s simple covariance structure (SCS) and unstructured covariance (UC), from the Bayesian point of view. The fundamental idea behind this procedure is to replace likelihood displacement in likelihood-based local influence method (see Subsection 5.1.1 in Chapter 5) with a Bayesian entropy, for example, the Kullback—Leibler divergence (KLD) addressed in Chapter 6. With SCS and UC, the two commonly used covariance structures, Bayesian Hessian matrices of the regression coefficient and the dispersion component in GCMs are studied under an abstract perturbation scheme, which serves as a basis of the Bayesian local influence analysis in these models. Also, some new properties of the Bayesian Hessian matrix are obtained as ancillary results. Similar to likelihood-based local influence analysis addressed in Chapter 5, a covariance-weighted perturbation scheme is employed to demonstrate the use of this procedure. To illustrate, the practical data sets discussed in previous chapters are reanalyzed using Bayesian local influence procedures. This analysis reveals that the Bayesian local in fluence method is a practical diagnostic approach.