Some applications of local influence diagnostics.

Abstract

The influence of observations on the outcome of an analysis is of importance in statistical data analysis. A practical and well-established approach to influence analysis is case deletion. However, it has its draw-backs when subsets of observations are jointly influential and offset each other's influence. Another approach is local influence proposed by Cook (1986).The local influence methodology of Cook (1986) is based on the curvature of the likelihood displacement surface formed by model/data perturbations. Wu and Luo (1993a, 1993b) further developed the idea and proposed the study of the perturbation-formed surface of a variable by evaluating the curvature of the surface in addition to its maximum slope. This thesis utilizes the local influence approach to develop influence diagnostic methods for four different topics.Firstly, we proposed a stepwise confirmatory procedure for the detection of multiple outliers in two-way contingency tables. The procedure begins with the identification of a reliable set of candidate outliers by evaluating the derivatives of the perturbation-formed surface of the Pearson goodness-of-fit statistic. An adding-back iterative algorithm is then applied to the candidate set to assess their relative discordancy. Using two real data sets, the proposed procedure is shown to be less susceptible to both masking and swamping problems than residual based measures. In a Monte Carlo study, the local influence diagnostics are also found to outperform standard residual-based methods in terms of efficiency and other criteria.Transformations of covariates are commonly applied in regression analysis. When a parametric transformation family is used, the maximum likelihood estimate of the transformation parameter is often sensitive to minor perturbations of the data. Diagnostics based on the local influence approach are derived to assess the influence of observations on the covariate transformation parameter in generalized linear models. Three numerical examples are presented to illustrate the usefulness of the proposed diagnostics. The need for transformation is also addressed in addition to assessing influence on the transformation parameter.A common method of choosing the link function in generalized linear models is to specify a parametric link family indexed by unknown parameters. The maximum likelihood estimates of such link parameters, however, often depend on one or several extreme observations. Diagnostics based on the local influence approach are derived to assess the sensitivity of the parametric link analysis. Two examples demonstrate that the proposed diagnostics can identify jointly influential observations on the link even when masking is present. The application of the diagnostics can also assist us in revising the link parameter and hence the form of the model.The portmanteau statistic is commonly used for testing goodness-of-fit of time series models. However, this lack of fit test may depend on one or several atypical observations in the series. We investigate the sensitivity of the portmanteau statistic in the presence of additive outliers. Diagnostics based on the local influence approach are developed to assess both local and global influence. Three practical examples demonstrate the usefulness of the proposed diagnostics.