Influence analysis of multilevel models

This thesis studies the problem of detecting outliers and influential observations in multilevel models. Three topics, namely case deletion diagnostics, outlier detection and local influence analysis are studied.;For outlier detection, the behavior of the IGLS estimators of the fixed and random parameters under a mean-shift outlier model is studied. Outlier tests are developed for general multilevel models and specialized to two-level models. Examples show that our proposed tests are more effective than those based on the commonly used one-step approximation if there are strongly influential observations for estimating the random parameter.;In local influence analysis, we focus on simultaneously perturbing the covariance matrix, responses and explanatory variables. Generalized Cook statistics for the fixed and random parameter estimators under these perturbations are derived and local diagnostic measures are obtained to assess joint influence of observations.;A new feature of this thesis is that we study influence diagnostics for estimators of the fixed parameter and the random parameter jointly, which overcomes the flaw of conducting diagnostics separately.;Under case deletion, the influence of a subset of observations on the iterative generalized least square (IGLS) estimators of the fixed parameter and the random parameter is investigated. Two approximate update formulae are developed and some influence measures based on Cook's distance are obtained. These measures can be used to study the influence of units at any level for both the fixed parameter estimation and the random parameter estimation.