Multivariate regression and ANOVA models with outliers: A comparative approach - Wolfgang Polasek (Institute for Advanced Studies (IHS), 2003)
Assuming a normal-Wishart modelling framework we compare two methods for finding outliers in a multivariate regression (MR) system. One method is the add-1-dummy approach which needs fewer parameters and a model choice criterion while the other method estimates the outlier probability for each observation by a Bernoulli mixing outlier location shift model. For the simple add-1-dummy model the Bayes factors and the posterior probabilities can be calculated explicitly. In the probabilistic mixing model we show how the posterior distribution can be obtained by a Gibbs sampling algorithm. The number of outliers is determined using the marginal likelihood criterion. The methods are compared for test scores of language examination data of Fuller (1987): The results are similar but differ in their strength of their empirical evidence.
Keywords: C11; C39; 330; multivariate regression; multivariate one-way ANOVA; outliers; Gibbs sampling; marginal likelihoods; sensitivity analysis; Multivariate Analyse; Sensitivitätsanalyse; Varianzanalyse; Maximum-Likelihood-Methode