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Principal component multinomial regression is a method for modellingthe relationship between a set of high-dimensional regressors and a categoricalresponse variable with more than two categories. This method uses as covariates ofthe multinomial model a reduced number of principal components of the regressors.Because the principal components are based on the eigenvectors of the empiricalcovariance matrix, they are very sensitive to anomalous observations. Severalmethods for robust principal component analysis have been proposed in literature. Afirst approach is obtained by replacing the classical covariance matrix by a robustcovariance estimator. A second group applies projection pursuit techniques. In thisstudy we consider ROBPCA method which combines the advantages of bothapproaches The new robust approach will be applied for assessing the servicequality.