Model choice and diagnostics for ordinal data with robust estimation

Ordinal regression models are commonly implemented for analysing an ordinal response variable as a function of some explanatory covariates. The Maximum Likelihood (ML) estimators are used for estimating the unknown parameters of these models but gross-errors in the response, specific deviations due to respondents’ behaviour, and outlying covariates may affects their reliability. The lack of robustness of these estimators has been formally shown in Iannario et al. (20017) by deriving their breakdown point and their influence function. A new robust M estimator able to produce reliable inference when data contamination occurs has been introduced. The speech presents diagnostic procedures derived by the analysis of generalized residuals and weights and suggests an open issue based on the model selection concerning Generalized Linear Models for ordinal data by following Ronchetti and Staudte, 1994; Cantoni and Ronchetti, 2001; Cantoni et al. 2005, among others.