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Discrete ordinal responses such as Likert scales are regularly proposed inquestionnaires and used as dependent variable in modeling. The responsedistribution for such scales is always discrete, with bounded support and oftenskewed. In addition, one particular level of the scale is frequently inflatedas it cumulates respondents who invariably choose that particular level(typically the middle or one extreme of the scale) without hesitation withthose who chose that alternative but might have selected a neighboring one. Theinflated discrete beta regression (IDBR) model addresses those four criticalcharacteristics that have never been taken into account simultaneously byexisting models. The mean and the dispersion of rates are jointly regressed oncovariates using an underlying beta distribution. The probability that choosersof the inflated level invariably make that choice is also regressed oncovariates. Simulation studies used to evaluate the statistical properties ofthe IDBR model suggest that it produces more precise predictions than competingmodels. The ability to jointly model the location and dispersion of (thedistribution of) an ordinal response, as well as to characterize the profile ofsubject selecting an "inflated" alternative are the most relevant features ofthe IDBR model. It is illustrated with the analysis of the politicalpositioning on a "left-right" scale of the Belgian respondents in the 2012European Social Survey.

Inflated Discrete Beta Regression Models for Likert and Discrete Rating Scale Outcomes