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A regression model is proposed for the analysis of an ordinal responsevariable depending on a set of multiple covariates containing ordinal andpotentially other variables. The proportional odds model (McCullagh (1980)) isused for the ordinal response, and constrained maximum likelihood estimation isused to account for the ordinality of covariates.  Ordinal predictors are coded by dummy variables. The parameters associated tothe categories of the ordinal predictor(s) are constrained, enforcing them tobe monotonic (isotonic or antitonic). A decision rule is introduced forclassifying the ordinal predictors' monotonicity directions, also providinginformation whether observations are compatible with both or no monotonicitydirection. In addition, a monotonicity test for the parameters of any ordinalpredictor is proposed. The monotonicity constrained model is proposed togetherwith three estimation methods and compared to the unconstrained one based onsimulations.  The model is applied to real data explaining a 10-Points Likert scale qualityof life self-assessment variable from ordinal and other predictors.

A constrained regression model for an ordinal response with ordinal predictors