A constrained regression model for an ordinal response with ordinal\n predictors

A regression model is proposed for the analysis of an ordinal response\nvariable depending on a set of multiple covariates containing ordinal and\npotentially other variables. The proportional odds model (McCullagh (1980)) is\nused for the ordinal response, and constrained maximum likelihood estimation is\nused to account for the ordinality of covariates.\n Ordinal predictors are coded by dummy variables. The parameters associated to\nthe categories of the ordinal predictor(s) are constrained, enforcing them to\nbe monotonic (isotonic or antitonic). A decision rule is introduced for\nclassifying the ordinal predictors' monotonicity directions, also providing\ninformation whether observations are compatible with both or no monotonicity\ndirection. In addition, a monotonicity test for the parameters of any ordinal\npredictor is proposed. The monotonicity constrained model is proposed together\nwith three estimation methods and compared to the unconstrained one based on\nsimulations.\n The model is applied to real data explaining a 10-Points Likert scale quality\nof life self-assessment variable from ordinal and other predictors.\n