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Keywords:

  • Compound models;
  • Generalized linear models;
  • Ordered categories;
  • Proportional odds;
  • Sequential models;
  • Logit models;
  • Regression models;
  • Ordinal response;
  • Two-step models

Abstract

A general class of sequential models for the analysis of ordered categorical variables is developed and discussed. The models apply if the ordinal response may be subdivided into two or more meaningful sets of response categories. The parametrization explicitly makes use of this subdivision. The models furnish a linear alternative to non-linear models which incorporate a scale parameter. They are shown to be special cases of multivariate generalized linear models. Applications are discussed with the use of several examples.