## Partial proportional odds models for ordinal response variables.(English)Zbl 0707.62154

Summary: The ordinal logistic regression model that McCullagh calls the proportional odds model is extended to models that allow non-proportional odds for a subset of the explanatory variables. The maximum likelihood method is used for estimation of parameters of general and restricted partial proportional odds models as well as for the derivation of Wald, Rao score and likelihood ratio tests. These tests assess association without assuming proportional odds and test proportional odds against various alternatives. Simulation results compare the score test for proportional odds with tests suggested by Koch, Amara and Singer that are based on a series of binary logistic models.

### MSC:

 62J99 Linear inference, regression 62F03 Parametric hypothesis testing 62J02 General nonlinear regression 62F10 Point estimation
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