Biao Zhang
Department of Mathematics
University of Toledo
Fitting and Testing Proportional Odds Models Based on Case-control Data
Proportional odds models are commonly used in modeling multicategory ordinal
responses. In this talk, we consider fitting and testing (prospective)
proportional odds model under a case-control sampling plan. By indicating
the equivalence between the proportional odds model and a semiparametric
selection bias model after reparameterization, we develop maximum
semiparametric likelihood estimation for the unconditional response
probabilities and the parameters in the proportional odds model. We also
establish an optimal property for the maximum semiparametric likelihood
estimator and point out a close connection between the semiparametric
likelihood approach and the pseudo-likelihood approach under discrete-choice
models. In addition, we propose a goodness of fit test for the proportional
odds model based on case-control data. The proposed test statistic is the
weighted average of the absolute differences between two estimated
distribution functions in each response category. Finally, we present a
bootstrap procedure along with some numerical results.
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