Abstract:

This study combines the proportional odds and semiparametric regression models to establish a general form of a semiparametric ordinal regression model. For the parametric and nonparametric parts of the model, a Bayesian estimator based on the finite dimensional distribution of the stochastic process is constructed, and the analytical expression of the estimator is given under normal conditions. Numerical simulation results reveal that, even in the case of small samples, the estimated values of the model parameters are close to the true values, and the estimated values of the non-parametric parts can describe the shape of the real function. An empirical analysis of predicted income levels based on household consumption structures shows that a difference exists in the consumption structures between urban residents and rural households at the same income level, and a better performance under extrapolation is identified.

Key words: semiparametric regression, ordinal variables, Bayesian estimation, finite dimensional distribution, income level prediction