Latent Single-Index Models for Ordinal Data


王海斌 教授(厦门大学数学科学学院)





We propose a latent semiparametric model for ordinal data in which the single-index model is used to evaluate the effects of the latent covariates on the latent response. We develop a Bayesian sampling-based method with free-knot splines to analyze the proposed model. As the index may vary from minus infinity to plus infinity, the traditional spline that is defined on a finite interval cannot be applied directly to approximate the unknown link function. We consider a modified version to address this problem by first transforming the index into the unit interval via a continuously cumulative distribution function and then constructing the spline bases on the unit interval. To obtain a rapidly-convergent algorithm, we make use of the partial-collapse and parameter expansion and reparameterization techniques, improve the movement step of Bayesian splines with free-knots so that all the knots can be relocated each time instead of only one knot, and design a generalized Gibbs step. We check the performance of the proposed model and estimation method by a simulation study, and apply them to analyze a real dataset.