Dimensional Reduction for Latent Scores Modeling Using Recursive Integration

Abstract

This article addresses the problem of estimating the cutpoints that are used to model ordinal categorical data from continuous latent variables. A Bayesian approach is taken, and the cutpoint estimates are obtained as the expectation of their posterior distribution. Ostensibly this involves a high-dimensional integral evaluation with the dimension equivalent to the number of cutpoints. However, it shows how recursive integration techniques can be used to reduce the calculation to a series of two-dimensional integral evaluations, resulting in a practical estimation algorithm whose computational complexity is only a linear function of the number of cutpoints. Observed covariates can also be incorporated into the model, and the efficient estimation of the cutpoints assists in the estimation of other parameters. The new methodology is illustrated with an application to credit risk rating modeling of Thai corporations, and the computational advantages over other standard approaches are demonstrated.

Keywords:

• 62F15
• 62P05

Keywords:

• Bayesian modeling
• Covariates
• credit risk ratings
• Cutpoints
• Latent variables
• Numerical integration
• Posterior expectation
• Recursive intregration

Acknowledgment

This work is supported in part by the Faculty of Commerce and Accountancy, Chulalongkorn University.