Multivariate ordinal regression models: an analysis of corporate credit ratings

Abstract

Correlated ordinal data typically arises from multiple measurements on a collection of subjects. Motivated by an application in credit risk, where multiple credit rating agencies assess the creditworthiness of a firm on an ordinal scale, we consider multivariate ordinal regression models with a latent variable specification and correlated error terms. Two different link functions are employed, by assuming a multivariate normal and a multivariate logistic distribution for the latent variables underlying the ordinal outcomes. Composite likelihood methods, more specifically the pairwise and tripletwise likelihood approach, are applied for estimating the model parameters. Using simulated data sets with varying number of subjects, we investigate the performance of the pairwise likelihood estimates and find them to be robust for both link functions and reasonable sample size. The empirical application consists of an analysis of corporate credit ratings from the big three credit rating agencies (Standard & Poor's, Moody's and Fitch). Firm-level and stock price data for publicly traded US firms as well as an unbalanced panel of issuer credit ratings are collected and analyzed to illustrate the proposed framework.

Weighted scores estimating equations and CL1 information criteria for longitudinal ordinal response

“…It is worth mentioning that the range of possible applications of our methods goes beyond biometric, disease or health data and is of interest also in other fields such as finance. A typical example are panel data of corporate credit ratings (e.g., Hirk et al 2019). A credit rating agency such as the Standard & Poor's assigns ratings on an ordinal scale with a considerable large number of categories and the dimension of the cluster is usually large.…”

New Approaches to Age Estimation Using Palatal Suture Fusion

“…The multivariate models were generated in order to provide the most mathematically correct approach to combining indicators in practice (39) as the palate aging indicators are biologically correlated to one another. The multivariate models use composite likelihood estimation (40,41), which differentiates them from the univariate models in this paper that employ maximum likelihood estimation. Consistent with Konigsberg et al (36,42,43), a Lagrange multiplier test for more than two categories (44–46) was applied to test the assumption of ordinal probit models that the unobserved error term is log‐normally distributed.…”

Machine learning methods for short-term probability of default: A comparison of classification, regression and ranking methods

“…Related to these techniques are ordinal classification and regression methods that exploit the ordinal nature of the dependent variable in the data. A few attempts have been made to apply these methods in the context of estimating the risk of companies (Swiderski et al, 2012) or expert ratings (Garc ıa et al, 2013) and credit ratings (Baourakis et al, 2009;Dikkers & Rothkrantz, 2005;Hirk et al, 2019;Kim & Ahn, 2012;Van Gestel et al, 2005). The used approaches include binary goal programming (Garc ıa et al, 2013), SVM variants for ordinal multi-class classification (Dikkers & Rothkrantz, 2005;Kim & Ahn, 2012;Swiderski et al, 2012), ordinal regression methods (Baourakis et al, 2009;Hirk et al, 2019) and combinations of ordinal regression and SVMs (Van Gestel et al, 2005).…”