Analysis of credit ratings of Korean corporate bonds using cumulative logit random effects models

Longitudinal data refers to data where the same subjects are measured repeatedly over time, implying the presence of correlations among repeated measurements.To explain this correlation, it is necessary to be decomposed into within correlation and between variance.This paper analyzes data concerning credit ratings of Korean corporate bonds, which are longitudinal ordinal data.To analyze these data, a cumulative logit random effects models are considered.In cumulative logit random effects models, there is an issue of integrating random effects, and since this integration is not in closed form, numerical integration method such as Laplace approximation and adaptive Gaussian quadrature are employed.After investigating the integration methods of random effects, simulation studies are conducted to compare their performances.Simulation studies compare cases with and without missing and also compare R library ordinal with SAS GLIMMIX.The results indicate that both statistical programming languages showed similar performance in parameter estimation.However, the adaptive Gaussian quadrature was superior under complete data, while the Laplace approximation was superior in the presence of missing data.Based on these performance comparisons, the actual data on credit ratings of Korean corporate bonds are analyzed.