Bayesian algorithms for analysis of categorical ordinal data

Abstract

This study describes and evaluates a package that implements extensions of the algorithm first presented by Nandram and Chen (1996), replacing Gaussian distribution (NCG) with Student’s t distribution (NCt) for Bayesian analysis of ordinal categorical data using mixed models. The algorithms described by Albert and Chib (1993) and Cowles (1996) were also implemented. Comparison was carried on using two different designs. A Steiner triple system with seven treatments used mostly to estimate fixed effects and a 10x10 square lattice designed to rank and select among random effects. Different situations for intraclass correlations were also considered. We reported the total number of iterations required for convergence diagnostics, and the mean square error (MSE) on posterior estimates of both random and fixed effects as well as posterior estimates of intraclass correlation. NCG and NCt algorithms resulted in lower MSE for both designs. This algorithm has also shown faster convergence rates. For the square lattice, NCG and NCt algorithms overestimated the intraclass correlation when the simulated value was large (0.8). But the bias on MSE relative to the other designs did not increase. A real experiment from plant breeding is given as an example of package use, an Incomplete Block Design to evaluate resistance of tomato varieties to late blight (caused by Phytophthora infestans). Gaussian distribution was the parcimonious choice for the latent trait. Algorithms are consistent with regard to the ranking of varieties.