Originally published as Genetics Published Articles Ahead of Print on September 15, 2006.

Genetics, Vol. 174, 1613-1624, November 2006, Copyright © 2006
doi:10.1534/genetics.106.060673

A Thurstonian Model for Quantitative Genetic Analysis of Ranks: A Bayesian Approach

Daniel Gianola*,{dagger},{ddagger},1 and Henner Simianer{dagger}

* Department of Animal Sciences, University of Wisconsin, Madison, Wisconsin 53706, {dagger} Institute of Animal Breeding and Genetics, Georg-August-University, 37075 Göttingen, Germany and {ddagger} Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, N-1432 Ås, Norway

1 Corresponding author: Department of Animal Sciences, University of Wisconsin, 1675 Observatory Dr., Madison, WI 53706.
E-mail: gianola{at}ansci.wisc.edu

A fully Bayesian method for quantitative genetic analysis of data consisting of ranks of, e.g., genotypes, scored at a series of events or experiments is presented. The model postulates a latent structure, with an underlying variable realized for each genotype or individual involved in the event. The rank observed is assumed to reflect the order of the values of the unobserved variables, i.e., the classical Thurstonian model of psychometrics. Parameters driving the Bayesian hierarchical model include effects of covariates, additive genetic effects, permanent environmental deviations, and components of variance. A Markov chain Monte Carlo implementation based on the Gibbs sampler is described, and procedures for inferring the probability of yet to be observed future rankings are outlined. Part of the model is rendered nonparametric by introducing a Dirichlet process prior for the distribution of permanent environmental effects. This can lead to potential identification of clusters of such effects, which, in some competitions such as horse races, may reflect forms of undeclared preferential treatment.