A Thurstonian model for quantitative genetic analysis of ranks: a Bayesian approach
Daniel Gianola 1* and Henner Simianer 2
1 University of Wisconsin-Madison
2 Georg-August University Goettingen
* To whom correspondence should be addressed. E-mail: gianola{at}ansci.wisc.edu.
Submitted on May 12, 2006
Revised on July 31, 2006
Accepted on 8 September 2006
 |
Abstract |
|---|
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 non-parametric 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.
Key Words:
Bayesian methods, Monte Carlo methods, latent variables, quantitative genetics, ranked data
