An assessor-specific Bayesian multi-threshold mixed model for analyzing ordered categorical traits in tree breeding

Abstract

Many traits of biological interest in tree breeding are assessed using more than two ordered discrete categories. These scores have a more or less arbitrary and subjective assignment by the assessors, which could lead to a strong departure from the Gaussian distribution. Different assessors may also use different regions of the available scale. This study describes the use of the multi-threshold mixed model proposed by Varona et al. (J Anim Sci 87:1210–1217, 2009), which allows different thresholds for different assessors on an underlying Gaussian distribution. This method was applied to a six-point score for stem quality in an open-pollinated progeny trial of Prosopis alba Griseb. Four mixed models were used: (1) a linear mixed model with observed score (LMM); (2) a linear mixed model with transformed “normal scores” (LMM_NS); (3) a threshold mixed model (TMM); and (4) an assessor-specific multi-threshold mixed model (MTMM). Dispersion parameters were estimated using Bayesian techniques via the Gibbs sampling with a data augmentation step. The proposed MTMM produced higher posterior mean heritabilities (0.096) than the commonly used LMM (0.077). Posterior mean heritabilities from LMM_NS (0.094) and TMM (0.097) were comparable to those obtained using MTMM; however, MTMM yielded slightly more precise estimates than TMM. Although correlations of the estimated breeding values were high between different models (from 0.88 to 0.99), the heterogeneity in the estimated posterior means of the thresholds between the three assessors caused notable changes in the top 10 families between TMM and MTMM. The proposed model is helpful in fitting subjective ordered categorical traits assessed by different assessors in tree breeding.