Estimation & Prediction

Multi-trait threshold-linear models in ssGBLUP: testing Newton-Raphson and Expectation-Maximization algorithms

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Abstract

Breeding companies and breeders' associations are now spending millions of dollars collecting extensive records for categorical traits related to health, fertility, disease resistance, and animal welfare. Threshold linear models (THR) are the gold-standard for the evaluation of categorical traits in animal breeding and genetics. Current mixed models (e.g., ssGBLUP), although ideal for large-scale evaluations, can accommodate only one categorical trait alongside many linear ones. Gibbs sampling can handle many categorical and continuous traits, but sampling methods are time and memory consuming and not suitable for large genomic datasets. Recently, two new algorithms were proposed to handle multiple categorical traits in ssGBLUP evaluations. We aimed to investigate the feasibility and performance of these algorithms in a broiler chicken population. The first is an adaptation of the expectation maximization (EM) algorithm proposed by Quaas in 1994; the second is a version of the Newton-Raphson (NR) algorithm. Both methods allow for general PCG-like solvers and, therefore, hold the promise for allowing large-scale genomic evaluations. We tested both algorithms (EM and NR) against Gibbs sampling in a poultry dataset. The data contained 180,998 records for at least one of the following traits: body weight (BW; oz), breast meat percent (BP, %), tibial dyschondroplasia (TD; 1-healthy or 2-affected), and mortality (MT; 1-alive or 2-dead), where the first two were linear and the last two were categorical. We used three generations of pedigree, totaling 183,335 animals, of which 18,047 were genotyped. We evaluated models' performance with respect to absolute differences, distribution overlap, scatter plots, and computing time. Mean absolute differences ranged from 0.00 to 0.09 across all traits. Spearman correlation between NR (or EM) and Gibbs sampling was high, ranging from 0.98 to 1.00. Finally, distributions showed sufficient overlap across all traits. While the Gibbs sampling took ~7 days, NR took 2 h and EM took 4 h. Overall, the breeding values from NR, EM, and Gibbs sampling were nearly identical, and differences are negligible for selection purposes. The EM method was the least stable, needing more PCG rounds to converge than NR. From our results, NR and EM are promising for large-scale multiple-trait threshold-linear genomic evaluations. We suggest that the NR could be the preferred method since it has the shortest running time and is more stable.

Keywords: 2026

How to Cite:

Busiman, F., Bermann, M., Legarra, A., Breen, V., Richter, J., Hidalgo, J., Misztal, I. & Lourenco, D., (2026) “Multi-trait threshold-linear models in ssGBLUP: testing Newton-Raphson and Expectation-Maximization algorithms”, World Congress on Genetics Applied to Livestock Production Digital Archive 2026(1): 2284195. doi: https://doi.org/10.31274/wcgalp.23554

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