Theory

This section covers the statistical models implemented across masreml and masbayes. Each page follows the same 7-section structure: Assumption · Linear model · GEBV calculation · Variance component & h² · When to Use · See it in code · References.

Pages

1. Biallelic & Multi-allelic — how the genotype matrix is built differently for SNP (biallelic) vs microhaplotype (multi-allelic) data, and what each construction feeds downstream.
2. Mixed Model & BLUP Family (Frequency-based) — PBLUP, GBLUP, GWABLUP (Meuwissen et al. 2024). One MME, three relationship matrices.
3. Bayesian Alphabet (Probabilistic) — BayesA (scaled inverse-\(\chi^2\)) and BayesR (4-component mixture), sharing the same linear model.
4. Continuous and Binary Trait — what changes when the response is binary: liability-scale modelling, Laplace approximation in masreml, Albert-Chib augmentation in masbayes, and the observed-versus-liability heritability transform.

Note

Every “See it in code” section uses the bundled demo dataset and calls only real exported functions of masreml / masbayes (cross-checked against the package source).