  The aim of this paper was to develop statistical models to estimate
individual breed composition based on the previously proposed idea of
regressing discrete random variables corresponding to counts of reference
alleles of biallelic molecular markers located across the genome on the allele
frequencies of each marker in the pure (base) breeds. Some of the existing
regression-based methods do not guarantee that estimators of breed composition
will lie in the appropriate parameter space and none of them account for
uncertainty about allele frequencies in the pure breeds, that is, uncertainty
about the design matrix. In order to overcome these limitations, we proposed
two Bayesian generalized linear models. For each individual, both models assume
that the counts of the reference allele at each marker locus follow independent
Binomial distributions, use the logit link, and pose a Dirichlet prior over the
vector of regression coefficients (which corresponds to breed composition).
This prior guarantees that point estimators of breed composition like the
posterior mean pertain to the appropriate space. The difference between these
models is that model termed BIBI does not account for uncertainty about the
design matrix, while model termed BIBI2 accounts for such an uncertainty by
assigning independent Beta priors to the entries of this matrix. We implemented
these models in a multibreed Angus-Brahman population. Posterior means were
used as point estimators of breed composition. In addition, the ordinary least
squares estimator proposed by Kuehn et al. (2011) (OLSK) was also computed.
BIBI and BIBI2 estimated breed composition more accurately than OLSK, and BIBI2
had an 8.3% improvement in accuracy as compared to BIBI.
