# The beta-binomial model for estimating heritabilities of binary traits

- Received:
- Accepted:

DOI: 10.1007/BF00222986

- Cite this article as:
- Magnussen, S. & Kremer, A. Theoret. Appl. Genetics (1995) 91: 544. doi:10.1007/BF00222986

## Abstract

Calculations of individual narrow-sense heritability and family mean heritability of a binary trait in stochastically simulated sib trials in completely randomized block experiments showed that in some situations estimates of “realized” heritabilities obtained from the mixed linear threshold model could be improved by application of a proposed beta-binomial model. The proposed model adopts the beta-binomial as the conjugate-prior for the distribution of probabilities of observing the binary trait in a genetic entry. Estimation of the beta parameters allows an estimation of selection response and, by linkage to a threshold model for the individual observations, the desired heritabilities can be obtained. The average bias in the betabinomial estimates of heritability and family mean heritability was less than 2%. Improvements over existing procedures were especially manifest at heritabilities above 0.3 and at low overall probabilities of observing the trait (*p* < 0.30). The lowest root mean square errors were consistently obtained with the algorithm proposed by Harville and Mee (1984). The beta-binomial framework, although restricted to a single random additive genetic effect, further facilitates general analysis, estimation of selection response, and calculation of reliable family mean heritability. Intraclass correlations can be estimated directly from the beta-binomial parameters.