title: A simple algorithm to estimate genetic variance in an animal threshold model using Bayesian inference.
abstract: BACKGROUND
  In the genetic analysis of binary traits with one observation per animal, animal threshold models frequently give biased heritability estimates. In some cases, this problem can be circumvented by fitting sire- or sire-dam models. However, these models are not appropriate in cases where individual records exist on parents. Therefore, the aim of our study was to develop a new Gibbs sampling algorithm for a proper estimation of genetic (co)variance components within an animal threshold model framework.
  
  
  METHODS
  In the proposed algorithm, individuals are classified as either "informative" or "non-informative" with respect to genetic (co)variance components. The "non-informative" individuals are characterized by their Mendelian sampling deviations (deviance from the mid-parent mean) being completely confounded with a single residual on the underlying liability scale. For threshold models, residual variance on the underlying scale is not identifiable. Hence, variance of fully confounded Mendelian sampling deviations cannot be identified either, but can be inferred from the between-family variation. In the new algorithm, breeding values are sampled as in a standard animal model using the full relationship matrix, but genetic (co)variance components are inferred from the sampled breeding values and relationships between "informative" individuals (usually parents) only. The latter is analogous to a sire-dam model (in cases with no individual records on the parents).
  
  
  RESULTS
  When applied to simulated data sets, the standard animal threshold model failed to produce useful results since samples of genetic variance always drifted towards infinity, while the new algorithm produced proper parameter estimates essentially identical to the results from a sire-dam model (given the fact that no individual records exist for the parents). Furthermore, the new algorithm showed much faster Markov chain mixing properties for genetic parameters (similar to the sire-dam model).
  
  
  CONCLUSIONS
  The new algorithm to estimate genetic parameters via Gibbs sampling solves the bias problems typically occurring in animal threshold model analysis of binary traits with one observation per animal. Furthermore, the method considerably speeds up mixing properties of the Gibbs sampler with respect to genetic parameters, which would be an advantage of any linear or non-linear animal model.
authors.affiliation: Nofima Marin, NO-1432 As, Norway. jorgen.odegard@nofima.no
authors.forename: Jørgen
authors.initials: J
authors.lastname: Ødegård
authors.forename: Theo H E
authors.initials: TH
authors.lastname: Meuwissen
authors.forename: Bjørg
authors.initials: B
authors.lastname: Heringstad
authors.forename: Per
authors.initials: P
authors.lastname: Madsen
mesh_terms: D000465:Algorithms; D000818:Animals; D001499:Bayes Theorem; D005260:Female; D014644:Genetic Variation; D040582:Inheritance Patterns / Q000235:genetics; D008297:Male; D023421:Models, Animal; D019655:Quantitative Trait, Heritable