Analysis of Multiple Binary Responses Using a Threshold Model

  • Ling-Yun Chang
  • Sajjad Toghiani
  • Ashley Ling
  • El H. Hay
  • Sammy E. Aggrey
  • Romdhane Rekaya
Article

Abstract

Several discrete responses, such as health status, reproduction performance and meat quality, are routinely collected for several livestock species. These traits are often of binary or discrete nature. Genetic evaluation for these traits is frequently conducted using a single-trait threshold model, or they are considered continuous responses either in univariate or in multivariate context. Implementation of threshold models in the presence of several binary responses or a mixture of binary and continuous responses is far from simple. The complexity of such implementation is primarily due to the incomplete randomness of the residual (co)variance matrix. In the current study, a multiple binary trait simulation was carried out in order to implement and validate a new procedure for dealing with the consequences of the restrictions imposed to the residual variance using threshold models. Using three and eight binary responses, the proposed method was able to estimate all unknown parameters without any noticeable bias. In fact, for simulated residual correlations ranging from −0.8 to 0.8, the resulting HPD 95% intervals included the true values in all cases. The proposed procedure involved limited additional computational cost and is straightforward to implement independent of the number of binary responses involved in the analysis. Monitoring of the convergence of the procedure must be conducted at the identifiable scale, and special care must be placed on the selection of the prior of the non-identifiable model. The latter could have serious consequences on the final results due to potential truncation of the parameter space.

Keywords

Binary responses Threshold model Continuous phenotype MCMC 

References

  1. Albert JH, Chib S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association. 88:669–679.MathSciNetCrossRefMATHGoogle Scholar
  2. Korsgaard IR, Andersen AH, Sorensen D. (1999). A useful reparameterisation to obtain samples from conditional inverse Wishart distributions. Genetics, Selection, Evolution. 31:177-181CrossRefPubMedCentralGoogle Scholar
  3. McCulloch R, Rossi P. (1994). An exact likelihood analysis of the multinomial probit model. Journal of Econometrics. 64:207–240.MathSciNetCrossRefGoogle Scholar
  4. McCulloch R, Polson N, Rossi P. (2000). A Bayesian analysis of the multinomial probit model with fully identified parameters. Journal of Econometrics. 99:173–193.CrossRefMATHGoogle Scholar
  5. Moreno C, Sorensen D, Garcia-Cortes LA, Varona L, Altarriba J. (1997). On biased inferences about variance components in the binary threshold model. Genetics, Selection, Evolution. 29: 145-160CrossRefPubMedCentralGoogle Scholar
  6. Rekaya R, Rodriguez-Zas SL, Gianola D, Shook GE. (1998). Test-day models for longitudinal binary responses: an application to mastitis in Holsteins. Book of Abstracts of the 49th Annual Meeting of the European Association for Animal Production.4: 44. Wageningen Pers.Google Scholar
  7. Sorensen D, Andersen S, Gianola D, Korsgaard IR. (1995). Bayesian inference in threshold models using Gibbs sampling. Genetics, Selection, Evolution. 27:229-249.CrossRefPubMedCentralGoogle Scholar
  8. Sorensen D. (1996). Gibbs sampling in quantitative genetics. Danish Institute of Agricultural Science; Interal Report 82, 192pp.Google Scholar

Copyright information

© International Biometric Society 2017

Authors and Affiliations

  1. 1.Department of Animal and Dairy ScienceUniversity of GeorgiaAthensUSA
  2. 2.Department of Poultry ScienceUniversity of GeorgiaAthensUSA
  3. 3.Institute of BioinformaticsUniversity of GeorgiaAthensUSA
  4. 4.Fort Keogh Livestock and Range Research LaboratoryUSDA-ARSMiles CityUSA

Personalised recommendations