|CHANG, LING-YUN - University Of Georgia|
|TOGHIANI, SAJJAD - University Of Georgia|
|LING, ASHLEY - University Of Georgia|
|Hay, El Hamidi|
|AGGREY, SAMUEL - University Of Georgia|
|ROMDHANE, REKAYA - University Of Georgia|
Submitted to: Journal of Agricultural, Biological, and Environmental Statistics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/18/2017
Publication Date: 12/1/2017
Citation: Chang, L., Toghiani, S., Ling, A., Hay, E.A., Aggrey, S., Romdhane, R. 2017. Analysis of multiple binary responses using a threshold model. Journal of Agricultural, Biological, and Environmental Statistics. 22:640-651. https://doi.org/10.1007/s13253-017-0305-6.
Interpretive Summary: Many economically important traits in the livestock industry are discrete in nature. The statistical methods often used in genetic evaluation for these traits suffer from several issues especially when having multiple discrete traits. In this study, a simulation of multiple binary traits data was conducted in order to implement a new statistical model and evaluate its performance. The proposed procedure involved limited additional computational cost and is straightforward to implement independent of the number of binary responses involved in the analysis.
Technical 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 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.