Abstract
The animal breeding values forecasting at futures times is a relevant technological innovation in the field of Animal Science, since its enables a previous indication of animals that will be either kept by the producer for breeding purposes or discarded. This study discusses an MCMC Bayesian methodology applied to panel data in a time series context. We consider Bayesian analysis of an autoregressive, AR(p), panel data model of order p, using an exact likelihood function, comparative analysis of prior distributions and predictive distributions of future observations. The methodology was tested by a simulation study using three priors: hierarchical Multivariate Normal-Inverse Gamma (model 1), independent Multivariate Student's t Inverse Gamma (model 2) and Jeffrey's (model 3). Comparisons by Pseudo-Bayes Factor favored model 2. The proposed methodology was applied to longitudinal data relative to Expected Progeny Difference (EPD) of beef cattle sires. The forecast efficiency was around 80%. Regarding the mean width of the EPD interval estimation (95%) in a future time, a great advantage was observed for the proposed Bayesian methodology over usual asymptotic frequentist method.
Highlights
The advantage of simultaneously modeling several time series, called panel data analysis, is the possibility of generating more accurate predictions for individual outcomes by pooling the data rather than generating predictions of individual outcomes using the data on the individual series only
This study discusses an Markov chain Monte Carlo (MCMC) Bayesian methodology applied to panel data in a time series context
Regarding the mean width of the Expected Progeny Difference (EPD) interval estimation (95%) in a future time, a great advantage was observed for the proposed Bayesian methodology over usual asymptotic frequentist method
Summary
The advantage of simultaneously modeling several time series, called panel data analysis, is the possibility of generating more accurate predictions for individual outcomes by pooling the data rather than generating predictions of individual outcomes using the data on the individual series only. The pooling takes place because the parameters of all time series are assumed to arise from the same distribution (Liu and Tiao, 1980). The convenience in the specification of this distribution indicates that the Bayesian procedure has a theoretical advantage over the frequentist approaches, since panel data analysis is directly related to prior information. The choice of a prior distribution is a relevant topic in the analysis of autoregressive panel data models.
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