A Bayesian model-based reduced major axis regression

Reduced major axis (RMA) regression, widely used in the fields of zoology, botany, ecology, biology, spectroscopy, and among others, outweighs the ordinary least square regression by relaxing the assumption that the covariates are without measurement errors. A Bayesian implementation of the RMA regression is presented in this paper, and the equivalence of the estimates of the parameters under the Bayesian and the frequentist frameworks is proved. This model-based Bayesian RMA method is advantageous since the posterior estimates, the standard deviations, as well as the credible intervals of the estimates can be obtained through Markov chain Monte Carlo methods directly. In addition, it is straightforward to extend to the multivariate RMA case. The performance of the Bayesian RMA approach is evaluated in the simulation study, and, finally, the proposed method is applied to analyze a dataset in the plantation.