Ranking crop species using mixed treatment comparisons

The mixed treatment comparison (MTC) method has been proposed to combine results across trials comparing several treatments. MTC allows coherent judgments on which of the treatments is the most effective. It produces estimates of the relative effects of each treatment compared with every other treatment by pooling direct and indirect evidence. In this article, we explore how this methodological framework can be used to rank a large number of agricultural crop species from yield data collected in field experiments. Our approach is illustrated in a meta-analysis of yield data obtained in 67 field studies for 36 different bioenergy crop species. The considered dataset defines a network of comparisons of crop species. We introduce several Bayesian MTC models based on baseline treatment contrasts and evaluate the practical advantages of these models to produce yield ratio estimates. We explore the consistency of some estimates by node-splitting and compare our results to those obtained with a classical two-way linear mixed model. Results reveal that the model showing the lowest deviance information criterion (DIC) includes both study random effects and study-specific residual variances. But all the tested models including study random effects lead to similar yield ratio estimates. The proposed Bayesian framework allows an in-depth analysis of the uncertainty in the species ranking.