Mixture Mixed Models: Biennial Growth as a Latent Variable in Coffee Bean Progenies

Statistical analysis of Coffea arabica L. progeny production has been a great challenge. In this species, genotypes may present differential biennial behaviors due to different physiological responses to the environmental conditions, indicating a mixture of two subpopulations in the tested progenies. Previously proposed statistical methods are unable to handle data overdispersion and/or bimodality because they assume the same stochastic process generating different phenotypes. This study proposes a finite mixture mixed model for modeling the biennial patterns. Production data for 21 S 0:1 progenies, evaluated through eight harvests, were used. Individual (per harvest) and repeated measures analyses were performed using conventional mixed models and Gaussian mixture mixed models. The proposed methodology is also illustrated in a simulation study. On a real dataset, the approximated prediction error variance, CV, and residual variance were drastically reduced using mixture mixed models, resulting in a higher estimated heritability and expected gain from selection. Residual dependence across years was lower for the mixture model, but no differences were observed in genetic correlations. The posterior probability matrix captured the biennial pattern, which indicates the probability of a progeny's physiological stage. The Spearman correlation coefficient (0.87) indicates that selection based on grouped means may not be efficient. In general, the proposed model was more efficient for higher subpopulations means differences. The results suggest that for analysis of C. arabica progenies exhibiting different biennial patterns, mixture mixed models are superior to traditional mixed models and to models that structure biennial effects using covariance matrices.