Mixed effects models for a directional response: a case study with loblolly pine microfibril angle

We propose methods for fitting mixed-effects regression models for an angular response and apply it to predict microfibril angle in loblolly pine (Pinus taeda L.) In this study, we generalize Presnell et al.s (1998) spherically projected multivariate linear model, based on the angular normal distribution, by inclusion of random effects to account for the within-cluster correlation typical of repeated measures, longitudinal data and other clustered data structures. In the microbril angle example, the data are clustered due to the presence of multiple measurements of the response on each sample tree. This study suggests that mixed-effects angular response models are superior to population level models based on several statistical indices. Model comparisons were done based on several criteria including Likelihood ratio tests (LRTs), Akaike information criterion (AIC) and Bayesian information criterion (BIC).