Delaying bud-break on pecan trees: a Bayesian longitudinal multinomial regression approach

A multivariate Bayesian Probit model is adapted to analyze a longitudinal multiclass-ordinal response, with a linear plateau as the longitudinal model. Measurements on pecan bud growth were collected on irregular time intervals, about a week apart from late March to mid April, using a six-level ordinal scale. The data are from two randomized complete block designs with four blocks each. The experiments were setup and initiated in 2018 in a pecan orchard, at two different locations, to evaluate the effect of two sets of four treatments on delaying growth of recently broken pecan buds to minimize bud loss due to low temperatures. A simulation study was successfully carried out to validate the model implementation. Treatment 3 of Experiment 1 was associated with the greatest reduction in bud growth rate. In Experiment 2, Treatments 2 and 3 had some effect on delaying bud growth. Although treatment effects were not statistically different in either experiment, this paper presents a practical and efficient modeling technique for longitudinal multinomial ordinal data, a common data type in applied agricultural research studies.