Mixed zeros inflated poisson model: an application in grape disease control

Abstract

Longitudinal data studies describe the behavior of a feature of observations over time through so-called mixed models, which bear this name because they contain fixed effects and random effects. Still, if many of the observations do not show such a characteristic, i.e., the amount of zeros observed is greater than expected, then we say that it is inflated data of zeros. This work aims to describe the applicability of a mixed zero inflated Poisson (ZIP) model to model the temporal progress of mildew (Plasmopara viticultura), which corresponds to fungal disease of the grape, more specifically in the cultivar BRS Vitória, and assess its tolerance for 6 different treatments. This is intended to evaluate the quality of the proposed model fit and to carry out tests comparing the treatment averages to point out which treatments are equally effective in the control of mildew, thus demonstrating the application of the mixed ZIP model in a real and significant problem. A mixed ZIP model was constructed based on methodologies found in the literature and for inference and estimation of the parameters the method of maximum likelihood was used. The results showed that the mixed ZIP model adjusted well to the data, and hypothesis testing for average pointed to equality in efficacy between some treatment groups, thus making it possible to obtain a treatment with fewer sprays within each group.