Spatio-temporal modelling of coffee berry borer infestation patterns accounting for inflation of zeroes and missing values Modelagem espaço-temporal do padrão de infestação da broca do café levando em consideração excesso de zeros e dados faltantes

The study of pest distributions in space and time in agricultural systems provides important information for the optimization of integrated pest management programs and for the planning of experiments. Two statistical problems commonly associated to the space-time modelling of data that hinder its implementation are the excess of zero counts and the presence of missing values due to the adopted sampling scheme. These problems are considered in the present article. Data of coffee berry borer infestation collected under Colombian field conditions are used to study the spatio-temporal evolution of the pest infestation. The dispersion of the pest starting from initial focuses of infestation was modelled considering linear and quadratic infestation growth trends as well as different combinations of random effects representing both spatially and not spatially structured variability. The analysis was accomplished under a hierarchical Bayesian approach. The missing values were dealt with by means of multiple imputation. Additionally, a mixture model was proposed to take into account the excess of zeroes in the beginning of the infestation. In general, quadratic models had a better fit than linear models. The use of spatially structured parameters also allowed a clearer identification of the temporal increase or decrease of infestation patterns. However, neither of the space-time models based on standard distributions was able to properly describe the excess of zero counts in the beginning of the infestation. This overdispersed pattern was correctly modelled by the mixture space-time models, which had a better performance than their counterpart without a mixture component.O estudo da distribuição de pragas em espaço e tempo em sistemas agrícolas fornece informação importante para a otimização de programas de manejo integrado de pragas e para o planejamento de experimentos. Dois problemas estatísticos comumente associados à modelagem espaço-temporal desse tipo de dados que dificultam sua implementação são o excesso de zeros nas contagens e a presença de dados faltantes devido ao esquema de amostragem adotado. Esses problemas são considerados no presente artigo. Para estudar a evolução da infestação da broca do café a partir de focos iniciais de infestação foram usados dados de infestação da praga coletados em condições de campo na Colômbia. Foram considerados modelos com tendência de crescimento da infestação linear e quadrática, assim como diferentes combinações de