Joint modeling of continuous proportions and overdispersed counts (2015)
Abstract: In the last few years biotechnolgy offers organic substances, defined as elicitors, which activate plant defenses to warding off atack by pathogens and herbivores. Application of this technology in crops induces a probabilistic defense mechanism whereby occur non identically distributed vector of bivariate data, which comprises both continuous proportions and overdispersed counts, where independence assumption cannot be hold. Hence, the goal of this work has been the joint modeling of continuous proportions and overdispersed counts, under the scientific context of induced resistance in plant protection. Theoretical framework was structured by one-par´ameter Clayton (CRM) and by two-par´ameter Joe and Hu (BB1) copulae, with Simplex and Generalized Poisson marginal distributions. Parameter estimations were done by Gauss-Newton type algorithm, variances by Jacknife and model selection by cross validation criterion. The theory was validated with experimental data on a roses crop exposed to an epidemiological complex plant:pathogen:herbivore, and with simulated data by computer as well. It concluded that, unlike classical analysis by Box and Cox adjusted normality and negative binomial, the constructed families of distributions capture the functional shape of bivariate relationship, the degree of dependence and marginal asymmetry, with easy to interpret parametrization and efficient estimators, according to the present study.