Influential Diagnostics for Zero-Adjusted Quasi-Gamma Models for Spatially Correlated Data

A multitude of phenomena of interest are indexed in space, where the distribution of the response variable is a mixture of discrete and continuous random variables. We propose a spatial model in which the response variable follows a mixed discrete-continuous distribution, with a probability mass at zero and a continuous gamma component for positive values. This distribution is known as the zero-adjusted gamma distribution. The model is based on two submodels. The probability mass at zero is formulated using logistic regression. For the continuous positive data, a quasi-likelihood model under the gamma distribution is adopted. Spatial dependence is incorporated into both submodels. Inferential aspects are discussed, and the performance of the estimators is assessed through a simulation study. Expressions for standard errors are derived, and residuals are proposed to evaluate the goodness of fit. The local influence methodology is used to identify potentially influential observations. The proposed approach is illustrated through the analysis of both simulated and real data. In the real-data application, we analyze the accumulated precipitation (in mm) recorded during August 2021 across the state of Pernambuco, Brazil. The dataset comprises 190 georeferenced observations, of which 13.68% are zero.