Abstract

A spatial model is proposed in which the response variable follows a mixed discrete-continuous distribution, with probability mass at zero and a gamma continuous component for the positive values. This distribution is known as the zero-adjusted or zero-augmented gamma distribution. The model construction is based on two submodels. The first submodel, which models the probability mass at zero, is carried out through logistic regression. A quasi-likelihood model under the gamma distribution is considered for the second submodel, for the continuous positive data. Spatial dependence is incorporated into both submodels. Inferential aspects are discussed, and the performance of the estimators is evaluated through a simulation study. Expressions for the standard errors are developed, and residuals are proposed to evaluate the goodness of fit. The local influence methodology is employed to identify potentially influential observations. This methodology is illustrated through the analysis of real data, namely the amount of accumulated precipitation (in millimeters) during August 2021 in the state of Pernambuco, Brazil.