We propose a new class of Tweedie mixed models applied to hierarchical spatial data that can model discrete, continuous and semicontinuous data. The presented approach is extended to model two or more responses observed on the same spatial domain connected by shared random effects. The modeling framework is built upon unbiased estimating equations in conjunction with the orthodox best linear unbiased predictor approach and adjusted Pearson estimators. Our model assumptions are robust to random effects distributions and are based only on the first and second moments of the random effects. We illustrate the usefulness of our approach through four motivating examples applied to health and environmental studies. A simulation study is conducted to assess the properties of our models. Backed up by the data analyses and simulation results presented in this work spatial Tweedie mixed models offer an appealing model framework to hierarchical spatial data that is robust to random effects distributions and is computationally efficient.
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