Abstract:
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In the framework of generalized linear models, we develop a zero-inflated Poisson regression model, which explains the variability of the responses given a set of covariates, and additionally allows for the distinction of two kinds of zeros: sampling ("bad luck" zeros), and structural (zeros due to the data-generating process). We adapt this model to the spatial setting by incorporating dependence via a quasi-likelihood strategy, which provides consistent, efficient and asymptotically normal estimators, even under erroneous assumptions of the covariance structure, which also overcomes the need for the complete specification of a probability model.
We additionally propose methods for the simulation of zero-inflated spatial stochastic processes. This is done by deconstructing the entire process into a mixed, marked spatial point process: we augment existing algorithms for the simulation of spatial marked point processes to comprise a stochastic mechanism to generate zero-abundant marks (counts) at each location. We propose several such mechanisms, and consider interaction and dependence processes for random locations as well as over a lattice.
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