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Abstract:
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The customary setting for zero-inflation modeling is for count data where two types of 0s can be considered, but much less attention has been given to data that are nonnegative and continuous. Models specifying point mass at 0 for such data include the familiar Tobit model, which creates mass at 0 through censoring of a latent regression. Alternatively, a much less studied zero-inflated Beta model adds an independent Bernoulli specification to create mass at 0, in the spirit of a hurdle model. Neither model is true zero-inflation in that there is only one type of 0. We address the gap in the literature by providing a zero-inflation model to capture both types of 0s in the context of Beta regression for data on the unit interval exhibiting an excess of 0s.
Our motivating dataset consists of percent cover of plant species at a collection of sites in the Cape Floristic Region of South Africa. We first develop the model as a spatial regression in environmental features and then extend the model to introduce spatial random effects. We specify models in a hierarchical fashion, employing latent variables, fit them within a Bayesian framework, and also present model comparison tools.
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