Introducing COZIGAM: An R Package for Constrained Zero-Inflated Generalized Additive Model Analysis

Zero-inflation problem is very common in ecological studies as well as other areas. Nonparametric regression with zero-inflated data may be studied via the zero-inflated generalized additive model (ZIGAM), which assumes that the zero-inflated responses come from a probabilistic mixture of zero and a regular component whose distribution belongs to the 1-parameter exponential family. With the further assumption that the probability of non-zero-inflation is some monotonic function of the mean of the regular component, we propose the constrained zero-inflated generalized additive model (COZIGAM) for analyzing zero-inflated data. When the hypothesized constraint obtains, the new approach provides a unified framework for modeling zero-inflated data, which is more parsimonious and efficient than the unconstrained ZIGAM. We have developed an R package COZIGAM which contains functions that implement an iterative algorithm for fitting ZIGAMs and COZIGAMs to zero-inflated data based on the penalized likelihood approach. Other functions included in the package are useful for model prediction and model selection. We demonstrate the use of the COZIGAM package via some simulation studies and a real application.