Constrained Generalized Additive Model with Zero-Inflated Data

Zero inflation problem is very common in ecological studies as well as other areas. We propose the COnstrained Zero-Inflated Generalized Additive Model (COZIGAM) for analyzing zero-inflated data. Our approach assumes that the response follows some distribution from the zero-inflated 1-parameter exponential family, with the further assumption that the probability of zero inflation is some monotone function of the mean response function. When the latter assumption obtains, the new approach provides a unified framework for modeling zero-inflated data. This bypasses the problems of two popular methods for analyzing zero-inflated data that either focus only on the non-zero data or model the presence-absence data and the non-zero data separately. We develop an iterative algorithm for penalized likelihood estimation with a COZIGAM, and derive formulas for constructing confidence intervals. The new approach is illustrated with both simulated data and two real applications.