Generalized additive models for zero-inflated data with partial constraints

Hai Liu, Kung Sik Chan

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Zero-inflated data abound in ecological studies as well as in other scientific fields. Non-parametric regression with zero-inflated response may be studied via the zero-inflated generalized additive model (ZIGAM) with a probabilistic mixture distribution of zero and a regular exponential family component. We propose the (partially) constrained ZIGAM, which assumes that some covariates affect the probability of non-zero-inflation and the regular exponential family distribution mean proportionally on the link scales. When the assumption obtains, the new approach provides a unified framework for modelling zero-inflated data, which is more parsimonious and efficient than the unconstrained ZIGAM. We develop an iterative estimation algorithm, and discuss the confidence interval construction of the estimator. Some asymptotic properties are derived. We also propose a Bayesian model selection criterion for choosing between the unconstrained and constrained ZIGAMs. The new methods are illustrated with both simulated data and a real application in jellyfish abundance data analysis.

Original languageEnglish (US)
Pages (from-to)650-665
Number of pages16
JournalScandinavian Journal of Statistics
Volume38
Issue number4
DOIs
StatePublished - Dec 1 2011

Fingerprint

Generalized Additive Models
Partial
Zero
Exponential Family
Bayesian Model Selection
Distribution of Zeros
Mixture Distribution
Model Selection Criteria
Nonparametric Regression
Estimation Algorithms
Inflation
Iterative Algorithm
Asymptotic Properties
Confidence interval
Generalized additive models
Covariates
Data analysis
Estimator
Exponential family
Modeling

Keywords

  • Asymptotic normality
  • Convergence rate
  • EM algorithm
  • Model selection
  • Penalized likelihood
  • Regression splines

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Generalized additive models for zero-inflated data with partial constraints. / Liu, Hai; Chan, Kung Sik.

In: Scandinavian Journal of Statistics, Vol. 38, No. 4, 01.12.2011, p. 650-665.

Research output: Contribution to journalArticle

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