Penalised estimation of partially linear additive zero-inflated Bernoulli regression models

Abstract

We develop a practical and computationally efficient penalised estimation approach for partially linear additive models to zero-inflated binary outcome data. To facilitate estimation, B-splines are employed to approximate unknown nonparametric components. A two-stage iterative expectation-maximisation (EM) algorithm is proposed to calculate penalised spline estimates. The large-sample properties such as the uniform convergence and the optimal rate of convergence for functional estimators, and the asymptotic normality and efficiency for regression coefficient estimators are established. Further, two variance-covariance estimation approaches are proposed to provide reliable Wald-type inference for regression coefficients. We conducted an extensive Monte Carlo study to evaluate the numerical properties of the proposed penalised methodology and compare it to the competing spline method [Li and Lu. ‘Semiparametric Zero-Inflated Bernoulli Regression with Applications’, Journal of Applied Statistics, 49, 2845–2869]. The methodology is further illustrated by an egocentric network study.

Keywords:

• Additive Bernoulli regression
• B-spline
• EM algorithm
• penalised estimation
• zero-inflated

AMS SUBJECT CLASSIFICATIONS:

• 62G05
• 62G20
• 62G08

Acknowledgments

The authors are grateful to the Editor, the Associate Editor, and two reviewers for their useful comments and constructive suggestions which led to significant improvement in the revised manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was partially supported by the National Institute on Drug Abuse (NIDA) of the National Institutes of Health under Award Number R01DA038185.