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

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.

Automated summary

We developed a practical and computationally efficient penalised estimation approach for partially linear additive models to deal with zero-inflated binary outcome data. The approach utilizes B-splines to approximate unknown nonparametric components and employs a two-stage iterative expectation-maximisation (EM) algorithm to calculate penalised spline estimates. We established the large-sample properties such as uniform convergence and optimal rate of convergence for functional estimators, as well as asymptotic normality and efficiency for regression coefficient estimators.