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Semiparametric zero-inflated Bernoulli regression with applications.

Chin-Shang Li1, Minggen Lu2

  • 1School of Nursing, The State University of New York, University at Buffalo, Buffalo, NY, USA.

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|September 12, 2022
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Summary
This summary is machine-generated.

A new spline-based zero-inflated Bernoulli (ZIB) regression model effectively handles excess zeros in binary data. This semiparametric approach offers improved prediction accuracy over standard parametric models.

Keywords:
41A1562F4062J12B-splineBernoulli regressionbootstrapspline likelihood estimatorzero-inflated

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Standard logistic regression may not adequately model binary data with a high proportion of zeros.
  • Zero-inflated Bernoulli (ZIB) models are often employed to address this overdispersion of zeros.
  • The complex, potentially nonlinear effects of continuous covariates can be challenging to capture with traditional parametric models.

Purpose of the Study:

  • To propose a novel spline-based zero-inflated Bernoulli (ZIB) regression model.
  • To effectively describe the nonlinear influence of continuous covariates on binary outcomes.
  • To develop a consistent variance estimation method for the proposed model parameters.

Main Methods:

  • Utilized spline functions to approximate unknown smooth functions of continuous covariates within a ZIB framework.
  • Developed an easily implementable and consistent method for estimating regression parameter variances.
  • Conducted extensive simulations to evaluate finite-sample performance.
  • Applied the methodology to a real-life dataset.

Main Results:

  • The spline-based ZIB model demonstrated consistent estimation of the smooth function and asymptotically normal regression parameter estimators.
  • The proposed variance estimation method was found to be consistent.
  • Simulation studies confirmed the finite-sample performance of the method.
  • Real-life data analysis showed superior prediction performance compared to a parametric ZIB model.

Conclusions:

  • The proposed spline-based ZIB regression model offers a flexible and accurate approach for analyzing binary data with excess zeros.
  • This semiparametric method provides enhanced predictive power over traditional parametric ZIB models.
  • The methodology is practical and offers improved modeling of nonlinear covariate effects.