## The Annals of Applied Statistics

### Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study

#### Abstract

The NEXT Generation Health study investigates the dating violence of adolescents using a survey questionnaire. Each student is asked to affirm or deny multiple instances of violence in his/her dating relationship. There is, however, evidence suggesting that students not in a relationship responded to the survey, resulting in excessive zeros in the responses. This paper proposes likelihood-based and estimating equation approaches to analyze the zero-inflated clustered binary response data. We adopt a mixed model method to account for the cluster effect, and the model parameters are estimated using a maximum-likelihood (ML) approach that requires a Gaussian–Hermite quadrature (GHQ) approximation for implementation. Since an incorrect assumption on the random effects distribution may bias the results, we construct generalized estimating equations (GEE) that do not require the correct specification of within-cluster correlation. In a series of simulation studies, we examine the performance of ML and GEE methods in terms of their bias, efficiency and robustness. We illustrate the importance of properly accounting for this zero inflation by reanalyzing the NEXT data where this issue has previously been ignored.

#### Article information

Source
Ann. Appl. Stat., Volume 9, Number 1 (2015), 275-299.

Dates
First available in Project Euclid: 28 April 2015

https://projecteuclid.org/euclid.aoas/1430226093

Digital Object Identifier
doi:10.1214/14-AOAS791

Mathematical Reviews number (MathSciNet)
MR3341116

Zentralblatt MATH identifier
06446569

#### Citation

Fulton, Kara A.; Liu, Danping; Haynie, Denise L.; Albert, Paul S. Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study. Ann. Appl. Stat. 9 (2015), no. 1, 275--299. doi:10.1214/14-AOAS791. https://projecteuclid.org/euclid.aoas/1430226093

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#### Supplemental materials

• Supplement to "Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study".: Supplement A: Additional simulation one. Examine the performance of the proposed model with a smaller sample size ($N=500$). Supplement B: Additional Simulation Two. Examine the sensitivity of assuming a constant zero-inflation probability when the probability is affected by covariates. Supplement C: Additional Simulation Three. Examine the performance of zero-inflated beta-binomial model.