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  • https://doi.org/10.1214/26-aoas2146Copy DOI Icon

A partially collapsed Gibbs sampling algorithm for regression with misreported response

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Abstract

In this paper our objective is to identify the risk factors associated with adolescent marijuana use in Washington State, utilizing data from the 2018 and 2021 Healthy Youth Survey (HYS). Despite the survey’s assurance of anonymity, the possibility of over- or underreporting exists due to various reasons, such as fear of being exposed, social stigma, and peer pressure. We are also interested in identifying factors that are associated with the occurrence of misreport. To achieve these goals, we develop a full Bayesian framework with a two-level latent linear regression model. The top level is for the true marijuana use response, and the second level is for the occurrence of misreporting. An informative prior is designed to seamlessly incorporate the domain knowledge or prior information while minimizing the risk of prior misspecification. We propose a partially collapsed Gibbs sampling algorithm with a Metropolis–Hastings step to sample the regression coefficients. Simulation studies have been conducted to demonstrate the superior performance of the proposed method over alternative approaches. Our analysis of HYS data discovers multiple factors for identifying at-risk adolescents and informing future prevention efforts.

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