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June 2015 Sex, lies and self-reported counts: Bayesian mixture models for heaping in longitudinal count data via birth–death processes
Forrest W. Crawford, Robert E. Weiss, Marc A. Suchard
Ann. Appl. Stat. 9(2): 572-596 (June 2015). DOI: 10.1214/15-AOAS809

Abstract

Surveys often ask respondents to report nonnegative counts, but respondents may misremember or round to a nearby multiple of 5 or 10. This phenomenon is called heaping, and the error inherent in heaped self-reported numbers can bias estimation. Heaped data may be collected cross-sectionally or longitudinally and there may be covariates that complicate the inferential task. Heaping is a well-known issue in many survey settings, and inference for heaped data is an important statistical problem. We propose a novel reporting distribution whose underlying parameters are readily interpretable as rates of misremembering and rounding. The process accommodates a variety of heaping grids and allows for quasi-heaping to values nearly but not equal to heaping multiples. We present a Bayesian hierarchical model for longitudinal samples with covariates to infer both the unobserved true distribution of counts and the parameters that control the heaping process. Finally, we apply our methods to longitudinal self-reported counts of sex partners in a study of high-risk behavior in HIV-positive youth.

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Forrest W. Crawford. Robert E. Weiss. Marc A. Suchard. "Sex, lies and self-reported counts: Bayesian mixture models for heaping in longitudinal count data via birth–death processes." Ann. Appl. Stat. 9 (2) 572 - 596, June 2015. https://doi.org/10.1214/15-AOAS809

Information

Received: 1 May 2014; Revised: 1 February 2015; Published: June 2015
First available in Project Euclid: 20 July 2015

zbMATH: 06499921
MathSciNet: MR3371326
Digital Object Identifier: 10.1214/15-AOAS809

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.9 • No. 2 • June 2015
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