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June 2008 Bayesian models to adjust for response bias in survey data for estimating rape and domestic violence rates from the NCVS
Qingzhao Yu, Elizabeth A. Stasny, Bin Li
Ann. Appl. Stat. 2(2): 665-686 (June 2008). DOI: 10.1214/08-AOAS160

Abstract

It is difficult to accurately estimate the rates of rape and domestic violence due to the sensitive nature of these crimes. There is evidence that bias in estimating the crime rates from survey data may arise because some women respondents are “gagged” in reporting some types of crimes by the use of a telephone rather than a personal interview, and by the presence of a spouse during the interview. On the other hand, as data on these crimes are collected every year, it would be more efficient in data analysis if we could identify and make use of information from previous data. In this paper we propose a model to adjust the estimates of the rates of rape and domestic violence to account for the response bias due to the “gag” factors. To estimate parameters in the model, we identify the information that is not sensitive to time and incorporate this into prior distributions. The strength of Bayesian estimators is their ability to combine information from long observational records in a sensible way. Within a Bayesian framework, we develop an Expectation-Maximization-Bayesian (EMB) algorithm for computation in analyzing contingency table and we apply the jackknife to estimate the accuracy of the estimates. Our approach is illustrated using the yearly crime data from the National Crime Victimization Survey. The illustration shows that compared with the classical method, our model leads to more efficient estimation but does not require more complicated computation.

Citation

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Qingzhao Yu. Elizabeth A. Stasny. Bin Li. "Bayesian models to adjust for response bias in survey data for estimating rape and domestic violence rates from the NCVS." Ann. Appl. Stat. 2 (2) 665 - 686, June 2008. https://doi.org/10.1214/08-AOAS160

Information

Published: June 2008
First available in Project Euclid: 3 July 2008

zbMATH: 05591293
MathSciNet: MR2524351
Digital Object Identifier: 10.1214/08-AOAS160

Keywords: Categorical data analysis , Contingency table , EMB algorithm , incompletely classified data , Jackknife method , panel survey , survey mode

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.2 • No. 2 • June 2008
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