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It is difficult to accurately estimate the rates of rape and domesticviolence due to the sensitive nature of these crimes. There is evidence thatbias in estimating the crime rates from survey data may arise because somewomen respondents are "gagged" in reporting some types of crimes by the use ofa telephone rather than a personal interview, and by the presence of a spouseduring the interview. On the other hand, as data on these crimes are collectedevery year, it would be more efficient in data analysis if we could identifyand make use of information from previous data. In this paper we propose amodel to adjust the estimates of the rates of rape and domestic violence toaccount for the response bias due to the "gag" factors. To estimate parametersin the model, we identify the information that is not sensitive to time andincorporate this into prior distributions. The strength of Bayesian estimatorsis their ability to combine information from long observational records in asensible way. Within a Bayesian framework, we develop anExpectation-Maximization-Bayesian (EMB) algorithm for computation in analyzingcontingency table and we apply the jackknife to estimate the accuracy of theestimates. Our approach is illustrated using the yearly crime data from theNational Crime Victimization Survey. The illustration shows that compared withthe classical method, our model leads to more efficient estimation but does notrequire more complicated computation.

Bayesian models to adjust for response bias in survey data for estimating rape and domestic violence rates from the NCVS