  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.
