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

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.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS160 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ranked Set Sampling for a Population Proportion:Allocation of Sample Units to Each Judgment Order Statistic

Ranked set sampling is an alternative to simple random sampling that has been shown to outperform simple random sampling in many situations by reducing the variance of an estimator, thereby providing the same accuracy with a smaller sample size than is needed in simple random sampling. Ranked set sampling involves preliminary ranking of potential sample units on the variable of interest using judgment or an auxiliary variable to aid in sample selection. Ranked set sampling prescribes the number of units from each rank order to be measured.   Balanced ranked set sampling assigns equal numbers of sample units to each rank order. Unbalanced ranked set sampling allows unequal allocation to the various ranks, but this allocation may be sensitive to the quality of information available to do the allocation.  In this paper we use a simulation study to conduct a sensitivity analysis of optimal allocation of sample units to each of the order statistics in unbalanced ranked set sampling. Our motivating example comes from the National Survey of Families and Households

Electronic resources: the Ohio state university EESEE project

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