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Abstract:
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In sample surveys with sensitive items, sampled individuals either do not respond (nonignorable nonresponse) or they respond untruthfully. For example, responders usually give negative answers to sensitive items when the responses should actually have been positive, thereby leading to an estimate of the sensitive population proportion that is too small. For this study, we have sparse binary data on college cheating, collected under an unrelated-question design, from several locations (small areas) on a US campus. We have used a hierarchical Bayesian model to capture the variation in the observed binomial counts from these locations and to estimate the sensitive proportions for all locations. For our application on college cheating, there are significant reductions in the posterior standard deviations of the sensitive proportions under the small-area model in comparison to an analogous individual-area model. A simulation study confirms the gain in precision and, surprisingly, shows the estimates under the small-area model are closer to the truth than the corresponding estimates under the individual-area model.
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