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Improved Estimation of Poisson Rate Distributions Through a Multimode Survey Design

Researchers interested in studying the frequency of events or behaviors among a population must rely on count data provided by sampled individuals. Often, this involves a decision between live event counting, such as a behavioral diary, and recalled aggregate counts. Diaries are generally more accurate, but their greater cost and respondent burden generally yield less data. The choice of survey mode, therefore, involves a potential trade-off between bias and variance of estimators. We use a case study comparing inferences about payment instrument use based on different survey designs to illustrate this dilemma. We then use a simulation study to show how and under what conditions a hybrid survey design can improve efficiency of estimation, in terms of mean-squared error. Overall, our work suggests that such a hybrid design can have considerable benefits, as long as there is nontrivial overlap in the diary and recall samples.