A-Optimal Split Questionnaire Designs for Multivariate Continuous Variables
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A split questionnaire design (SQD), an alternative to full questionnaires, can reduce the response burden and improve survey quality. One can design a split questionnaire to reduce the information loss from missing data induced by the split questionnaire. This study develops a methodology for finding optimal SQD (OSQD) for multivariate continuous variables, applying a probabilistic design and optimality criterion approach. Our method employs previous survey data to compute the Fisher information matrix and A-optimality criterion to find OSQD for the current survey study. We derive theoretical findings on the relationship between the correlation structure and OSQD and the robustness of local OSQD. We conduct simulation studies to compare local and two global OSQDs; mini-max OSQD and Bayes OSQD) to baselines. We also apply our method to the 2016 Pet Demographic Survey (PDS) data. In both simulation studies and the real data application, local and global OSQDs outperform the baselines.
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