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Abstract:
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Multiple matrix sampling is a component of survey design that divides a questionnaire into subsets of questions, and administers these subsets to different subsamples of respondents, so that data are missing completely at random by design. The promise of the method is in reducing survey burden and its associated problems such as unit and item nonresponse, and satisficing. There are two matrix sampling design challenges. The first is to determine the optimal allocation of individual items or scales to each subset of questions or questionnaire form. The second is to determine the optimal number of completed forms per subsample to achieve sufficiently stable survey estimates. This paper provides the power analysis framework for regression modeling with matrix-sampled data, and derives the asymptotic variances of regression estimates that use full information maximum likelihood estimation methods, such as structural equation modeling with missing values, or multiple imputation. Using selected psychological traits from the Big Five Inventory as an example, we demonstrate how to obtain optimal multiple matrix sampling plans that maximize the precision of the regression estimates, discuss sensitivity to the assumptions, and implications for survey practice.
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