A Split Questionnaire Survey Design

Abstract This article develops a survey design where the questionnaire is split into components and individuals are administered the varying subsets of the components. A multiple imputation method for analyzing data from this design is developed, in which the imputations are created by random draws from the posterior predictive distribution of the missing parts, given the observed parts by using Gibbs sampling under a general location scale model. Results from two simulation studies that investigate the properties of the inferences using this design are reported. In the first study several random split questionnaire designs are imposed on the complete data from an existing survey collected using a long questionnaire, and the corresponding data elements are extracted to form split data sets. Inferences obtained using the complete data and the split data are then compared. This comparison suggests that little is lost, at least in the example considered, by administering only parts of the questionnaire to each sampled individual. The second simulation study reports on the investigation of the efficiency of the split questionnaire design and the robustness of the estimates to the distributional assumptions used to create imputations. In this study several complete and split data sets were generated under a variety of distributional assumptions, and the imputations for the split data sets were created assuming the normality of the distributions. The sampling properties of the point and interval estimates of the regression coefficient in a particular logistic regression model using both the complete and split data sets were compared. This comparison suggests that the loss in efficiency of the split questionnaire design decreases as the correlation among the variables that are within different parts increases. The proposed multiple imputation method seems to be sensitive to the skewness and relatively insensitive to the kurtosis, contrary to the assumed normality of the distribution for the observables. Key Words: Gibbs samplingMultiple imputationNonresponseResponder burden