A split questionnaire survey design in the context of statistical matching

In this paper, we tackle the problem of splitting a long (potentially time consuming) questionnaire into two parts, where each participant only responds to a fraction of the questions, and all respondents obtain a common portion of questions. We propose a method that combines regression models to the two independent samples (questionnaires) in the survey. Each sample includes the common response variable Y and common covariate x, while two vectors of specific covariates z and w are recorded such that no single sampling unit has answered both z and w. This corresponds to the problem of statistical matching that we tackle under the assumption of conditional independence. In the statistical matching context, we use a macro approach to estimate parameters of a regression model. This means that we can estimate the joint distribution of all variables of interest with available data utilizing the assumption of conditional independence. We make use of this here by fitting three regression models with the same response variable for each model. Combining the three models allows us to obtain a prediction model with all covariates in common. We compare the performance of our proposed method in simulation studies as well as a real data example. Our method gives better results as compared to commonly used alternative methods. The proposed routine is easy to apply in practice and it neither requires the formulation of a model for the covariates itself nor an imputation model for the missing covariates vectors z and w.