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.

在本文中，我们解决了将一个较长的（可能很耗时）问卷分为两部分的问题，其中每个参与者仅回答一部分问题，而所有受访者都获得了相同部分的问题。我们提出了一种将回归模型结合到调查中的两个独立样本（问卷）的方法。每个样本都包括公共响应变量Y和公共协变量x，同时记录了两个特定协变量z和w的向量，因此没有一个采样单元同时回答z和w。这对应于我们在条件独立性假设下解决的统计匹配问题。在统计匹配上下文中，我们使用宏方法来估计回归模型的参数。这意味着我们可以利用条件独立性的假设，通过可用数据估算所有关注变量的联合分布。我们在这里通过将三个回归模型拟合为每个模型具有相同的响应变量来利用这一点。结合这三个模型，我们可以获得具有所有共同变量的预测模型。我们在仿真研究和实际数据示例中比较了我们提出的方法的性能。与常用的替代方法相比，我们的方法可提供更好的结果。z和w。