Leibniz Institute for Science and Mathematics Education.
Centre for International Student Assessment.
Multivariate Behav Res. 2020 May-Jun;55(3):361-381. doi: 10.1080/00273171.2019.1640104. Epub 2019 Jul 31.
When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., ) or are included in interaction terms (e.g., ·). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.
当估计具有不完全预测变量的多元回归模型时，有必要为预测变量指定联合分布。一个方便的假设是，该分布是多元正态分布，这也是许多统计软件包中的默认分布。如果具有缺失数据的预测因子具有非线性效应（例如， ）或包含在交互项中（例如， ·），则该分布通常会被错误指定。在本文中，我们介绍了一种基于最大似然估计的缺失数据回归模型的因子回归建模方法。在这种方法中，模型似然函数被分解为两部分，一部分是由于感兴趣的模型，另一部分是由于不完全预测因子的模型。在三项模拟研究中，我们表明，在广泛的条件下，对于具有缺失值的分类或连续预测变量的回归模型，因子回归建模方法产生了对交互作用和非线性效应的有效估计。我们开发了 R 包 mdmb，它方便了因子回归建模方法的用户友好应用，并提供了一个实际数据示例，说明了该软件的灵活性。
