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 joint normal distribution, the default in many statistical software packages. This distribution will in general be misspecified if the predictors with missing data have nonlinear effects (e.g., x2) or are included in interaction terms (e.g., x·z). In the present article, we discuss a sequential modeling approach that can be applied to decompose the joint distribution of the variables into 2 parts: (a) a part that is due to the model of interest and (b) a part that is due to the model for the incomplete predictors. We demonstrate how the sequential modeling approach can be used to implement a multiple imputation strategy based on Bayesian estimation techniques that can accommodate rather complex substantive regression models with nonlinear effects and also allows a flexible treatment of auxiliary variables. In 4 simulation studies, we showed that the sequential modeling approach can be applied to estimate nonlinear effects in regression models with missing values on continuous, categorical, or skewed predictor variables under a broad range of conditions and investigated the robustness of the proposed approach against distributional misspecifications. We developed the R package mdmb, which facilitates a user-friendly application of the sequential modeling approach, and we present a real-data example that illustrates the flexibility of the software. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

中文翻译：

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涉及带有缺失数据的非线性效应的回归模型：一种使用贝叶斯估计的顺序建模方法。

当使用不完整的预测变量估计多个回归模型时，有必要为预测变量指定一个联合分布。一个方便的假设是，此分布是联合正态分布，这是许多统计软件包中的默认分布。如果缺少数据的预测变量具有非线性影响（例如x2）或包含在交互项中（例如x·z），则通常会错误地指定此分布。在本文中，我们讨论了一种顺序建模方法，该方法可用于将变量的联合分布分解为两个部分：（a）由于感兴趣的模型而产生的部分（b）由于感兴趣的模型而产生的部分不完整预测变量的模型。我们演示了如何使用顺序建模方法基于贝叶斯估计技术来实施多重插补策略，该方法可以容纳具有非线性效应的相当复杂的实质回归模型，并且还可以灵活处理辅助变量。在4个模拟研究中，我们证明了在较宽的条件范围内，连续建模方法可用于估计连续值，分类值或偏斜的预测变量缺少值的回归模型的非线性影响，并研究了该方法对分布的鲁棒性规格不正确。我们开发了R包mdmb，它促进了顺序建模方法的用户友好型应用，并提供了一个实际数据示例，说明了软件的灵活性。