Two-stage methodology for regression, path analysis, and structural equation models with item-level missingness

拟议的研究的目标是发展和评价一种处理不完整数据的新方法，这种方法与个别项目数据缺失的独特情况有关，但统计模型处于复合水平（项目总和）。这种情况经常发生在社会科学领域。例如，在心理学中，模型中的变量通常是量表分数。如果在回归中使用变量“自尊”，它将被计算为组成自尊量表的10个项目的总和得分。第二个应用是结构方程模型（sem）——复杂的多元回归模型，可能涉及潜在变量，并允许测试复杂的心理学理论。在这种情况下，相对于心理学中常用的典型样本量，模型通常较大。建议通过将项目组合到复合材料中来减小模型大小。***拟议的研究将最近开发的两阶段（TS）方法扩展到不完整数据（Savalei & Bentler, 2009; Savalei & Falk, 2014）到复合材料的场景。它被认为是一种不会因丢失数据而丢失任何信息的方法。上下文是连续的正态分布数据，具有对非正态数据的扩展。缺失数据的现代处理方法包括最大似然（ML）和多重输入（MI）。无论何时可用，ML都更简单、更优雅，并提供了独特的解决方案。然而，机器学习方法不适用于复合的情况，因为它不能处理不直接进入模型的变量上的缺失数据。两阶段（TS）过程是一个基于ml的过程，将缺失数据处理与模型拟合分开。这样，就可以对复合材料进行直接处理。在阶段1中，ML被应用于获得具有缺失数据的原始变量的均值和协方差矩阵以及相关信息矩阵的估计。然后将估计转换为对应于组合的适当数量。在阶段2中，模型拟合到阶段1中组合的均值和协方差矩阵，基本上将这些数量视为来自完整数据。使用三明治估计器获得标准误差的一致估计，其中阶段1的复合材料的信息矩阵位于三明治的“肉”中。在本研究中，我将扩展TS方法用于复合材料。我将与SEM的免费R包（lavaan）的开发人员一起在R中实现这个方法。因为这个方法即使在简单的回归中也是有用的，所以我将编写一个R包来允许在不使用SEM包的情况下在这种情况下实现一个简单的实现。将对该方法进行广泛的评价。这种方法的发展、研究和普及将极大地有利于处理不完整数据的社会科学家。＊＊＊＊＊

The proposed research has the goal of developing and evaluating a new methodology to deal with incomplete data, relevant for the unique situation when data are missing on the individual items, but the statistical model is at the level of composites (sums of items). This scenario often occurs in the social sciences. For example, in psychology the variables in the model are often scale scores. If the variable "self-esteem" is to be used in regression, it will be computed as the sum score of 10 items that comprise the self-esteem scale. A second application is in the context of structural equation models (SEMs)--complex multivariate regression models that may involve latent variables and allow for testing of complex psychological theories. In this case, models are often large relative to the typical sample sizes commonly used in psychology. It is recommended to reduce model size by combining items into composites. ***The proposed research extends the recently developed two-stage (TS) methodology for incomplete data (Savalei & Bentler, 2009; Savalei & Falk, 2014) to the scenario with composites. It is argued to be the method that does not lose any information due to missing data. The context is continuous normally distributed data, with extensions to nonnormal data. Modern approaches to missing data include maximum likelihood (ML) and multiple imputation (MI). Whenever available, ML is simpler and more elegant, and provides a unique solution. However, the ML methodology is not available for the case with composites as it cannot handle missing data on variables that do not directly enter the model. The two-stage (TS) procedure is an ML-based procedure that separates missing data treatment from model fitting. In doing so, it allows for a straight-forward treatment of composites. In Stage 1, ML is applied to obtain estimates of means and covariance matrix, as well as of the associated information matrix, of the original variables that have missing data. The estimates are then transformed to correspond to the appropriate quantities for the composites. In Stage 2, the model is fit to the means and covariance matrix of the composites from Stage 1, essentially treating these quantities as if they had come from complete data. Consistent estimates of standard errors are obtained using the sandwich estimator, where the information matrix for the composites from Stage 1 is in the "meat" of the sandwich. ***In this research, I will extend the TS methodology for use with composites. I will work with the developer of a free R package for SEM (lavaan) to implement this methodology in R. Because this methodology is useful even in simple regression, I will write an R package to allow a simple implementation in this context without the use of SEM packages. Extensive evaluations of the methodology will be conducted. The development, study, and popularization of this methodology will greatly benefit social scientists working with incomplete data. *****