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

用于回归、路径分析和具有项目级缺失的结构方程模型的两阶段方法

• 批准号: RGPIN-2015-05251
• 负责人: Savalei, Victoria
• 金额: $ 1.02万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=613440
• 关键词: Two; stage; methodology; regression; path

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.

拟议的研究的目标是开发和评估一种新的方法来处理不完整的数据，相关的独特的情况下，数据丢失的个别项目，但统计模型是在复合材料（项目的总和）的水平。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。如果变量“自尊”将用于回归，则将计算为自尊量表的10个项目的总分。第二个应用是在结构方程模型（SEM）的背景下-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理论。在这种情况下，模型通常相对于心理学中常用的典型样本大小来说很大。建议通过将项目合并到组合中来减小模型大小。 拟议的研究扩展了最近开发的不完整数据的两阶段（TS）方法（Savalei & Bentler，2009; Savalei & Falk，2014）到复合材料的场景。它被认为是一种不会因数据缺失而丢失任何信息的方法。上下文是连续的正态分布数据，扩展到非正态数据。缺失数据的现代方法包括最大似然法（ML）和多重插补法（MI）。只要可用，ML就更简单，更优雅，并提供独特的解决方案。然而，ML方法不适用于复合材料的情况，因为它无法处理未直接进入模型的变量的缺失数据。两阶段（TS）程序是一种基于ML的程序，将缺失数据处理与模型拟合分开。在这样做的过程中，它允许对复合材料进行直接处理。在第1阶段，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值。然后将估计值转换为对应于复合材料的适当数量。在第2阶段，模型拟合第1阶段的复合数据的均值和协方差矩阵，基本上将这些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，其中来自阶段1的复合材料的信息矩阵在三明治的“肉”中。 在这项研究中，我将扩展TS方法用于复合材料。我将与SEM（lavaan）的免费R软件包的开发人员合作，在R中实现这种方法。因为这种方法即使在简单的回归中也很有用，所以我将编写一个R包，以便在此上下文中进行简单的实现，而无需使用SEM包。将对方法进行广泛的评价。这一方法的发展、研究和推广将使从事不完全数据工作的社会科学家受益匪浅。