Improving Fit Assessment and Incomplete Data Diagnostics in Structural Equation Modeling

这项拟议的研究的目标是开发和评估处理缺失数据的新方法。在心理学研究中，数据缺失是很常见的，特别是在随着时间推移而发生的研究中，这些研究发生在现实世界中，而不是在实验室里，而且这些研究从参与者那里收集了大量数据。在分析具有缺失数据的数据集时，如果不使用适当的统计技术来处理缺失数据，尤其是当缺失不是随机的时，则结论可能是有偏见的。其他具有挑战性的条件也经常出现在社会科学数据集中，例如非正态分布，即偏离钟形分布。如何估计和评价适合于正态和非正态缺失数据的理论模型的拟合度是本文研究的重点。这项建议是在结构方程模型(SEM)的背景下提出的，结构方程模型是心理学中非常流行的一类统计模型。这些模型可以包括潜在变量，即不能直接观察到的变量，而只有其后果是可观察到的。这些变量通常被认为是心理结构的适当表现，例如人格特征和心理状态。SEMS包括更多的标准统计模型，如作为特例的回归。当评估所建议的结构方程描述数据的程度时，使用模型拟合统计。如果数据集包含缺失值，则这些统计数据将是有偏差的，如果数据集中的某些变量是非正常的，则更是如此。如何调整模型拟合统计量的计算，使其在这些具有挑战性的情况下不再有偏差，是本提案勾勒出的第一个研究方向。第二个方向是制定措施，在单一的汇总统计数据中评估缺失数据对模型和数据集的总体影响。这类统计数据尚未开发或研究过。它们的发展将有助于研究人员衡量缺失数据对模型估计质量的整体影响，也将帮助其他方法学家在评估新的统计方法时更好地捕捉缺失数据的稳健性。最终，能够从具有挑战性的数据集中得出正确的统计结论将提高心理学和相关领域的科学质量。

The proposed research has the goal of developing and evaluating new methodologies to deal with missing data. Missing data are common in psychological research, particularly in studies that take place over time, take place in the real world rather than in the lab, and that collect a lot of data from participants. When analyzing a dataset with missing data, conclusions may be biased if missing data are not treated using appropriate statistical techniques, particularly when missingness is not random. Other challenging conditions are also often present in social science datasets, such as nonnormality, i.e., deviation from bell-shaped distributions. How to estimate and evaluate the fit of theoretical models that are fit to normal and nonnormal data with missing values is the focus of the present proposal. The proposal is in the context of structural equation models (SEMs), a class of statistical models that are very popular in psychology. These models can include latent variables, i.e., that are not directly observable but instead only their consequences are observable. Such variables are frequently viewed as appropriate representations for psychological constructs, such as personality traits and psychological states. SEMs include more standard statistical models such as regression as a special case. When evaluating how well a proposed SEM describes the data, model fit statistics are used. These statistics will be biased if the dataset contains missing values, and more so if some variables in the dataset are nonnormal. How to adjust the computations of model fit statistics so that they are no longer biased under these challenging circumstances is the first research direction outlined in this proposal. The second direction is to develop measures that evaluate the overall impact of missing data on models and datasets in a single summary statistic. Such statistics have not been developed or studied. Their development will help researchers gauge the overall impact of missing data on the quality of estimation of their models, and it will also help other methodologists better capture the robustness to missing data when evaluating new statistical methods. Ultimately, being able to draw correct statistical conclusions from challenging datasets will improve the quality of the science in psychology and related fields.