Improving Fit Assessment and Incomplete Data Diagnostics in Structural Equation Modeling

提出的研究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，尤其是在长期进行的研究中，这些研究发生在现实世界中，而不是在实验室中，并且从参与者那里收集了大量数据。在分析数据缺失的数据集时，如果没有使用适当的统计技术处理缺失的数据，特别是在缺失不是随机的情况下，结论可能会有偏差。其他具有挑战性的条件也经常出现在社会科学数据集中，如非正态性，即偏离钟形分布。如何对具有缺失值的正态和非正态数据拟合的理论模型进行拟合估计和评价是本文研究的重点。该建议是在结构方程模型（sem）的背景下提出的，这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，而只能观察到它们的结果。这些变量通常被视为心理构念的适当表征，如人格特征和心理状态。sem包含更多标准的统计模型，例如作为特殊情况的回归。当评估一个提议的SEM如何很好地描述数据时，使用模型拟合统计。如果数据集包含缺失值，这些统计数据将会有偏差，如果数据集中的一些变量是非正态的，则会更有偏差。如何调整模型拟合统计的计算，使其在这些具有挑战性的情况下不再有偏差，是本提案概述的第一个研究方向。第二个方向是制定措施，评估单个汇总统计中缺失数据对模型和数据集的总体影响。这类统计数据尚未得到开发或研究。它们的发展将帮助研究人员衡量缺失数据对其模型估计质量的总体影响，并且还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鲁棒性。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.