Collaborative Research: Structural Misspecification in Latent Variable Models: Symptoms, Consequences, and Diagnostic Tests

结构性误设是指统计模型中的缺陷，例如遗漏变量，具有错误数量的潜变量来表示概念，或制定不正确的变量之间的关系。 结构性错误设定的研究不足，特别是考虑到他们的频率和解释，预测和理解结果变量的严重后果。 该项目解决了潜在变量结构方程模型（SEMs）中出现的四个常见的结构性错误指定问题，这些问题尚未得到广泛接受的解决方案。 这些是：（1）方差的负样本估计值，（2）绝对值大于或等于1的样本相关性估计值，（3）潜变量的维度检验，以及（4）潜变量（如随机效应或方法因子）存在的检验。 前两个问题反映了抽样波动或结构性错定。 最后两个问题是检查隐变量的必要性。 这些问题中的每一个目前的条件下，通常的显着性检验是不合理的经典最大似然理论和显着性检验。 本研究项目探讨了通常的经典显着性检验的鲁棒性等问题，并开发替代显着性检验，应该是强大的这些条件下，在大样本。 该项目使用分析结果来证明稳健显著性检验的合理性，并采用经验示例和蒙特卡罗模拟技术来检查各种正确和不正确模型的经典和稳健显著性检验的有限样本性能。 该项目将为研究人员使用经典和稳健显著性检验的条件提出建议，并为研究人员提供诊断工具，以评估其统计模型的质量。 例如，该项目将提供最佳方法来测试不正确的解决方案，如负误差方差估计或绝对值超过1的相关性估计，是否是由于样本波动或由于模型中更严重的错误。 它还将测试两个潜在变量是否真的是同一个变量，或者模型中是否真的需要一些潜在变量。 由于SEMS作为社会学、心理学、教育学、营销学以及其他社会和自然科学的分析工具广泛普及，本项目中开发的SEMS方法论的改进将提高这些领域的研究质量和研究结果的有效性。科学。 这将导致更好地理解社会和自然过程的结构方程模型的研究手段。 这项研究得到了方法、测量和统计方案以及联邦统计机构联合会的支持，作为支持调查和统计方法研究的联合活动的一部分。

Structural misspecifications refer to flaws in a statistical model such as omitted variables, having the erroneous number of latent variables to represent a concept, or formulating the incorrect set of relationships between variables. Structural misspecifications are understudied, particularly considering their frequency and their serious consequences for explaining, predicting, and understanding outcome variables. The project addresses four common structural misspecification problems that emerge in latent variable Structural Equation Models (SEMs) for which there have been no widely accepted solutions. These are: (1) negative sample estimates of variances, (2) sample correlation estimates with absolute values greater than or equal to one, (3) tests of dimensionality of latent variables, and (4) tests of the presence of latent variables such as random effects or method factors. The first two problems reflect either sampling fluctuations or structural misspecification. The last two problems are checks on the necessity for latent variables. Each of these problems present conditions under which the usual significance tests are not justified by classical maximum likelihood theory and significance tests. This research project examines the robustness of the usual classical significance tests for such problems and develops alternative significance tests that should be robust to these conditions in large samples. The project uses analytic results to justify the robust significance tests and employs empirical examples and Monte Carlo simulation techniques to examine the finite sample performance of the classical and the robust significance tests for a variety of correct and incorrect models. The project will lead to recommendations of the conditions under which researchers should employ classical and robust significance tests.This project will provide researchers with diagnostic tools to assess the quality of their statistical models. For example, the project will provide the best way to test whether improper solutions such as negative error variance estimates or correlation estimates whose absolute value exceeds one are due to sample fluctuations or due to a more serious error in the model. It also will provide tests of whether two latent variables are really the same variable or whether some latent variables are really needed in a model. Due to wide proliferation of SEMs as an analytical tool in sociology, psychology, education, marketing, and other social and natural sciences, the refinements in the methodology of SEMs developed in this project will improve the quality of research and validity of the findings in those areas of science. This will lead to better understanding of social and natural processes studied by means of structural equation models. The research is supported by the Methodology, Measurement, and Statistics Program and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.