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

结构性错误说明指的是统计模型中的缺陷，例如遗漏变量、潜在变量数量错误来表示概念、或变量之间的关系表述不正确。结构性错误规范的研究不足，特别是考虑到它们的频率及其对解释、预测和理解结果变量的严重后果。该项目解决了潜变量结构方程模型(SEM)中出现的四个常见的结构性错误说明问题，对于这些问题还没有广泛接受的解决方案。它们是：(1)方差的负样本估计，(2)绝对值大于或等于1的样本相关估计，(3)潜在变量的维度检验，以及(4)诸如随机效应或方法因素等潜在变量的存在的检验。前两个问题要么反映了抽样波动，要么反映了结构性的错误说明。后两个问题是对潜变量必要性的检验。这些问题中的每一个都提出了通常的显着性检验不被经典的最大似然理论和显着性检验所证明是合理的条件。这项研究项目检验了通常的经典显着性检验对这类问题的稳健性，并开发了替代的显着性检验，在大样本中应该对这些条件具有稳健性。该项目使用分析结果来证明稳健显著性检验的合理性，并使用经验例子和蒙特卡洛模拟技术来检验各种正确和错误模型的经典检验和稳健显着检验的有限样本性能。该项目将导致建议研究人员应在哪些条件下采用经典和稳健的显著性检验。该项目将为研究人员提供诊断工具，以评估其统计模型的质量。例如，该项目将提供最好的方法来测试不适当的解决方案，如绝对值超过1的负误差方差估计或相关估计，是由于样本波动还是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相同的变量，或者模型中是否真的需要一些潜在变量。由于中小企业作为社会学、心理学、教育学、营销学和其他社会科学和自然科学中的一种分析工具的广泛普及，本项目中制定的中小企业方法的改进将提高研究的质量和这些科学领域的研究结果的有效性。这将有助于更好地理解通过结构方程模型研究的社会和自然过程。作为支持调查和统计方法研究的联合活动的一部分，这项研究得到了方法学、测量和统计计划和一个联邦统计机构联盟的支持。

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.