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.
