Structural Equation Modeling with a Small Number of Observations (N) and a Large Number of Variables (p)

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

This research project will develop structural equation modeling (SEM) methodology that can be applied to data with a small number of observations (N) and a large number of variables (p). The new methods will broaden the applicability of SEM to important areas of research where the number of observations may be quite small, such as data from hard-to-reach populations. Data and methods for data analysis are key to advancing science. SEM is used by many disciplines, including psychology, education, sociology, management, health sciences, and medicine. Existing SEM methodology requires the number of observations to be proportional to the square of the number of variables. However, it may be difficult to collect the large number of observations required by SEM to reach reliable conclusions. The new methodology is expected to yield reliable results when N is either larger than 30 or two times the number of variables. The research has the potential to both improve data analyses and reduce data collection costs. The methods will be implemented in freely available, user-friendly software. With small N and/or large p, existing methods for SEM face four major practical issues: (1) near singular sample covariance matrices and the related issue of nonconvergence in parameter estimation; (2) inefficient parameter estimates with non-normal data; (3) unreliable model test statistics; and (4) inaccurate standard errors. The project will address the first issue by adding a proper diagonal matrix to the sample covariance matrix or the ridge method, an approach that has been shown to be effective. The other issues will be addressed by a new method termed empirical modeling, in which the empirical behavior of a test statistic/standard error is modeled under a variety of conditions. By combining empirical modeling and the ridge method, the project is expected to produce efficient parameter estimates and reliable model inference.