Skip to main content

Research

Structural equation modeling (SEM) is a powerful statistical modeling tool that allows scientists to fit complex multivariate models with multiple observed and latent variables, with causal chains, and with linear and nonlinear constraints. SEM subsumes other statistical techniques such as regression, path analysis, and factor analysis. One benefit of SEM is that it provides estimates of the relationships between latent factors, controlling for measurement error. Another benefit is that SEM produces a test of fit for the entire model.

The increasing popularity of SEM has created a need for new developments that are better suited for the types of data that many behavioral scientists have: namely, data that are far from “ideal” but are instead nonnormally distributed, contain missing values, are categorical in nature (e.g., Likert items), or constitute a relatively small sample. A major research direction of our lab has been to develop and evaluate new methods for the SEM analysis of data with one or more of these characteristics, with a special focus on fit assessment. A particular interest is in the two-stage maximum likelihood (TSML) estimation method with missing data, which our lab continues to develop, test, and implement in R.

Another major research direction is critical evaluation of the “rites and rituals” of SEM analyses, which often culminates in offering new methods or guidelines. Models of interest are those that are extremely popular in psychology, such as bifactor models, models for the assessment of measurement invariance, and other measurement models.

An emerging research direction is a focus on disaggregated modeling and/or fit assessment. This research direction reconsiders one of the main touted advantages of SEM, namely that the entire model is fit and evaluated all at once: can this actually be a disadvantage? The goal is to develop fit indices for nested models, which permit sequential evaluation of model constraints. Recently, a particular focus has been measurement invariance. Another goal is to develop fit indices following so-called limited information estimation methods, which are designed to be more robust to model misspecification.

Student-Led Projects

In our lab, students are free to pursue their own interests. As a result, students often work on topics that interest them, even if they don’t neatly fit into one of the research directions listed above! See brief descriptions of some current projects below.

  • Dynamic SEMs with composites – A set of projects led by Sijia Li
  • Composite-level measurement invariance – Project co-authored with Malina Lemmons
  • Sample size planning in CFA – Project led by Adrien Ward (with undergraduate student Atharv Murali)
  • Latent interactions in SEM – Project led by Cindy Yu