Department of Statistics, University of Washington - Fred Hutchinson Cancer Research Center
Structural equation models and mixed effects models have independent histories of development and occupy distinct niches in statistical research and application. SEMS are multivariate formulations that evolved from the traditions of psychometrics, factor analysis, and causal modeling; they are implemented by programs such as LISREL, EQS, and CALIS, which use sample covariance matrices, rather than raw data, as both fitting criteria and input. Mixed effects models are primarily univariate formulations that evolved from the linear model tradition of regression and analysis of variance; they are implemented by programs such as SAS PROC MIXED (linear) and NONMEM (nonlinear, particularly pharmacodynamic/pharmacokinetic models), which maximize model fit with respect to raw data.
Traditional differences in focus and application obscure the similarities underlying these two approaches. When viewed through the lens of clinical longitudinal data, SEMS and MEMS reveal a surprising convergence and conceptual unity. Understanding these relationships allows the researcher to use available commercial software to formulate and test an extremely wide range of SEMS, MEMS, and hybrid models for longitudinal data.