Genomic SEM provides substantial user flexibility with respect to the particular SEM that is specified to produce the model-implied covariance matrix ∑(θ) that approximates the empirical covariance matrix, S. SEMs can be partitioned into two sets of equations, one describing the measurement model, and the other describing the structural model. In the measurement model, the genetic components of k “indicator” phenotypes are described as linear functions of a smaller set of m (continuous) latent variables, y=Λη+ε. In this equation, y is a k×1 vector of indicators, ε is a k×1 vector of residuals, η is an m×1 vector of latent variables, and Λ is a k×m matrix of factor loadings, i.e. regressions relating the latent variables to the set of indicators. In a typical application of Genomic SEM, each indicator is a function of exactly one of the latent variables (though this so-called “simple structure” restriction may be relaxed). In a confirmatory factor analysis (CFA) model, only the measurement model is specified, and the set of latent variables are allowed to freely covary. Thus, the model-implied covariance matrix of a
