Structural Equations with Latent Variables
In Chapter 2 we have discussed and demonstrated CFA models or measurement models. Once the factorial structure of the underlying constructs is validated using CFA, the measurement model is ready to be used for further studies on relationships involving latent variables/factors. Observed variables can be included into the CFA model to study relationships between latent variables and observed covariates. A CFA model with covariates is also called a MIMIC model that can be used to study not only the relationships between factors and covariates, but also measurement invariance and population heterogeneity. When any covariance/correlation between latent variables/factors (represented by a curved line with an arrow in both directions in the model diagram) is replaced with a causal effect (represented by a line with an arrow in one direction in the model diagram), the model becomes a general SEM model, in which a specific factor can be specified to predict other factors or is influenced by other factors. Not only observed exogenous variables or covariates can be included to predict latent variables/factors, and the latter can also be used to predict observed endogenous dependent variables. We start with discussion of the MIMIC model that is a special case of SEM.