ABSTRACT
This chapter explores the flavors of factor analysis that have come to be termed confirmatory factor analysis (CFA), in which the analyst specifies the number of latent variables, and the pattern of dependence of observables on those latent variables. It describes a Bayesian approach and illustrative examples. The chapter explains a Bayesian approach to CFA using summary statistics rather than individual data points. CFA models typically specify the pattern of loadings, meaning that they express which observables load on which latent variables. When there are multiple latent variables, the authors often specify many fixed loadings, which can make for a cluttered DAG. There are a number of similarities between the graphical modeling approach in the DAGs and the path diagrammatic approach from conventional structural equation modelling (SEM) traditions. The chapter also focuses on CFA as expressed from an SEM perspective.
