Next Steps in Bayesian Structural Equation Models: Comments on, Variations of, and Extensions to Muthen and Asparouhov (2012)

Muthen and Asparouhov (2012) made a strong case for the advantages of Bayesian methodology in factor analysis and structural equation models. I show additional extensions and adaptations of their methods and show how non-Bayesians can take advantage of many (though not all) of these advantages by using interval restrictions on parameters. By keeping parameters restricted to intervals (such as loadings between -.3 and .3 to produce small loadings), frequentists using standard structural equation modeling software can do something similar to what a Bayesian does by putting prior distributions on these parameters.