Structural equation modeling using gllamm, confa, and gmm
In this talk, I introduce the main ideas of structural equation models (SEMs) with latent variables and Stata tools that can be used for such models. The two approaches most often used in applied work are numeric integration of the latent variables and covariance structure modeling. The first approach is implemented in Stata via gllamm, which was developed by Sophia Rabe-Hesketh. The second approach is currently implemented in confa for confirmatory factor analysis models. Also, introduction of the generalized method of moments (GMM) estimation and testing framework in Stata 11 make it possible to estimate SEMs by using moderately complex parameter and matrix manipulations. I provide working examples with some popular datasets (Holzinger–Swineford factor analysis model and Bollen’s industrialization and political democracy model).
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