Chapter 22: Maximum Likelihood and Bayesian Estimation for Nonlinear Structural Equation Models

Melanie M. Wall & Melanie M. Wall

Maximum likelihood and bayesian estimation for nonlinear structural equation models Structural equation modeling (SEM) began at its roots as a method for modeling linear relationships among latent variables. The well-known software for SEM name LISREL (Jöreskog and Sörbom, 1996) stands for ‘ Linear Structural Relations’. But, in many cases, the restriction to linearity is not adequate or flexible enough to explain the phenomena of interest. For example, if the slope between two continuous latent variables is directly affected or ‘moderated’ by a third continuous latent variable, this relationship which can be modeled via a cross-product term between the two latent variables, cannot be estimated via the traditional SEM methods. The difficulty is that traditional estimation methods appropriate for fitting linear structural models are focused on minimization of a discrepancy function between the observed and modeled covariance matrix and this cannot be extended in a straightforward way to handle nonlinear Kenny ...

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