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Structural equation analysis has been used widely in behavioral and social sciences. In practice, for continuous-type observed variables, linear structural equation models have been used nearly exclusively. The use of models that are nonlinear in latent vari­ ables has been limited to simple situations with a linear measurement model and with a single polynomial structural relationship, usually containing only one quadratic or crossproduct term. This paper introduces a general structural equation model with a non­ linear measurement model and a simultaneous system of nonlinear and non-polynomial structural relationships. For such a model, a parameterization useful for identification and interpretation is presented. For model fitting and parameter inferences, the max­ imum likelihood approach is considered. A method for obtaining parameter estimates and their asymptotic covariance matrix estimate is developed based on a new version of the Monte Carlo EM algorithm. This method is described comprehensively, includ­ ing initial values, convergence assessment, Monte Carlo sample size determination, and

Likelihood based procedures for general nonlinear structural equation analysis