The use of structural equation modelling has become increasingly common in the social and behavioural sciences. Based on a stochastic analysis of the multivariate density function of indicator variables, latent moderated structural Equations (LMS) implements iterative maximum likelihood estimation for the model parameters. K. A. Bollen developed a general method that makes use of the two stage least squares for structural equation models with nonlinear functions of latent variables. In structural equation modelling, the latent variables in the equation are usually linearly related. But in some cases, theory suggests that in addition to the linear effects a product of the latent predictor variables may have an additional effect on a latent criterion variable. In view of non-normality problems with latent interaction models, a stochastic analysis of the density functions involved by interaction models could provide a theoretical background for the development of efficient estimation methods and a better understanding of the major problems associated with latent interaction.
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