latent interaction effects, mixture distribution, ML estimation, structural equation modeling (SEM), EM algorithm,

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Abstract. Challenges in evaluating nonlinear effects in multiple regression analyses include reliability, validity, multicollinearity, and dichotomization of continuous variables. While reliability and validity issues are solved by employing nonlinear structural equation modeling, multicollinearity remains a problem which may even be aggravated when using latent variable approaches. Further challenges of nonlinear latent analyses comprise the distribution of latent product terms, a problem especially relevant for approaches using maximum likelihood estimation methods based on multivariate normally distributed variables, and unbiased estimates of nonlinear effects under multicollinearity. The only methods that explicitly take the nonnormality of nonlinear latent models into account are latent moderated structural equations (LMS) and quasi-maximum likelihood (QML). In a small simulation study both methods yielded unbiased parameter estimates and correct estimates of standard errors for inferential statistics. The advantages and limitations of nonlinear structural equation modeling are discussed.

An extension of latent state-trait (LST) theory to hierarchical LST models is presented. In hierarchical LST models, the covariances between 2 or more latent traits are explained by a general 3rd-order factor, and the covariances between latent state residuals pertaining to different traits measured on the same measurement occasion are explained by 2nd-order latent occasion-specific factors. Analogous to recent developments in multitrait-multimethod methodology, all factors are interpreted in relation to factors taken as comparison standards. An empirical example from test anxiety research illustrates how estimates of additive variance components due to general trait, specific trait, occasion, state residual, method, and measurement error can be obtained using confirmatory factor analysis. Advantages and limitations of these models are discussed.