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In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly efficient and that the likelihood ratio test of nonlinear effects is robust and outperforms alternative testing procedures. The new method is applied to empirical data of middle-aged men, where a latent interaction between physical fitness and flexibility in goal adjustment on complaint level is hypothesized. A model with 5 simultaneous nonlinear effects is analyzed, and the hypothesized interaction is quantified and tested positively against an additive model with quadratic and linear effects. (Contains 4 tables.)

In this article, a heterogeneous latent growth curve model for modeling heterogeneity of growth rates is proposed. The suggested model is an extension of a conventional growth curve model and a complementary tool to mixed growth modeling. It allows the modeling of heterogeneity of growth rates as a continuous function of latent initial status and time-invariant covariates. A quasi-ML parameter estimation method and a likelihood-ratio test for heterogeneity of growth is developed, and the new methodology is applied to an empirical example on math achievement data. The example illustrates that the proposed model gives more accurate confidence intervals for the prediction of future math achievement than a conventional growth curve model and identifies the subgroup of subjects which show the most homogeneous growth. (Contains 4 figures and 3 tables.)

The generalizability of K. M. Cramer's (1999) help-seeking model was examined for Asian and Asian American college students. The construct of acculturation was then added to Cramer's model to determine if it would improve the model fit. Asian and Asian American (n=202) students completed help-seeking measures and behavioral and value-based measures of acculturation. White (n=336) students completed only help-seeking measures. Although path analyses showed that Cramer's model fit both samples, structural invariance analysis indicated differential model functioning between groups that can be primarily attributed to self-concealment, a concept central to understanding Asians' and Asian Americans' attitudes toward help seeking. The addition of acculturation, especially adherence to Asian value, to Cramer's model improved model fit.

For the assessment of model fit in linear structural equation modeling (SEM), several fit measures have been developed that use an unconstrained mean and covariance structure, but cannot be readily applied to SEM with quadratic and interaction effects. In this article, we propose the novel quasi-likelihood ratio test (Q-LRT) to evaluate global fit of nonlinear SEM models. The Q-LRT is based on a simplification of the quasi-maximum likelihood method for the estimation of model parameters. An empirical application of the Q-LRT is demonstrated for data in a study about aging in men. Results from a Monte Carlo study show that the Q-LRT performs reliably when sample size is sufficiently large. Also, simulations suggest robustness of Q-LRT for moderately skewed latent exogenous variables. [ABSTRACT FROM AUTHOR]

The cohort growth model (CGM) is a method for estimating the parameters of a latent growth model (LGM) based on cross-sectional data. The CGM models the interindividual differences in the growth rate, and it models how subjects' growth rate is related to their initial status. We derive model identification for the CGM and illustrate, in a simulation study, that the CGM provides unbiased parameter estimates in most simulation conditions. Based on empirical data we compare the estimates of the CGM with the estimates of the LGM. The results were comparable for both models. Although the estimates of the (co)-variances were different, the estimates of both models led to similar conclusions on the developmental change. Finally, we discuss the advantages and limitations of the CGM, and we provide recommendations for its use in empirical research. [ABSTRACT FROM AUTHOR]

This article investigates likelihood-based difference statistics for testing nonlinear effects in structural equation modeling using the latent moderated structural equations (LMS) approach. In addition to the standard difference statisticTD, 2 robust statistics have been developed in the literature to ensure valid results under the conditions of nonnormality or small sample sizes: the robustTDRand the “strictly positive”TDRP. These robust statistics have not been examined in combination with LMS yet. In 2 Monte Carlo studies we investigate the performance of these methods for testing quadratic or interaction effects subject to different sources of nonnormality, nonnormality due to the nonlinear terms, and nonnormality due to the distribution of the predictor variables. The results indicate thatTDis preferable to bothTDRandTDRP. Under the condition of strong nonlinear effects and nonnormal predictors,TDRoften produced negative differences andTDRPshowed no desirable power. [ABSTRACT FROM AUTHOR]