In the SEM literature, simplex and latent growth models have always been considered competing approaches for the analysis of longitudinal data, even if they are strongly connected and both of specific importance. General dynamic models, which simultaneously estimate autoregressive structures and latent curves, have been recently proposed in the…

The topic of this article is the interpretation of structural equation modeling (SEM) solutions. Its purpose is to augment structural modeling's metatheoretic resources while enhancing awareness of how problematic is the causal significance of SEM-parameter solutions. Part I focuses on the nonuniqueness and consequent dubious interpretability of…

Throughout much of the social and behavioral sciences, latent growth modeling (latent curve analysis) has become an important tool for understanding individuals' longitudinal change. Although nonlinear variations of latent growth models appear in the methodological and applied literature, a notable exclusion is the treatment of growth following…

The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main…

Incomplete or missing data is a common problem in almost all areas of empirical research. It is well known that simple and ad hoc methods such as complete case analysis or mean imputation can lead to biased and/or inefficient estimates. The method of maximum likelihood works well; however, when the missing data mechanism is not one of missing…

Differential item functioning (DIF) occurs when an item on a test or questionnaire has different measurement properties for 1 group of people versus another, irrespective of mean differences on the construct. This study focuses on the use of multiple-indicator multiple-cause (MIMIC) structural equation models for DIF testing, parameterized as item…

Evaluating the fit of a structural equation model via bootstrap requires a transformation of the data so that the null hypothesis holds exactly in the sample. For complete data, such a transformation was proposed by Beran and Srivastava (1985) for general covariance structure models and applied to structural equation modeling by Bollen and Stine…

This article is a methodological-substantive synergy. Methodologically, we demonstrate latent-variable contextual models that integrate structural equation models (with multiple indicators) and multilevel models. These models simultaneously control for and unconfound measurement error due to sampling of items at the individual (L1) and group (L2)…

The usefulness of structural equation modeling methodology for studying change is explored, considering individual and group change model classes. The relationship between the constant rate of change and simplex models as representatives of either class is examined, and both models are shown to be special cases of comprehensive latent curve…

The determinacy of variables in a structural equation model is considered, and it is shown that when the variables in the structural model are all manifest, the error-terms (disturbances) are uniquely determined given the parameters of the data. When the variables are all latent, the error-terms have indeterminate components. (SLD)

Contrasting positions about the evaluation of multiple tests of constraints and control of Type I errors in structural equation modeling (SEM) are presented. It is argued that researchers should consider controlling for Type I errors in evaluating multiple tests of constraints for other than exploratory analyses. (SLD)

Structural equation modelling is becoming increasingly popular in education. This article examines and compares a number of alternative assumptions governing nondirected paths in structural equation models without latent variables vis-a-vis a data set on lung ventilation. Some problems with the conventional procedures in path analysis are pointed…

Some problems of multiple-group factor rotation based on the parallel proportional profiles and confactor rotation of R. B. Cattell are described, and several alternative modeling solutions are proposed. Benefits and limitations of the structural-modeling approach to oblique confactor resolution are examined, and opportunities for research are…

Model evaluation is one of the most important aspects of structural equation modeling (SEM). Many model fit indices have been developed. It is not an exaggeration to say that nearly every publication using the SEM methodology has reported at least one fit index. Most fit indices are defined through test statistics. Studies and interpretation of…

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…