In an addendum to his seminal 1969 article Joreskog stated two sets of conditions for rotational identification of the oblique factor solution under utilization of fixed zero elements in the factor loadings matrix (Joreskog in "Advances in factor analysis and structural equation models," pp. 40-43, 1979). These condition sets, formulated under…

Recent research reflects a growing awareness of the value of using structural equation models to analyze repeated measures data. However, such data, particularly in the presence of covariates, often lead to models that either fit the data poorly, are exceedingly general and hard to interpret, or are specified in a manner that is highly data…

Despite wide applications of both mediation models and missing data techniques, formal discussion of mediation analysis with missing data is still rare. We introduce and compare four approaches to dealing with missing data in mediation analysis including list wise deletion, pairwise deletion, multiple imputation (MI), and a two-stage maximum…

Starting with Kenny and Judd ("Psychol. Bull." 96:201-210, 1984) several methods have been introduced for analyzing models with interaction terms. In all these methods more information from the data than just means and covariances is required. In this paper we also use more than just first- and second-order moments; however, we are aiming to…

The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we study tests of measurement…

We propose a new method of structural equation modeling (SEM) for longitudinal and time series data, named Dynamic GSCA (Generalized Structured Component Analysis). The proposed method extends the original GSCA by incorporating a multivariate autoregressive model to account for the dynamic nature of data taken over time. Dynamic GSCA also…

The G-DINA ("generalized deterministic inputs, noisy and gate") model is a generalization of the DINA model with more relaxed assumptions. In its saturated form, the G-DINA model is equivalent to other general models for cognitive diagnosis based on alternative link functions. When appropriate constraints are applied, several commonly used…

A distinction is proposed between measures and predictors of latent variables. The discussion addresses the consequences of the distinction for the true-score model, the linear factor model, Structural Equation Models, longitudinal and multilevel models, and item-response models. A distribution-free treatment of calibration and…

The paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package "rsem" to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of the saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables…

OpenMx is free, full-featured, open source, structural equation modeling (SEM) software. OpenMx runs within the "R" statistical programming environment on Windows, Mac OS-X, and Linux computers. The rationale for developing OpenMx is discussed along with the philosophy behind the user interface. The OpenMx data structures are…

Structural equation models are increasingly used as a modeling tool for multivariate time series data in the social and behavioral sciences. Standard error estimators of SEM models, originally developed for independent data, require modifications to accommodate the fact that time series data are inherently dependent. In this article, we extend a…

This paper proposes a structural analysis for generalized linear models when some explanatory variables are measured with error and the measurement error variance is a function of the true variables. The focus is on latent variables investigated on the basis of questionnaires and estimated using item response theory models. Latent variable…

As pointed out by Sijtsma ("in press"), coefficient alpha is inappropriate as a single summary of the internal consistency of a composite score. Better estimators of internal consistency are available. In addition to those mentioned by Sijtsma, an old dimension-free coefficient and structural equation model based coefficients are…

The general use of coefficient alpha to assess reliability should be discouraged on a number of grounds. The assumptions underlying coefficient alpha are unlikely to hold in practice, and violation of these assumptions can result in nontrivial negative or positive bias. Structural equation modeling was discussed as an informative process both to…

A method is presented for estimating reliability using structural equation modeling (SEM) that allows for nonlinearity between factors and item scores. Assuming the focus is on consistency of summed item scores, this method for estimating reliability is preferred to those based on linear SEM models and to the most commonly reported estimate of…