The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be…

This article presents the use of an ant colony optimization (ACO) algorithm for the development of short forms of scales. An example 22-item short form is developed for the Diabetes-39 scale, a quality-of-life scale for diabetes patients, using a sample of 265 diabetes patients. A simulation study comparing the performance of the ACO algorithm and…

Horn's parallel analysis (PA) is the method of consensus in the literature on empirical methods for deciding how many components/factors to retain. Different authors have proposed various implementations of PA. Horn's seminal 1965 article, a 1996 article by Thompson and Daniel, and a 2004 article by Hayton, Allen, and Scarpello all make assertions…

Multitrait-multimethod (MTMM) confirmatory factor models were combined with longitudinal structural equation models to examine trait and method stability over time. A longitudinal correlated-trait correlated-method (CT-CM) model allowed for the study of trait and method variance in observed scores over time. Longitudinal measurement invariance was…

One can distinguish statistical models used in causal modeling from the causal interpretations that align them with substantive hypotheses. Causal modeling typically assumes an efficient causal interpretation of the statistical model. Causal modeling can also make use of mereological causal interpretations in which the state of the parts…

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…

This article provides the theory and application of the 2-stage maximum likelihood (ML) procedure for structural equation modeling (SEM) with missing data. The validity of this procedure does not require the assumption of a normally distributed population. When the population is normally distributed and all missing data are missing at random…

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)…

Controversy surrounding the use of race-conscious admissions can be partially resolved with improved empirical knowledge of the effects of racial diversity in educational settings. We use a national sample of law students nested in 64 law schools to test the complex and largely untested theory regarding the effects of educational diversity on…

A procedure is proposed to generate non-normal data for simulation of structural equation models. The procedure uses a simple transformation of univariate random variables for the generation of data on latent and error variables under some restrictions for the elements of the covariance matrices for these variables. (SLD)

The interpretation of a Thurstonian model for paired comparisons where the utilities' covariance matrix is unrestricted proved to be difficult due to the comparative nature of the data. We show that under a suitable constraint the utilities' correlation matrix can be estimated, yielding a readily interpretable solution. This set of identification…

Presents a necessary and sufficient condition for the equivalence of structural-equation models that is applicable to models with parameter restrictions and models that may or may not fulfill assumptions of the rules. Illustrates the application of the approach for studying model equivalence. (SLD)

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…