The procedures of carrying out factorial invariance to validate a construct were well developed to ensure the reliability of the construct that can be used across groups for comparison and analysis, yet mainly restricted to the frequentist approach. This motivates an update to incorporate the growing Bayesian approach for carrying out the Bayesian…

Structural equation models comprise a large class of popular statistical models, including factor analysis models, certain mixed models, and extensions thereof. Model estimation is complicated by the fact that we typically have multiple interdependent response variables and multiple latent variables (which may also be called random effects or…

This article discusses the internationalization capacity building project at the Karaganda Technical University ('KTU') in Kazakhstan. The project, entitled "Capacity building for the internationalization of a technical university by means of digital learning technologies," was supported by the fund "Scientific foundations…

Principal component analysis (PCA) is one of the most important and powerful methods in chemometrics as well as in a wealth of other areas. Running a PCA results in two main elements, the score plot and the loading plot; the score plot provides the location of the samples, and the loading plot indicates correlations among variables, the trends in…

This paper presents heuristic explanations of factor scores, structure coefficients, and communality coefficients. Common misconceptions regarding these topics are clarified. In addition, (a) the regression (b) Bartlett, (c) Anderson-Rubin, and (d) Thompson methods for calculating factor scores are reviewed. Syntax necessary to execute all four…

The increasing use of ordinal variables in different fields has led to the introduction of new statistical methods for their analysis. The performance of these methods needs to be investigated under a number of experimental conditions. Procedures to simulate from ordinal variables are then required. In this article, we deal with simulation from…

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger and Swineford ("Psychometrika" 47:41-54, 1937). The bi-factor model has a general factor, a number of group factors, and an explicit bi-factor structure. Jennrich and Bentler ("Psychometrika" 76:537-549, 2011) introduced an exploratory form of bi-factor…

Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus…

State-space modeling techniques have been compared to structural equation modeling (SEM) techniques in various contexts but their unique strengths have often been overshadowed by their similarities to SEM. In this article, we provide a comprehensive discussion of these 2 approaches' similarities and differences through analytic comparisons and…

Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be…

The standardization of loadings gives a metric to the corresponding latent variable and thus scales the variance of this latent variable. By assigning an appropriately estimated weight to all the loadings on the same latent variable it can be achieved that the average squared loading is 1 as the result of standardization. As a consequence, there…

This article describes why measurement invariance is a critical issue to quantitative theory building within the field of human resource development. Readers will learn what measurement invariance is and how to test for its presence using techniques that are accessible to applied researchers. Using data from a LibQUAL+[TM] study of user…

In this article, I describe studies conducted over 25 years with secondary and post-secondary L2 learners in the United States. The evidence from these studies shows that there are important connections between students' early L1 skills and their L2 aptitude and L2 proficiency and that individual differences in students' L1 skills in elementary…

The use of an independent clusters basis for restricted factor analysis can be recommended in cases where the known structure of a subset of variables serves to determine the structure of the remaining variables in the set. A comparison of this technique with an appropriate form of restricted factor analysis is illustrated on a large set of…

The authors provide generalizations of R. J. Boik's (1993) studentized maximum root (SMR) procedure that allow for simultaneous inference on families of product contrasts including simple effect contrasts and differences among simple effect contrasts in coherent analyses of data from 2-factor fixed-effects designs. Unlike the F-based simultaneous…