Researchers continue to choose PCA in scale development and adaptation studies because it is the default setting and overestimates measurement quality. When PCA is utilized in investigations, the explained variance and factor loadings can be exaggerated. PCA, in contrast to the models given in the literature, should be investigated in…

Factor analysis is widely utilized to identify latent factors underlying the observed variables. This paper presents a comprehensive comparative study of two widely used methods for determining the optimal number of factors in factor analysis, the K1 rule, and parallel analysis, along with a more recently developed method, the bass-ackward method.…

The alternative human capital evaluation method proposed is implemented via two methods: principal component analysis and discriminant analysis. The first method classifies the research laboratory activities in homogeneous clusters, while the second method standardizes their scores. The proposed method is sitting in the activity-based management…

The measurement error in principal components extracted from a set of fallible measures is discussed and evaluated. It is shown that as long as one or more measures in a given set of observed variables contains error of measurement, so also does any principal component obtained from the set. The error variance in any principal component is shown…

This manuscript's purpose is to introduce Q as a methodology before providing clarification about the preferred factor analytical choices of centroid and theoretical (hand) rotation. Stephenson, the creator of Q, designated that only these choices allowed for scientific exploration of subjectivity while not violating assumptions associated with…

This article argues that strong interrelations between methodological and theoretical advances exist. Progress in, especially comparative, methods may have important impacts on theory evaluation. By using the example of the "Varieties of Capitalism" approach and an international comparison of higher education systems, it can be shown…

This article reviews the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) in model selection and the appraisal of psychological theory. The focus is on latent variable models, given their growing use in theory testing and construction. Theoretical statistical results in regression are discussed, and more important…

There is a lack of research on the effects of outliers on the decisions about the number of factors to retain in an exploratory factor analysis, especially for outliers arising from unintended and unknowingly included subpopulations. The purpose of the present research was to investigate how outliers from an unintended and unknowingly included…

This study explored motivation and engagement among North American (the United States and Canada; n = 1,540), U.K. (n = 1,558), Australian (n = 2,283), and Chinese (n = 3,753) secondary school students. Motivation and engagement were assessed via students' responses to the Motivation and Engagement Scale-High School (MES-HS). Confirmatory factor…

Higher education institutions are interested in the impact that they and concurrent life experiences may have on students' sustainability attitudes, but they lack formal processes to monitor changes. We used the NEP to monitor changes in students' ecological-worldviews. We were interested in what variation there would be in a multidisciplinary…

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…

A common problem in exploratory factor analysis is how many factors need to be extracted from a particular data set. We propose a new method for selecting the number of major common factors: the Hull method, which aims to find a model with an optimal balance between model fit and number of parameters. We examine the performance of the method in an…

When comparing latent variables among groups, it is important to first establish the equivalence or invariance of the measurement model across groups. Confirmatory factor analysis (CFA) is a commonly used methodological approach to examine measurement equivalence/invariance (ME/I). Within the CFA framework, the chi-square goodness-of-fit test and…

A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category…

A common question in test evaluation is whether an a priori assignment of items to subtests is supported by empirical data. If the analysis results indicate the assignment of items to subtests under study is not supported by data, the assignment is often adjusted. In this study the authors compare two methods on the quality of their suggestions to…