Most existing studies on the relationship between factor analysis (FA) and principal component analysis (PCA) focus on approximating the common factors by the first few components via the closeness between their loadings. Based on a setup in Bentler and de Leeuw (Psychometrika 76:461-470, 2011), this study examines the relationship between FA…

Exploratory structural equation (ESEM) has received increased attention in the methodological literature as a promising tool for evaluating latent variable measurement models. It overcomes many of the limitations attached to exploratory factor analysis (EFA) and confirmatory factor analysis (CFA), while capitalizing on the benefits of each. Given…

Conceptualizing two-variable disturbances preventing good model fit in confirmatory factor analysis as item-level method effects instead of correlated residuals avoids violating the principle that residual variation is unique for each item. The possibility of representing such a disturbance by a method factor of a bifactor measurement model was…

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.…

This note demonstrates that the widely used Bayesian Information Criterion (BIC) need not be generally viewed as a routinely dependable index for model selection when the bifactor and second-order factor models are examined as rival means for data description and explanation. To this end, we use an empirically relevant setting with…

Regression factor score predictors have the maximum factor score determinacy, that is, the maximum correlation with the corresponding factor, but they do not have the same inter-correlations as the factors. As it might be useful to compute factor score predictors that have the same inter-correlations as the factors, correlation-preserving factor…

This note demonstrates that measurement invariance does not guarantee meaningful and valid group comparisons in multiple-population settings. The article follows on a recent critical discussion by Robitzsch and Lüdtke, who argued that measurement invariance was not a pre-requisite for such comparisons. Within the framework of common factor…

This dissertation compares the performance of equivalence test (EQT) and null hypothesis test (NHT) procedures for identifying invariant and noninvariant factor loadings under a range of experimental manipulations. EQT is the statistically appropriate approach when the research goal is to find evidence of group similarity rather than group…

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…

Thurstonian forced-choice modeling is considered to be a powerful new tool to estimate item and person parameters while simultaneously testing the model fit. This assessment approach is associated with the aim of reducing faking and other response tendencies that plague traditional self-report trait assessments. As a result of major recent…

This study aimed to develop a parent rating scale (PRSG) for screening children for further identification process in terms of giftedness. The participants of the study were 255 parents of gifted and non-gifted students. The PRSG, consisting of 30 items, was created by consulting parents and reviewing instruments existent in the literature. As…

The patient health questionnaire-9 (PHQ-9) is widely utilized in assessing individuals' depression levels. Nevertheless, research regarding its factor structure and measurement invariance remains inadequate. The aim of this study was to delve into the factor structure of the PHQ-9 and to further investigate its measurement invariance across gender…

I present a new model of the self-regulation of virtue that integrates perspectives on emotion, cognition, and motivation. Across three vignette-based studies in US/UK (N = 1,540), I developed through exploratory and confirmatory factor analysis a multi-item measure of broadening and defensive responses, the Self-Regulation of Virtue Inventory…

Researchers in second language (L2) and education domain use different statistical methods to assess their constructs of interest. Many L2 constructs emerge from elements/parts, i.e., the elements "define" and "form" the construct and not the other way around. These constructs are referred to as emergent variables (also called…

In this study, we take a critical look at the degree to which the measurement of bullying and sense of belonging at school is invariant across groups of students defined by immigrant status. Our study focuses on the invariance of these constructs as measured on a recent PISA administration and includes a discussion of two statistical methods for…