Most methods for structural equation modeling (SEM) focused on the analysis of covariance matrices. However, "Historically, interesting psychological theories have been phrased in terms of correlation coefficients." This might be because data in social and behavioral sciences typically do not have predefined metrics. While proper methods…

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.…

A two-level data set can be structured in either long format (LF) or wide format (WF), and both have corresponding SEM approaches for estimating multilevel models. Intuitively, one might expect these approaches to perform similarly. However, the two data formats yield data matrices with different numbers of columns and rows, and their "cols :…

Among all, Cronbach's Alpha and McDonald's Omega are commonly used for reliability estimations. The alpha uses inter-item correlations while omega is based on a factor analysis result. This study uses simulated ordinal data sets to test whether the alpha and omega produce different estimates. Their performances were compared according to the…

When testing a statistical mediation model, it is assumed that factorial measurement invariance holds for the mediating construct across levels of the independent variable X. The consequences of failing to address the violations of measurement invariance in mediation models are largely unknown. The purpose of the present study was to…

When researchers fit statistical models to multiply imputed datasets, they have to fit the model separately for each imputed dataset. Since there are multiple datasets, there are always multiple sets of model results. It is possible for some of these sets of results not to converge while some do converge. This study examined occurrence of such a…

This article offers an approach to examining differential item functioning (DIF) under its item response theory (IRT) treatment in the framework of confirmatory factor analysis (CFA). The approach is based on integrating IRT- and CFA-based testing of DIF and using bias-corrected bootstrap confidence intervals with a syntax code in Mplus.

Evaluations of measurement invariance provide essential construct validity evidence--a prerequisite for seeking meaning in psychological and educational research and ensuring fair testing procedures in high-stakes settings. However, the quality of such evidence is partly dependent on the validity of the resulting statistical conclusions. Type I or…

The normal-distribution-based likelihood ratio statistic T[subscript ml] = nF[subscript ml] is widely used for power analysis in structural Equation modeling (SEM). In such an analysis, power and sample size are computed by assuming that T[subscript ml] follows a central chi-square distribution under H[subscript 0] and a noncentral chi-square…

In this article, an overview is given of four methods to perform factor score regression (FSR), namely regression FSR, Bartlett FSR, the bias avoiding method of Skrondal and Laake, and the bias correcting method of Croon. The bias correcting method is extended to include a reliable standard error. The four methods are compared with each other and…

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation…

Determining sample size requirements for structural equation modeling (SEM) is a challenge often faced by investigators, peer reviewers, and grant writers. Recent years have seen a large increase in SEMs in the behavioral science literature, but consideration of sample size requirements for applied SEMs often relies on outdated rules-of-thumb.…

Analyses of attempts to prevent the worsening of environmental problems on Earth often identify two key lines of critique about contemporary school curriculum: first, its role in entrenching anthropocentrism as the dominant paradigm for people-environment relations, and then, also compounding this, their combined role in furthering a loss of…

The current study aimed to construct a questionnaire that measures students' personality traits related to "striving for understanding" and "learning value of geometry" and then examine its psychometric properties. Through the use of multiple methods on two independent samples of 402 and 521 middle school students, two studies…

Recently a new mean scaled and skewness adjusted test statistic was developed for evaluating structural equation models in small samples and with potentially nonnormal data, but this statistic has received only limited evaluation. The performance of this statistic is compared to normal theory maximum likelihood and 2 well-known robust test…