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…

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…

This study investigated the small sample biasness of the ordered logit model parameters under multicollinearity using Monte Carlo simulation. The results showed that the level of biasness associated with the ordered logit model parameters consistently decreases for an increasing sample size while the distribution of the parameters becomes less…

Composite reliability, or coefficient omega, can be estimated using structural equation modeling. Composite reliability is usually estimated under the basic independent clusters model of confirmatory factor analysis (ICM-CFA). However, due to the existence of cross-loadings, the model fit of the exploratory structural equation model (ESEM) is…

Item parameter drift (IPD) is the systematic differentiation of parameter values of items over time due to various reasons. If it occurs in computer adaptive tests (CAT), it causes errors in the estimation of item and ability parameters. Identification of the underlying conditions of this situation in CAT is important for estimating item and…

The purpose of this study was to investigate the Type I Error findings and power rates of the methods used to determine dimensionality in unidimensional and bidimensional psychological constructs for various conditions (characteristic of the distribution, sample size, length of the test, and interdimensional correlation) and to examine the joint…

A simulation study was conducted to explore the impact of differential item functioning (DIF) on general factor difference estimation for bifactor, ordinal data. Common analysis misspecifications in which the generated bifactor data with DIF were fitted using models with equality constraints on noninvariant item parameters were compared under data…

In education research, conceptual models are becoming more complex and more challenging to fit. In response, many researchers have turned to multi-step model fitting processes; first fitting confirmatory factor analyses (CFA) to their data, then extracting the latent factor scores; converting them to observed variables to use in additional…

Exploratory factor analysis (EFA) is widely used by researchers in the social sciences to characterize the latent structure underlying a set of observed indicator variables. One of the primary issues that must be resolved when conducting an EFA is determination of the number of factors to retain. There exist a large number of statistical tools…

The aim of the present research study was to compare the findings from the nonparametric MSA, DIMTEST and DETECT and the parametric dimensionality determining methods in various simulation conditions by utilizing exploratory and confirmatory methods. For this purpose, various simulation conditions were established based on number of dimensions,…

Measurement invariance is crucial for making valid comparisons across different groups (Kline, 2016; Vandenberg, 2002). To address the challenges associated with invariance testing such as large sample size requirements, the complexity of the model, etc., applied researchers have incorporated parcels. Parcels have been shown to alleviate skewness,…

This simulation study was conducted to compare the performances of Frequentist and Bayesian approaches in the context of power to detect model misspecification in terms of omitted cross-loading in CFA models with respect to the several variables (number of omitted cross-loading, magnitude of main loading, number of factors, number of indicators…

Parallel analysis (PA) assesses the number of factors in exploratory factor analysis. Traditionally PA compares the eigenvalues for a sample correlation matrix with the eigenvalues for correlation matrices for 100 comparison datasets generated such that the variables are independent, but this approach uses the wrong reference distribution. The…

Weighted least squares (WLS), weighted least squares mean-and-variance-adjusted (WLSMV), unweighted least squares mean-and-variance-adjusted (ULSMV), maximum likelihood (ML), robust maximum likelihood (MLR) and Bayesian estimation methods were compared in mixed item response type data via Monte Carlo simulation. The percentage of polytomous items,…