Parallel analysis has been considered one of the most accurate methods for determining the number of factors in factor analysis. One major advantage of parallel analysis over traditional factor retention methods (e.g., Kaiser's rule) is that it addresses the sampling variability of eigenvalues obtained from the identity matrix, representing the…

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.…

Determining the number of factors in exploratory factor analysis is arguably the most crucial decision a researcher faces when conducting the analysis. While several simulation studies exist that compare various so-called factor retention criteria under different data conditions, little is known about the impact of missing data on this process.…

Measurement of latent constructs is one of the most challenging tasks in psychological research. Unlike physical variables, latent constructs are not directly observable but are inferred through individuals' responses to a set of items often referred to as measurement instruments, tests, surveys, or assessments. For decades, exploratory factor…

A number of psychometricians have suggested that parallel analysis (PA) tends to yield more accurate results in determining the number of factors in comparison with other statistical methods. Nevertheless, all too often PA can suggest an incorrect number of factors, particularly in statistically unfavorable conditions (e.g., small sample sizes and…

The purpose of this two-part study is to evaluate methods for multiple group analysis when the comparison group is at the within level with multilevel data, using a multilevel factor mixture model (ML FMM) and a multilevel multiple-indicators multiple-causes (ML MIMIC) model. The performance of these methods was evaluated integrally by a series of…

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…

This study compares two missing data procedures in the context of ordinal factor analysis models: pairwise deletion (PD; the default setting in Mplus) and multiple imputation (MI). We examine which procedure demonstrates parameter estimates and model fit indices closer to those of complete data. The performance of PD and MI are compared under a…

Properties of psychological variables at the mean or variance level can differ between persons and within persons across multiple time points. For example, cross-sectional findings between persons of different ages do not necessarily reflect the development of a single person over time. Recently, there has been an increased interest in the…

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,…

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…

Bayesian confirmatory factor analysis (CFA) offers an alternative to frequentist CFA based on, for example, maximum likelihood estimation for the assessment of reliability and validity of educational and psychological measures. For increasing sample sizes, however, the applicability of current fit statistics evaluating model fit within Bayesian…

Principal component analysis is an important statistical technique for dimension reduction and exploratory data analysis. However, it is not robust to outliers and may obfuscate important data structure such as clustering. We propose a version of principal component analysis based on the robust L2E method. The technique seeks to find the principal…

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…

The aim of this simulation study, determine the relationship between true latent scores and estimated latent scores by including various control variables and different statistical models. The study also aimed to compare the statistical models and determine the effects of different distribution types, response formats and sample sizes on latent…