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 (EFA) is crucial because it affects the rest of the analysis and the conclusions of the study. Researchers have developed various methods for deciding the number of factors to retain in EFA, but this remains one of the most difficult decisions in the EFA. The purpose of this study is…

Factor mixture modeling (FMM) is generally complex with both unobserved categorical and unobserved continuous variables. We explore the potential of item parceling to reduce the model complexity of FMM and improve convergence and class enumeration accordingly. To this end, we conduct Monte Carlo simulations with three types of data, continuous,…

Chi-square tests based on maximum likelihood (ML) estimation of covariance structures often incorrectly over-reject the null hypothesis: [sigma] = [sigma(theta)] when the sample size is small. Reweighted least squares (RLS) avoids this problem. In some models, the vector of parameter must contain means, variances, and covariances, yet whether RLS…

Statistical mediation analysis allows researchers to identify the most important mediating constructs in the causal process studied. Identifying specific mediators is especially relevant when the hypothesized mediating construct consists of multiple related facets. The general definition of the construct and its facets might relate differently to…

Two new methods for the meta-analysis of factor loadings are introduced and evaluated by Monte Carlo simulations. The direct method pools each factor loading individually, whereas the indirect method synthesizes correlation matrices reproduced from factor loadings. The results of the two simulations demonstrated that the accuracy of…

This study compares the performance of two approaches in analysing four-point Likert rating scales with a factorial model: the classical factor analysis (FA) and the item factor analysis (IFA). For FA, maximum likelihood and weighted least squares estimations using Pearson correlation matrices among items are compared. For IFA, diagonally weighted…

This simulation study examined the performance of the curve-of-factors model (COFM) when autocorrelation and growth processes were present in the first-level factor structure. In addition to the standard curve-of factors growth model, 2 new models were examined: one COFM that included a first-order autoregressive autocorrelation parameter, and a…

Numerous procedures have been suggested for determining the number of factors to retain in factor analysis. However, previous studies have focused on comparing methods using normal data sets. This study had two phases. The first phase explored the Kaiser method, Scree test, Bartlett's chi-square test, Minimum Average Partial (1976&2000),…

Exploratory factor analysis (EFA) is generally regarded as a technique for large sample sizes ("N"), with N = 50 as a reasonable absolute minimum. This study offers a comprehensive overview of the conditions in which EFA can yield good quality results for "N" below 50. Simulations were carried out to estimate the minimum required "N" for different…

Whether "more is ever too much" for the number of indicators per factor in confirmatory factor analysis was studied by varying sample size and indicators per factor in 35,000 Monte Carlo solutions. Results suggest that traditional rules calling for fewer indicators for smaller sample size may be inappropriate. (SLD)

Whether "more is ever too much" for the number of indicators (p) per factor (p/f) in confirmatory factor analysis (CFA) was studied by varying sample size (N) from 50 to 1,000 and p/f from 2 to 12 items per factor in 30,000 Monte Carlo simulations. For all sample sizes, solution behavior steadily improved (more proper solutions and more…

In recent years, confirmatory factor analytic (CFA) techniques have become the most common method of testing for measurement equivalence/invariance (ME/I). However, no study has simulated data with known differences to determine how well these CFA techniques perform. This study utilizes data with a variety of known simulated differences in factor…

A simulation study was conducted to examine the effect of item parceling on confirmatory factor analysis parameter estimates and their standard errors at different levels of sample size, number of indicators per factor, size of factor structure/pattern coefficients, magnitude of interfactor correlations, and variations in item-level data…

This study of maximum likelihood confirmatory factor analysis found effects of practical significance due to sample size, the number of indicators per factor, and the number of factors for Joreskog and Sorbom's (1981) goodness-of-fit index (GFI), GFI adjusted for degrees of freedom, and the root mean square residual. (Author/BW)