When comparing relations and means of latent variables, it is important to establish measurement invariance (MI). Most methods to assess MI are based on confirmatory factor analysis (CFA). Recently, new methods have been developed based on exploratory factor analysis (EFA); most notably, as extensions of multi-group EFA, researchers introduced…

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…

The replication crisis in social and behavioral sciences has raised concerns about the reliability and validity of empirical studies. While research in the literature has explored contributing factors to this crisis, the issues related to analytical tools have received less attention. This study focuses on a widely used analytical tool -…

Factor score regression (FSR) is widely used as a convenient alternative to traditional structural equation modeling (SEM) for assessing structural relations between latent variables. But when latent variables are simply replaced by factor scores, biases in the structural parameter estimates often have to be corrected, due to the measurement error…

This study investigates the performance of robust maximum likelihood (ML) estimators when fitting and evaluating small sample latent growth models with non-normal missing data. Results showed that the robust ML methods could be used to account for non-normality even when the sample size is very small (e.g., N < 100). Among the robust ML…

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…

Goodness-of-fit testing in factor analysis is based on the assumption that the test statistic is asymptotically chi-square, but this property may not hold in small samples even when the factors and errors are normally distributed in the population. Robust methods such as Browne's (1984) asymptotically distribution-free method and Satorra Bentler's…

A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category…

The robustness of a partial credit (PC) model-based computerized adaptive test's (CAT's) ability estimation to items that did not fit the PC model was investigated. A CAT program was written based on the PC model. The program used maximum likelihood estimation of ability. Item selection was on the basis of information. The simulation terminated…