Multiple imputation (MI) is one of the recommended techniques for handling missing data in ordinal factor analysis models. However, methods for computing MI-based fit indices under ordinal factor analysis models have yet to be developed. In this short note, we introduced the methods of using the standardized root mean squared residual (SRMR) and…

Testing for differential item functioning (DIF) has undergone rapid statistical developments recently. Moderated nonlinear factor analysis (MNLFA) allows for simultaneous testing of DIF among multiple categorical and continuous covariates (e.g., sex, age, ethnicity, etc.), and regularization has shown promising results for identifying DIF among…

Measurement invariance (MI) is an essential part of validity evidence concerned with ensuring that tests function similarly across groups, contexts, and time. Most evaluations of MI involve multigroup confirmatory factor analyses (MGCFA) that assume simple structure. However, recent research has shown that constraining non-target indicators to…

Cross-loadings are common in multiple-factor confirmatory factor analysis (CFA) but often ignored in measurement invariance testing. This study examined the impact of ignoring cross-loadings on the sensitivity of fit measures (CFI, RMSEA, SRMR, SRMRu, AIC, BIC, SaBIC, LRT) to measurement noninvariance. The manipulated design factors included the…

This note demonstrates that measurement invariance does not guarantee meaningful and valid group comparisons in multiple-population settings. The article follows on a recent critical discussion by Robitzsch and Lüdtke, who argued that measurement invariance was not a pre-requisite for such comparisons. Within the framework of common factor…

Confirmatory factor analyses (CFA) are often used in psychological research when developing measurement models for psychological constructs. Evaluating CFA model fit can be quite challenging, as tests for exact model fit may focus on negligible deviances, while fit indices cannot be interpreted absolutely without specifying thresholds or cutoffs.…

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…

Coefficient omega indices are model-based composite reliability estimates that have become increasingly popular. A coefficient omega index estimates how reliably an observed composite score measures a target construct as represented by a factor in a factor-analysis model; as such, the accuracy of omega estimates is likely to depend on correct…

We conducted an extensive Monte Carlo study of factor-rotation local solutions (LS) in multidimensional, two-parameter logistic (M2PL) item response models. In this study, we simulated more than 19,200 data sets that were drawn from 96 model conditions and performed more than 7.6 million rotations to examine the influence of (a) slope parameter…

Simple matrix sampling planned missing (SMS PD) design, introduce missing data patterns that lead to covariances between variables that are not jointly observed, and create difficulties for analyses other than mean and variance estimations. Based on prior research, we adopted a new multigroup confirmatory factor analysis (CFA) approach to handle…

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…

The most common effect size when using a multiple-group confirmatory factor analysis approach to measurement invariance is [delta]CFI and [delta]TLI with a cutoff value of 0.01. However, this recommended cutoff value may not be ubiquitously appropriate and may be of limited application for some tests (e.g., measures using dichotomous items or…

In conducting confirmatory factor analysis with ordered response items, the literature suggests that when the number of responses is five and item skewness (IS) is approximately normal, researchers can employ maximum likelihood with robust standard errors (MLR). However, MLR can yield biased factor loadings (FL) and FL standard errors (FLSE) when…

The consistency of psychometric properties across waves of data collection provides valuable evidence that scores can be interpreted consistently. Evidence supporting the consistency of psychometric properties can come from using a longitudinal extension of item factor analysis to account for the lack of independence of observation when evaluating…

This note is concerned with the benefits that can result from the use of the maximal reliability and optimal linear combination concepts in educational and psychological research. Within the widely used framework of unidimensional multi-component measuring instruments, it is demonstrated that the linear combination of their components that…