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…

This study aims to compare item and student parameters of dichotomously scored multidimensional constructs estimated based on unidimensional and multidimensional Item Response Theory (IRT) under different conditions of sample size, interdimensional correlation and number of dimensions. This research, conducted with simulations, is of a basic…

In order to detect a wide range of aberrant behaviors, it can be useful to incorporate information beyond the dichotomous item scores. In this paper, we extend the l[subscript z] and l*[subscript z] person-fit statistics so that unusual behavior in item scores and unusual behavior in item distractors can be used as indicators of aberrance. Through…

The multiple imputation two-stage (MI2S) approach holds promise for evaluating the model fit of structural equation models for ordinal variables with multiply imputed data. However, previous studies only examined the performance of MI2S-based residual-based test statistics. This study extends previous research by examining the performance of two…

In latent growth curve modeling (LGCM), overall fit indices have garnered increased disputation for model selection, and model fit evaluation based on the mean structure has becoming popularity. The present study developed a versatile fit index, named Weighted Root Mean Squared Errors (WRMSE), based on individual case residuals (ICRs) with the aim…

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…

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 measuring latent constructs, for example, language ability, we use statistical models to specify appropriate relationships between the latent construct and observe responses to test items. These models rely on theoretical assumptions to ensure accurate parameter estimates for valid inferences based on the test results. This dissertation…

A standard assumption of latent class (LC) analysis is conditional independence, that is the items of the LC are independent of the covariates given the LCs. Several approaches have been proposed for identifying violations of this assumption. The recently proposed likelihood ratio approach is compared to residual statistics (bivariate residuals…

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…

A full structural equation model (SEM) typically consists of both a measurement model (describing relationships between latent variables and observed scale items) and a structural model (describing relationships among latent variables). However, often researchers are primarily interested in testing hypotheses related to the structural model while…

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…

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…

This study examined the false positive (FP) rates and sensitivity of Bayesian fit indices to structural misspecification in Bayesian structural equation modeling. The impact of measurement quality, sample size, model size, the magnitude of misspecified path effect, and the choice or prior on the performance of the fit indices was also…