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…

Conceptualizing two-variable disturbances preventing good model fit in confirmatory factor analysis as item-level method effects instead of correlated residuals avoids violating the principle that residual variation is unique for each item. The possibility of representing such a disturbance by a method factor of a bifactor measurement model was…

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…

Consistency and coverage are two core parameters of model fit used by configurational comparative methods (CCMs) of causal inference. Among causal models that perform equally well in other respects (e.g., robustness or compliance with background theories), those with higher consistency and coverage are typically considered preferable. Finding the…

Accounting for model misspecification in Bayesian structural equation models is an active area of research. We present a uniquely Bayesian approach to misspecification that models the degree of misspecification as a parameter--a parameter akin to the correlation root mean squared residual. The misspecification parameter can be interpreted on its…

Item response theory (IRT) models the relationship between the possible scores on a test item against a test taker's attainment of the latent trait that the item is intended to measure. In this study, we compare two models for tests with polytomously scored items: the optimal scoring (OS) model, a nonparametric IRT model based on the principles of…

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…

In recent years, proponents of configurational comparative methods (CCMs) have advanced various dimensions of robustness as instrumental to model selection. But these robustness considerations have not led to computable robustness measures, and they have typically been applied to the analysis of real-life data with unknown underlying causal…

In the literature of modern psychometric modeling, mostly related to item response theory (IRT), the fit of model is evaluated through known indices, such as X[superscript 2], M2, and root mean square error of approximation (RMSEA) for absolute assessments as well as Akaike information criterion (AIC), consistent AIC (CAIC), and Bayesian…

The purpose of this study was to evaluate the degree of classification quality in the basic latent class model when covariates are either included or are not included in the model. To accomplish this task, Monte Carlo simulations were conducted in which the results of models with and without a covariate were compared. Based on these simulations,…

Diagnostic classification models (DCMs) are psychometric models that can be used to estimate the presence or absence of psychological traits, or proficiency on fine-grained skills. Critical to the use of any psychometric model in practice, including DCMs, is an evaluation of model fit. Traditionally, DCMs have been estimated with maximum…

The patient health questionnaire-9 (PHQ-9) is widely utilized in assessing individuals' depression levels. Nevertheless, research regarding its factor structure and measurement invariance remains inadequate. The aim of this study was to delve into the factor structure of the PHQ-9 and to further investigate its measurement invariance across gender…

Person-fit analyses are commonly used to detect aberrant responding in self-report data. Nonparametric person fit statistics do not require fitting a parametric test theory model and have performed well compared to other person-fit statistics. However, detection of aberrant responding has primarily focused on dominance response data, thus the…

Composite reliability, or coefficient omega, can be estimated using structural equation modeling. Composite reliability is usually estimated under the basic independent clusters model of confirmatory factor analysis (ICM-CFA). However, due to the existence of cross-loadings, the model fit of the exploratory structural equation model (ESEM) is…

Engagement and academic achievement are generally correlated among elementary school students without learning disabilities (LDs). However, it is unclear if this pattern holds for students with LDs, who have lower achievement and engagement than their peers. This study examined whether links between achievement and student-reported behavioral…