It is meaningful to create a comprehensive score to extract information from mass continuous data when they measure the same latent concept. Therefore, this study adopts the logic of psychometrics to conduct scales on continuous data under the Rasch models. This study also explores the effect of different data discretization methods on scale…

This paper presents the item and test information functions of the Rank two-parameter logistic models (Rank-2PLM) for items with two (pair) and three (triplet) statements in forced-choice questionnaires. The Rank-2PLM model for pairs is the MUPP-2PLM (Multi-Unidimensional Pairwise Preference) and, for triplets, is the Triplet-2PLM. Fisher's…

Exploratory structural equation (ESEM) has received increased attention in the methodological literature as a promising tool for evaluating latent variable measurement models. It overcomes many of the limitations attached to exploratory factor analysis (EFA) and confirmatory factor analysis (CFA), while capitalizing on the benefits of each. Given…

This paper is concerned with the process of selecting between the increasingly popular bi-factor model and the second-order factor model in measurement research. It is indicated that in certain settings widely used in empirical studies, the second-order model is nested in the bi-factor model and obtained from the latter after imposing appropriate…

It is common to find mixed-format data results from the use of both multiple-choice (MC) and constructed-response (CR) questions on assessments. Dealing with these mixed response types involves understanding what the assessment is measuring, and the use of suitable measurement models to estimate latent abilities. Past research in educational…

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…

Percentage of uncontaminated correlations (PUC), explained common variance (ECV), and omega hierarchical ([omega]H) have been used to assess the degree to which a scale is essentially unidimensional and to predict structural coefficient bias when a unidimensional measurement model is fit to multidimensional data. The usefulness of these indices…

When selecting fillers to include in a police lineup, one must consider the level of similarity between the suspect and potential fillers. In order to reduce misidentifications, an innocent suspect should not stand out. Therefore, it is important that the fillers share some degree of similarity. Importantly, increasing suspect-filler similarity…

This note demonstrates that the widely used Bayesian Information Criterion (BIC) need not be generally viewed as a routinely dependable index for model selection when the bifactor and second-order factor models are examined as rival means for data description and explanation. To this end, we use an empirically relevant setting with…

In this paper, we develop a mixed stochastic approximation expectation-maximization (MSAEM) algorithm coupled with a Gibbs sampler to compute the marginalized maximum a posteriori estimate (MMAPE) of a confirmatory multidimensional four-parameter normal ogive (M4PNO) model. The proposed MSAEM algorithm not only has the computational advantages of…

In this paper, we develop a mixed stochastic approximation expectation-maximization (MSAEM) algorithm coupled with a Gibbs sampler to compute the marginalized maximum a posteriori estimate (MMAPE) of a confirmatory multidimensional four-parameter normal ogive (M4PNO) model. The proposed MSAEM algorithm not only has the computational advantages of…

The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be…

Human ratings are ubiquitous in creativity research. Yet, the process of rating responses to creativity tasks -- typically several hundred or thousands of responses, per rater -- is often time-consuming and expensive. Planned missing data designs, where raters only rate a subset of the total number of responses, have been recently proposed as one…

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…

The purpose of this study was to investigate multidimensional DIF with a simple and nonsimple structure in the context of multidimensional Graded Response Model (MGRM). This study examined and compared the performance of the IRT-LR and Wald test using MML-EM and MHRM estimation approaches with different test factors and test structures in…