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 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…

Symmetry considerations are important in science, and Group Theory is a theory of symmetry. Classical Measurement Theory is the most used measurement theory in the social and behavioral sciences. In this article, the author uses Matrix Lie (Lee) group theory to formulate a measurement model. Symmetry is defined and illustrated using symmetries of…

This article outlines a readily applicable procedure for point and interval estimation of the population discrepancy between reliability and the popular Cronbach's coefficient alpha for unidimensional multi-component measuring instruments with uncorrelated errors, which are widely used in behavioral and social research. The method is developed…

The default risk, one of the main risk factors for bonds, should be measured and reflected in the bond yield. Particularly, in the case of financial companies that treat bonds as a major product, failure to properly identify and filter customers' workout status adversely affects returns. This study proposes a two-stage classification algorithm for…

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…

Survey score interpretations are often plagued by sources of construct-irrelevant variation, such as response styles. In this study, we propose the use of an IRTree Model to account for response styles by making use of self-report items and anchoring vignettes. Specifically, we investigate how the IRTree approach with anchoring vignettes compares…

Utilizing the perspective of finite mixture modeling, this note considers whether a finding of a plausible one-parameter logistic model could be spurious for a population with substantial unobserved heterogeneity. A theoretically and empirically important setting is discussed involving the mixture of two latent classes, with the less restrictive…

The Next Generation Science Standards (NGSS) delineate three interrelated dimensions that describe what students should know and how they should engage in science learning. These present significant challenges for assessment because traditional assessments may not be able to capture the ways in which students engage with content. Science…

It is demonstrated that the popular three-parameter logistic model can lead to markedly inaccurate individual ability level estimates for mixture populations. A theoretically and empirically important setting is initially considered where (a) in one of two subpopulations (latent classes) the two-parameter logistic model holds for each item in a…

"Game-Based Assessments: A Promising Way to Create Idiographic Perspectives" (Adrienne Walker and George Englehard) comments on: "How Task Features Impact Evidence from Assessments Embedded in Simulations and Games" by Russell G. Almond, Yoon Jeon Kim, Gertrudes Velasquez, and Valerie J. Shute. Here, Walker and Englehard write…

In his opening statements, Humphry takes a critical attitude with respect to psychometric modeling. As he advances and discusses Michell's well-known criticisms, the reader is certain that this paper must have something on offer that deviates considerably from conventional psychometrics. After all "most psychometricians have either explicitly or…

In this rejoinder, the authors provide their thoughts on each of the commentaries of the seven respondents to their article. They find that the response of Kyngdon differs markedly from the others in questioning some basic elements of the methods of analysis that they propose for the construction of a "road map." The authors emphasize that they…

Humphry (this issue) deserves credit for drawing attention to the long-neglected fact that differences in item discrimination parameters are often due to empirical factors and not the product of random error components. In doing so, Humphry offers a psychometrically elegant, coherent, and practically important new model that is more flexible while…