Current methods that simultaneously model differential testlet functioning (DTLF) and differential item functioning (DIF) constrain the variances of latent ability and testlet effects to be equal between the focal and the reference groups. Such a constraint can be stringent and unrealistic with real data. In this study, we propose a multigroup…

Bayesian item response theory (IRT) modeling stages include (a) specifying the IRT likelihood model, (b) specifying the parameter prior distributions, (c) obtaining the posterior distribution, and (d) making appropriate inferences. The latter stage, and the focus of this research, includes model criticism. Choice of priors with the posterior…

María Oliveri, and Saad Khan write that the article: "How Task Features Impact Evidence from Assessments Embedded in Simulations and Games" provided helpful illustrations regarding the implementation of evidence-centered assessment design (Mislevy & Haertel, 2006; Mislevy, Steinberg, & Almond, 1999) with games and simulations.…

In "How Task Features Impact Evidence from Assessments Embedded in Simulations and Games," Almond, Kim, Velasquez, and Shute have prepared a thought-provoking piece contrasting the roles of task model variables in a traditional assessment of mathematics word problems to their roles in "Newton's Playground," a game designed…

In his commentary on "How Task Features Impact Evidence from Assessments Embedded in Simulations and Games" by Almond et al., Mike Timms writes that his own research has involved the use of embedded assessments using simulations in interactive learning environments, and the Evidence Centered Design (ECD) approach has provided a solid…

One of the key ideas of evidence-centered assessment design (ECD) is that task features can be deliberately manipulated to change the psychometric properties of items. ECD identifies a number of roles that task-feature variables can play, including determining the focus of evidence, guiding form creation, determining item difficulty and…

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…

This commentary examines the role of the unit from the perspective of the definition of measurement in physics as the ratio of two magnitudes, one of which is defined as the unit; it is an important and timely contribution to measurement in the social sciences. There are many different points that could be commented upon, but the author will…

Compared to traditional test theory, where person measures are typically referenced to the distribution of a population, item response theory allows for a much more meaningful interpretation of measures as they can be directly compared to item locations. However, Stephen Humphry shows that the crucial role of the unit of measurement has been…

This author has always felt a bit uneasy about the three parameter logistic (3PL) model because it seems about as prone to discovering guessing when guessing does not take place, as the Rasch model is reluctant to admit that guessing might ever take place at all. However, the author has attributed this to the prior "magic" employed when estimating…

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…

Humphry (this issue) has written a thought-provoking piece on the interpretation of item discrimination parameters as scale units in item response theory. One of the key features of his work is the description of an item response theory (IRT) model that he calls the logistic measurement function that combines aspects of two traditions in IRT that…

Behavioral scientists have struggled with units of measurement for as long as they have struggled with measurement itself. Psychology's sole attempt at an explicit unit of measurement--the Lexile Framework for Reading (Stenner, Burdick, Sanford, & Burdick, 2006)--has been and continues to be ignored by the psychometric "cognoscenti."…

The purpose of this article is to examine the role of the unit in physics in order to clarify the role of the unit in psychometrics. Based on this examination, metrological conventions are used to formulate the relationship between discrimination and the unit of a scale in item response theory. Seminal literature in two lines of item response…

This article presents Stephen Humphry's response to the commentaries for his article "The Role of the Unit in Physics and Psychometrics." The commentaries covered a range of important considerations and implications. Given that the author fully agrees with the majority of the content, attention will be confined mainly to points that call…