Despite over a century of aligning test and examination scales, the theory of linking has received relatively little attention. Recently, though, frameworks for classifying linking relationships have proliferated, both in England and the United States. Limitations of U.S. frameworks, particularly the idea that linking relationships ought to be…

Test equating under the NEAT design is, at best, a necessary evil. At bottom, the procedure aims to reach a conclusion on what a tested person would have done, if he or she were administered a set of items that were in fact never administered. It is not possible to infer such a conclusion from the data, because one simply has not made the required…

CBAL (Cognitively Based Assessment of, for, and as Learning) is a research initiative intended to create a model for an innovative K-12 assessment system that documents what students have achieved ("of learning"); helps identify how to plan instruction ("for learning"); and is considered by students and teachers to be a worthwhile educational…

Standard setting is a systematic process that uses a combination of judgmental and empirical procedures to make recommendations about where on the score continuum "cut scores" should be placed. Cut scores divide the score scale into categories consistent with the descriptions of student performance associated with multiple levels of achievement.…

This article presents lessons learned from a story of a snowy and dangerous intersection where there was no way for pedestrians to cross. The basic theme of this paper is that if political economy is preoccupied largely with the measurement of externalities, then a goal for the testing and assessment policy community should be to devise strategies…

Test-based accountability is now the cornerstone of U.S. education policy, and it is becoming more important in many other nations as well. Educators sometimes respond to test-based accountability in ways that produce score inflation. In the past, score inflation has usually been evaluated by comparing trends in scores on a high-stakes test to…

The duplex design by Bock and Mislevy for school-based testing is revisited and evaluated as a potential platform in test-based accountability assessments today. We conclude that the model could be useful in meeting the many competing demands of today's test-based accountability assessments, although many research questions will need to be…

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…

The goal of this commentary is to provide some additional results to the interesting and provocative paper of Maris and Bechger ("On Interpreting the Model Parameters for the Three Parameter Logistic Model," this issue). In this article, the authors have three aims. First, the authors distinguish between three fundamental concepts that are…

If questioned about their beliefs, psychometricians in one camp would argue the firm conviction that the Rasch model is mathematically elegant and intuitive as well as plausible for practitioners, pointing out the advantages of a simple model that "counts" every item in the same way. Psychometricians of another camp would argue that the three…

This paper addresses two problems relating to the interpretability of the model parameters in the three parameter logistic model. First, it is shown that if the values of the discrimination parameters are all the same, the remaining parameters are nonidentifiable in a nontrivial way that involves not only ability and item difficulty, but also the…

Maris and Bechger's article is an exercise in technical virtuosity and provides much to be learned by students of psychometrics. In this commentary, the author begins with making two observations. The first is that the title, "On Interpreting the Model Parameters for the Three Parameter Logistic Model," belies the generality of parts of Maris and…

The paper by Maris, G., & Bechger, T. (2009) entitled, "On the Interpreting the Model Parameters for the Three Parameter Logistic Model," addressed two important questions concerning the three parameter logistic (3PL) item response theory (IRT) model (and in a broader sense, concerning all IRT models). The first one is related to the model…

In this article, the authors aim to initiate an open discussion about many of the often unspoken assumptions, beliefs, and myths surrounding "diagnostic classification models" (DCMs). Reading the inspired exchange in the commentaries that the authors have received for their article, it is more apparent to them than ever that they are ready to talk…

This author states that, while the article by Gunter Maris and Timo Bechger ("On Interpreting the Model Parameters for the Three Parameter Logistic Model," this issue) is highly interesting, the interest is not so much in the practical implications, but rather in the issue of the meaning and role of statistical models in psychometrics and…