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…

Selection decisions have a major impact on our education, occupation, and quality of life, and the role of standardized tests in selection has always been a source of controversy. Here, I consider various definitions of fairness in measurement and selection--those emerging from within educational measurement and statistics, those from philosophy,…

Educational and psychological constructs are normally measured by multifaceted dimensions. The measured construct is defined and measured by a set of related subdomains. A bifactor model can accurately describe such data with both the measured construct and the related subdomains. However, a limitation of the bifactor model is the orthogonality…

This paper presents a noncompensatory latent trait model, the multicomponent latent trait model for diagnosis (MLTM-D), for cognitive diagnosis. In MLTM-D, a hierarchical relationship between components and attributes is specified to be applicable to permit diagnosis at two levels. MLTM-D is a generalization of the multicomponent latent trait…

Correct dimensionality identification (i.e., a correct decision on the number of factors to retain) is crucial not only in educational and psychological measurement, but also in various fields such as medicine and sociology that use exploratory factor analysis (EFA) in developing theories. However, to date, no single method has been endorsed for…

There has been a steady increase in the use of mixed-format tests, that is, tests consisting of both multiple-choice items and constructed-response items in both classroom and large-scale assessments. This calls for appropriate equating methods for such tests. As Item Response Theory (IRT) has rapidly become mainstream as the theoretical basis for…

A simultaneous equating of four new test forms to each other and to one previous form was accomplished through a complex design incorporating seven separate equating links. Each new form was linked to the reference form by four different paths, and each path produced a different score conversion. The procedure used to resolve these inconsistencies…

This dissertation proposes a new factor-analytic technique for detecting cheating on exams. Person-fit statistics have been developed to assess the extent to which examinees' response patterns are consistent with expectation, with expectation defined in the context of some model. Response patterns that are inconsistent with expectation are said to…

Classification testing has been widely used to make categorical decisions by determining whether an examinee has a certain degree of ability required by established standards. As computer technologies have developed, classification testing has become more computerized. Several approaches have been proposed and investigated in the context of…

Are teachers' impacts on students' test scores ("value-added") a good measure of their quality? This question has sparked debate largely because of disagreement about (1) whether value-added (VA) provides unbiased estimates of teachers' impacts on student achievement and (2) whether high-VA teachers improve students' long-term outcomes.…

Computerized versions of paper-and-pencil tests (PPT) have emerged over the past few decades, and some practitioners are using both formats concurrently. But computerizing a PPT may not yield equivalent scores across the two administration modes. Comparability studies are required to determine if the scores are equivalent before treating them as…

Various applications of item response theory often require linking to achieve a common scale for item parameter estimates obtained from different groups. This article used a simulation to examine the relative performance of four different item response theory (IRT) linking procedures in a random groups equating design: concurrent calibration with…

This book meets a demand in the science education community for a comprehensive and introductory measurement book in science education. It describes measurement instruments reported in refereed science education research journals, and introduces the Rasch modeling approach to developing measurement instruments in common science assessment domains,…

Traditional comparisons of test score means identify group differences in broad academic areas, but fail to provide substantive description of how the groups differ on the specific cognitive attributes required for success in the academic area. The rule space method (RSM) allows for group comparisons at the cognitive attribute level, which…

Samejima ("Psychometrika "65:319--335, 2000) proposed the logistic positive exponent family of models (LPEF) for dichotomous responses in the unidimensional latent space. The objective of the present paper is to propose and discuss a graded response model that is expanded from the LPEF, in the context of item response theory (IRT). This…