Heterogeneity in response styles can affect the conclusions drawn from rating scale data. In particular, biased estimates can be expected if one ignores a tendency to middle categories or to extreme categories. An adjacent categories model is proposed that simultaneously models the content-related effects and the heterogeneity in response styles.…

The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

An overview of popular software packages for conducting dimensionality assessment in multidimensional models is presented. Specifically, five popular software packages are described in terms of their capabilities to conduct dimensionality assessment with respect to the nature of analysis (exploratory or confirmatory), types of data (dichotomous,…

This paper introduces five commonly used approaches to analyzing multiple-choice test data. They are classical test theory, factor analysis, cluster analysis, item response theory, and model analysis. Brief descriptions of the goals and algorithms of these approaches are provided, together with examples illustrating their applications in physics…

This article considers a structured latent curve model for multiple repeated measures. In a structured latent curve model, a smooth nonlinear function characterizes the mean response. A first-order Taylor polynomial taken with regard to the mean function defines elements of a restricted factor matrix that may include parameters that enter…

Based on seminal work by Lord and Hambleton, Swaminathan, and Rogers, this article is an analytical, graphical, and conceptual reminder that item response theory (IRT) parameter invariance only holds for perfect model fit in multiple populations or across multiple conditions and is thus an ideal state. In practice, one attempts to quantify the…

We illustrate a class of multidimensional item response theory models in which the items are allowed to have different discriminating power and the latent traits are represented through a vector having a discrete distribution. We also show how the hypothesis of unidimensionality may be tested against a specific bidimensional alternative by using a…

The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…

Advances in cognitive research increase the need for assessment that can address the processes and the strategies by which persons solve problems. Several psychometric models have been introduced to handle claims cast in information-processing terms, explicitly modeling performance in terms of theory-based predictions of performance. Cognitively…

Randomized response (RR) is a well-known method for measuring sensitive behavior. Yet this method is not often applied because: (i) of its lower efficiency and the resulting need for larger sample sizes which make applications of RR costly; (ii) despite its privacy-protection mechanism the RR design may not be followed by every respondent; and…

Discussion of expert systems and computerized adaptive tests describes two versions of EXSPRT, a new approach that combines uncertain inference in expert systems with sequential probability ratio test (SPRT) stopping rules. Results of two studies comparing EXSPRT to adaptive mastery testing based on item response theory and SPRT approaches are…

This article presents an interview with R. Darrell Bock. He served as president of the Psychometric Society from 1972-1973. He has received the National Council on Measurement in Education award for "Contributions to the Design and Analysis of Educational Assessment" in 1990, the Educational Testing Service award for "Distinguished Contributions…