Building on prior research on the relationships between key concepts in item response theory and classical test theory, this note contributes to highlighting their important and useful links. A readily and widely applicable latent variable modeling procedure is discussed that can be used for point and interval estimation of the individual person…

This study applies the conceptual framework of Positive Deviance, the theoretical framework of critical race theory, and the lens of marronage to understand the problem of low Black student enrollment at one American Bar Association accredited law school. The purpose of this study was to understand what current Black law students perceive to be…

Local dependence (LD) for binary IRT models can be diagnosed using Chen and Thissen's bivariate X[superscript 2] statistic and the score test statistics proposed by Glas and Suarez-Falcon, and Liu and Thissen. Alternatively, LD can be assessed using general purpose statistics such as bivariate residuals or Maydeu-Olivares and Joe's M[subscript r]…

In item response theory (IRT) modeling, the item parameter error covariance matrix plays a critical role in statistical inference procedures. When item parameters are estimated using the EM algorithm, the parameter error covariance matrix is not an automatic by-product of item calibration. Cai proposed the use of Supplemented EM algorithm for…

This article presents an application of Monte Carlo methods for developing and assembling multistage adaptive tests (MSTs). A major advantage of the Monte Carlo assembly over other approaches (e.g., integer programming or enumerative heuristics) is that it provides a uniform sampling from all MSTs (or MST paths) available from a given item pool.…

This study extended prior Law School Admission Council (LSAC) research related to the item response theory (IRT) local item independence assumption into the realm of classical test theory. Initially, results from the Law School Admission Test (LSAT) and two other tests were investigated to determine the approximate state of local item independence…

Presents an integer programming approach to item bank design that can be used to calculate an optimal blueprint for an item bank in order to support an existing testing program. Demonstrates the approach empirically using an item bank designed for the Law School Admission Test. (SLD)

Relations between latent trait and latent class models for item response data are examined. Conditions are given for two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Results are illustrated with data from the Law School Admission Test. (SLD)

This study represented a first attempt to evaluate the impact of local item dependence (LID) for Item Response Theory (IRT) scoring in computerized adaptive testing (CAT). The most basic CAT design and a simplified design for simulating CAT item pools with varying degrees of LID were applied. A data generation method that allows the LID among…

This paper provides a brief overview of some of the research that has examined the relationship between item response theory (IRT) and nonlinear factor analysis (NFA), and outlines three NLFA models, emphasizing their major strengths and weaknesses for practical applications. The focus is on: (1) R. McDonald's polynomial approximation of a normal…

Developed a multilevel item response (IRT) model that allows for differences between the distributions of item parameters of families of item clones. Results from simulation studies based on an item pool from the Law School Admission Test illustrate the accuracy of the item pool calibration and adaptive testing procedures based on the model. (SLD)

An integer programming approach to item pool design is presented that can be used to calculate an optimal blueprint for an item pool to support an existing testing program. The results are optimal in the sense that they minimize the efforts involved in actually producing the items as revealed by current item writing patterns. Also, an adaptation…

This study investigated the practical effects of local item dependence (LID) on item response theory (IRT) true-score equating. A scenario was defined that emulated the Law School Admission Test (LSAT) preequating model, and data were generated to assess the impact of different degrees of LID on final equating outcomes. An extreme amount of LID…

Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and in the population of examinees. This definition underlies, for example, the well-known approximation to the standard error of equating by Lord (1982).…

Differential item functioning (DIF) analyses are conducted to investigate how items function in various subgroups. The Mantel-Haenszel (MH) DIF statistic is used at the Law School Admission Council and other testing companies. When item functioning can be well-described in terms of a one- or two-parameter logistic item response theory (IRT) model…