Van der Linden's hierarchical model for responses and response times can be used in order to infer the ability and mental speed of test takers from their responses and response times in an educational test. A standard approach for this is maximum likelihood estimation. In real-world applications, the data of some test takers might be partly…

Cognitive diagnosis models (CDMs) typically assume skill attributes with discrete (often binary) levels of skill mastery, making the existence of skill continuity an anticipated form of model misspecification. In this article, misspecification due to skill continuity is argued to be of particular concern for several CDM applications due to the…

When cut scores for classifications occur on the total score scale, popular methods for estimating classification accuracy (CA) and classification consistency (CC) require assumptions about a parametric form of the test scores or about a parametric response model, such as item response theory (IRT). This article develops an approach to estimate CA…

As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting…

The effect of violating the assumption of nonspeededness on ability and item parameter estimates in item response theory was studied through simulation under three speededness conditions. Results indicate that ability estimation was least affected by speededness but that substantial effects on item parameter estimates were found. (SLD)

The simultaneous assessment of differential item functioning (DIF) for a collection of test items through an index that measures the variance of DIF on a test as an indicator of the degree to which different items show DIF in different directions is proposed and evaluated through simulations. (SLD)

A statistical method, W. F. Stout's statistical test of essential unidimensionality (1990), for exploring the lack of unidimensionality in test data was studied using Monte Carlo simulations. The statistical procedure is a hypothesis test of whether the essential dimensionality is one or exceeds one, regardless of the traditional dimensionality.…

Analyzed examinee responses to conventional (multiple-choice) and innovative item formats in a computer-based testing program for item response theory (IRT) information with the three parameter and graded response models. Results for more than 3,000 adult examines for 2 tests show that the innovative item types in this study provided more…

The precision of the group-based item-response theory (IRT) model applied to school ability estimation is described, assuming use of Bayesian estimation with precision represented by the standard deviation of the posterior distribution. Similarities with and differences between the school-based model and the individual-level IRT are explored. (SLD)

Using simulated and real data, this study compares the performance of three methodologies for assessing unidimensionality: (1) DIMTEST; (2) the approach of Holland and Rosenbaum; and (3) nonlinear factor analysis. All three models correctly confirm unidimensionality, but they differ in their ability to detect the lack of unidimensionality.…

Two methods of computing test equating coefficients under item response theory by the following authors are compared: (1) B. H. Loyd and H. D. Hoover (1980); and (2) M. L. Stocking and F. M. Lord (1983). Conditions under which the method of Stocking and Lord is preferable are described. (SLD)

A procedure is presented for examining the influence of instruction on responses to test items by extending item response theory to incorporate variables illustrating different amounts of opportunity to learn. Data from the Second International Mathematics Study (grade 8 scores for about 7,000 students) illustrate the discussion. (SLD)