The issue of compensation in multidimensional response modeling is addressed. We show that multidimensional response models are compensatory in their ability parameters if and only if they are monotone. In addition, a minimal set of assumptions is presented under which the MLEs of the ability parameters are also compensatory. In a recent series of…

Optimal test-design methods are applied to rule-based item generation. Three different cases of automated test design are presented: (a) test assembly from a pool of pregenerated, calibrated items; (b) test generation on the fly from a pool of calibrated item families; and (c) test generation on the fly directly from calibrated features defining…

Automated test assembly uses the methodology of mixed integer programming to select an optimal set of items from an item bank. Automated test-form generation uses the same methodology to optimally order the items and format the test form. From an optimization point of view, production of fully formatted test forms directly from the item pool using…

Three plausible assumptions of conditional independence in a hierarchical model for responses and response times on test items are identified. For each of the assumptions, a Lagrange multiplier test of the null hypothesis of conditional independence against a parametric alternative is derived. The tests have closed-form statistics that are easy to…

It is shown how the time limit on a test can be set to control the probability of a test taker running out of time before completing it. The probability is derived from the item parameters in the lognormal model for response times. Examples of curves representing the probability of running out of time on a test with given parameters as a function…

The probability of test takers changing answers upon review of their initial choices is modeled. The primary purpose of the model is to check erasures on answer sheets recorded by an optical scanner for numbers and patterns that may be indicative of irregular behavior, such as teachers or school administrators changing answer sheets after their…

An application of a hierarchical IRT model for items in families generated through the application of different combinations of design rules is discussed. Within the families, the items are assumed to differ only in surface features. The parameters of the model are estimated in a Bayesian framework, using a data-augmented Gibbs sampler. An obvious…

Although response times on test items are recorded on a natural scale, the scale for some of the parameters in the lognormal response-time model (van der Linden, 2006) is not fixed. As a result, when the model is used to periodically calibrate new items in a testing program, the parameter are not automatically mapped onto a common scale. Several…

Two different traditions of response-time (RT) modeling are reviewed: the tradition of distinct models for RTs and responses, and the tradition of model integration in which RTs are incorporated in response models or the other way around. Several conceptual issues underlying both traditions are made explicit and analyzed for their consequences. We…

A bivariate lognormal model for the distribution of the response times on a test by a pair of test takers is presented. As the model has parameters for the item effects on the response times, its correlation parameter automatically corrects for the spuriousness in the observed correlation between the response times of different test takers because…

An adaptive testing method is presented that controls the speededness of a test using predictions of the test takers' response times on the candidate items in the pool. Two different types of predictions are investigated: posterior predictions given the actual response times on the items already administered and posterior predictions that use the…

Current modeling of response times on test items has been strongly influenced by the paradigm of experimental reaction-time research in psychology. For instance, some of the models have a parameter structure that was chosen to represent a speed-accuracy tradeoff, while others equate speed directly with response time. Also, several response-time…

In experiments with paired comparisons, judges are occasionally allowed to express indifference between alternatives. For the analysis of such data, models for paired comparisons with ties are needed. Several models with tie parameters are reviewed. All are extensions of the basic models of L. L. Thurstone (1927) and R. A. Bradley and M. E. Terry…

A statistical test for detecting answer copying on multiple-choice items is presented. The test is based on the exact null distribution of the number of random matches between two test takers under the assumption that the response process follows a known response model. The null distribution can easily be generalized to the family of distributions…

Proposes a model for constrained computerized adaptive testing in which the information in the test at the trait level (theta) estimate is maximized subject to the number of possible constraints on the content of the test. Test assembly relies on a linear-programming approach. Illustrates the approach through simulation with items from the Law…