In this paper, we introduce a mathematical model for collaborative learning and the answering process for multiple-choice questions. The collaborative learning model is inspired by the Ising spin model and the model for answering multiple-choice questions is based on their difficulty level. An intensive simulation study predicts the possibility of…

In Guttman-type quantification of contingency tables and multiple-choice data (incidence data), the trivial solution because of marginal constraints is typically removed before quantification. Relevant formulas are presented for cases affected by the trivial solution and those that are not. (SLD)

Methodology is suggested for several statistical procedures to detect polytomously scored items that function differently for two subgroups of examinees. The 3 methods are alternative ways of combining the data from 2 x "k" tables. Simulation results demonstrate the superiority of two of the methods, designated HW1 and HW3. (SLD)

A new approach to the development of the item characteristic curve (ICC), which expresses the functional relationship between the level of performance on a given task and an independent variable that is relevant to the task, is presented. The approach focuses on knowledge states, decision processes, and other circumstances underlying responses to…

Three methods of estimating test score distributions that may improve on using the observed frequencies (OBFs) as estimates of a population test score distribution are considered: the kernel method (KM); the polynomial method (PM); and the four-parameter beta binomial method (FPBBM). The assumption each method makes about the smoothness of the…

Bias, standard error, and reliability of five ability estimators were evaluated using Monte Carlo estimates of the unknown conditional means and variances of the estimators. Results indicate that estimates based on Bayesian modal, expected a posteriori, and weighted likelihood estimators were reasonably unbiased with relatively small standard…

A nonparametric multicategorical model for multiple-choice data is proposed as an extension of the binary spline model of J. O. Ramsay and M. Abrahamowicz (1989). Results of two Monte Carlo studies illustrate the model, which approximates probability functions by rational splines. (SLD)

A method for analyzing test-item responses is proposed to examine differential item functioning (DIF) in multiple-choice items within the latent class framework. Different models for detection of DIF are formulated, defining the subgroup as a latent variable. An efficient estimation method is described and illustrated. (SLD)

The shortcomings of the conventional way of using and interpreting multiple-choice tests are summarized. Some theories and methodologies that can be applied for better use multiple-choice test items are described. Empirical facts are introduced to support the theoretical observations. New strategies are proposed that will reduce "noise"…

Results from the Maryland School Performance Assessment Program for 5,392 elementary school students and from the Comprehensive Tests of Basic Skills (multiple choice) for a national sample are used to explore local item independence (LID) of test items. Some strategies are suggested for measuring LID in performance assessments. (SLD)

This study compares the fit of the 3-parameter model to the Ability Removing Random Guessing (ARRG) model on data from a wide range of tests of cognitive ability in three representative samples. When the guessing parameters under the 3-parameter model are estimated individually for each item, the 3-parameter model yields the better fit to…

Detecting differential item functioning (DIF) on test items constructed to favor 1 group over another was investigated on parameter estimates from 2 item response theory-based computer programs--BILOG and LOGIST--using data for 1,000 White and 1,000 Black college students. Use of prior distributions and marginal-maximum a posteriori estimation is…