An extension of the Bock-Samejima model for multiple choice items is introduced. The model provides for varying probabilities of the response alternative when the examinee guesses. A marginal maximum likelihood method is devised for estimating the item parameters, and likelihood ratio tests for comparing more and less constrained forms of the…

A method for determining invariant item parameters is presented, along with a scheme for obtaining test scores which are interpretable in terms of a common metric. The method assumes a unidimensional latent trait and uses a three parameter normal ogive model. The assumptions of the model are explored, and the methods for calculating the proposed…

This is a continuation of a previous study in which a new method of estimating the operating characteristics of discrete item responses based upon an Old Test, which has a non-constant test information function, was tested upon each of two subtests of the original Old Test, Subtests 1 and 2. The results turned out to be quite successful. In the…

In order to evaluate our methods and approaches of estimating the operating characteristics of discrete item responses, it is necessary to try other comparable methods on similar sets of data. LOGIST 5 was taken up for this reason, and was tried upon the hypothetical test items, which follow the normal ogive model and were used frequently in…

Optimal appropriateness indices, recently introduced by Levine and Drasgow (1984), provide the highest rates of detection of aberrant response patterns that can be obtained from item responses. These optimal appropriateness indices are used to study three important problems in appropriateness measurement. First, the maximum detection rates of two…

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…

A variety of locally dependent models are introduced having individual difference parameters that may be interpreted as reflecting effective learning abilities. One version is a univariate extension of the Rasch model with a Markov property: the probability that a given individual will pass an item depends on previous items only through 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)

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…