Fisher's information measure for the item difficulty parameter in the Rasch model and its marginal and conditional formulations are investigated. It is shown that expected item information in the unconditional model equals information in the marginal model, provided the assumption of sampling examinees from an ability distribution is made. For the…

A procedure for the sequential optimization of the calibration of an item bank is given. The procedure is based on an empirical Bayes approach to a reformulation of the Rasch model as a model for paired comparisons between the difficulties of test items in which ties are allowed to occur. First, it is indicated how a paired-comparisons design…

Children learn arithmetic procedures by rote, rather than by constructing them with an understanding of numbers. Rote learning produces lack of flexibility, nonsensical errors, and other difficulties. Proposed is a theory of conceptual understanding and its role in learning and executing arithmetic procedures. The basic hypothesis is that…

As useful as LISREL may be in model estimation and testing, its most significant contribution to date is the encouragement and example it gives for right thinking about research and right planning of research. The encouragement to hypothesize the best possible model for the process that is the object of study, and to plan measurements that…

In an analysis of multitrait-multimethod matrices the criteria for discriminant validity are shown to include a "structure" criterion as an invariance of traits structure to methods. The criterion is meant to fit data to an additive model with traits and methods but not interaction terms. The importance of the structure criterion and the…

The Pearson and likelihood ratio statistics are frequently used for assessing the absolute fit of probability models. Researchers are often interested in comparing fits provided by different models which may have a subsuming or non-subsuming relation. A subsuming relation exists when the parameters of the reduced model form a subset of those…

Explored are two theoretical approaches that attempt to cope with omitted responses, that is, when an examinee omits (fails to respond to) an item and therefore the item response formula cannot be used. Preliminary considerations are discussed, and it is shown that a conveniently simple application of equivalent items leads to internal…

A mathematical setting based on a statistical sampling probability mechanism is described. In this setting, a mathematical meaning is given for the information function; and it becomes possible to study the relative merits of various ability-estimating procedures. The maximum likelihood estimation procedure under the one-, two-, three-parameter…

This proposal attempts to follow in Allan Birnbaum's tradition by using Bayesian ideas to show that his mental test model possesses even broader applicability than previously realized. Birnbaum's two significant contributions to the theories of statistics and educational testing are: (1) the proof that the sufficiency and conditionality principles…

There are currently three main approaches to parameter estimation in item response theory (IRT): (1) joint maximum likelihood, exemplified by LOGIST, yielding maximum likelihood estimates; (2) marginal maximum likelihood, exemplified by BILOG, yielding maximum likelihood estimates of item parameters (ability parameters can be estimated…

The purpose of this paper is to present a generalization of the concept of item difficulty to test items that measure more than one dimension. Three common definitions of item difficulty were considered: the proportion of correct responses for a group of individuals; the probability of a correct response to an item for a specific person; and the…

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data…

Use of syntactic trace as an access strategy for large files containing arbitrary languages for which thesaurus-based and multiple attribute search techniques are unsuitable. (LS)

Presents a mechanical analog designed to reduce the conceptual difficulties experienced by many students in thinking about age distribution concepts in demography. (JR)