Topic models are mathematical and statistical models used to analyze textual data. The objective of topic models is to gain information about the latent semantic space of a set of related textual data. The semantic space of a set of textual data contains the relationship between documents and words and how they are used. Topic models are becoming…

Many organizations utilize some form of automation in the test assembly process; either fully algorithmic or heuristically constructed. However, one issue with heuristic models is that when the test assembly problem changes the entire model may need to be re-conceptualized and recoded. In contrast, mixed-integer programming (MIP) is a mathematical…

A procedure for obtaining Rasch model estimates of item difficulty and of ability is detailed. The procedure approximates the optimal but difficult to obtain "unconditional" estimates. (JKS)

A model of test item dependency is presented and used to illustrate the effect that violations of local independence have on the behavior of item characteristic curves. The dependency model is flexible enough to simulate the interaction of a number of factors including item difficulty and item discrimination, varying degrees of item dependence,…

This research simulated responses of 75 subjects to 30 items under the Birnbaum model and attempted a fit to the data using the Rasch model. When item discriminations varied from a variance of .05 to .25, there was only a slight increase in lack of fit as the variances increased. (Author/CTM)

This article organizes models for categorical item response data into three distinct classes. "Difference models" are appropriate for ordered responses, "divide-by-total" models for either ordered or nominal responses, and "left-side added" models for multiple-choice responses with guessing. Details of the taxonomy…

Wilcox has described three probability models which characterize a single test item in terms of a population of examinees (ED 156 718). This note indicates indicates that similar models can be derived which characterize a single examinee in terms of an item domain. A numerical illustration is given. (Author/JKS)

A method for detecting and interpreting disturbances of the local-independence assumption among items that share common stimulus material or other features is presented. Dichotomous and polytomous Rasch models are used to analyze structure of the learning outcome superitems. (SLD)

It is demonstrated, theoretically and empirically, that item sets can be selected that meet the unidimensionality assumption of most item response theory models, even though they require more than one ability for a correct response. A method for identifying such item sets for test development purposes is presented. (SLD)

Concern has been expressed over the item response theory (IRT) assumption that a person's ability can be estimated in a unidimensional latent space. To examine whether or not the response to an item requires only a single latent ability, unidimensional ability estimates were compared for data generated from the multidimensional item response…

Angoff's method for identifying possible biased test items was applied to four computer-generated hypothetical tests, two of which contained no biased items and two of which contained a few biased items. The tests were generated to match specifications of a latent trait model. Angoff's method compared item difficulty estimates for two different…

A theory and a procedure are presented for estimating a domain parameter and item parameters for test items in a homogeneous domain, such that the combined domain and item parameters account for observed proportions right for each item in a test. (CTM)

An alternative definition has been developed of the delta scale of item difficulty used at Educational Testing Service. The traditional delta scale uses an inverse normal transformation based on normal ogive models developed years ago. However, no use is made of this fact in typical uses of item deltas. It is simply one way to make the probability…

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…

This paper develops and applies three nonparametric comparisons of the shapes of two item characteristic surfaces: (1) proportional latent odds; (2) uniform relative difficulty; and (3) item sensitivity. A method is presented for comparing the relative shapes of two item characteristic curves in two examinee populations who were administered an…