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…

Two procedures for Rasch, sample-free item calibration are reviewed and compared for accuracy. The theoretically ideal "conditional" procedure is impractical for more than fifteen items. The more practical but biased "unconditional" procedure is discussed in detail. (Author/JKS)

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…

Study compares the Rasch and the Guttman models of measurement and thus adds to the description of the characteristics of Rasch's logistic model. Such knowledge is of importance in making decisions as to which model and which statistics should be used in evaluations of tests. (Author/CB)

This paper will discuss the results of a series of computer simulations comparing the Rasch logistic model to a series of models departing to various degrees from its assumption of equal discrimination power for all items. The results have implications for test construction and test scoring, indicating how closely the conventional raw score…

The purpose of this study was to compare the relative robustness of the one-, two-, and modified two-parameter latent trait logistic models for the Iowa Tests of Educational Development. Results suggest that the modified two-parameter model may provide the best representation of the data. (Author/BW)

A detailed description of five latent structure models of achievement measurement is presented. The first project paper, by David L. McArthur, analyzes the history of mental testing to show how conventional item analysis procedures were developed, and how dissatisfaction with them has led to fragmentation. The range of distinct conceptual and…

Five comparisons were made relative to the quality of estimates of ability parameters and item calibrations obtained from the one-parameter and three-parameter logistic models. The results indicate: (1) The three-parameter model fit the test data better in all cases than did the one-parameter model. For simulation data sets, multi-factor data were…

The purpose of this paper is to link empirical Bayes methods with two specific topics in item response theory--item/subtest regression, and testing the goodness of fit of the Rasch model--under the assumptions of local independence and sufficiency. It is shown that item/subtest regression results in empirical Bayes estimates only if the Rasch…

Two methods of item selection were used to select sets of 40 items from a 50-item verbal analogies test, and the resulting item sets were compared for relative efficiency. The BICAL program was used to select the 40 items having the best mean square fit to the one parameter logistic (Rasch) model. The LOGIST program was used to select the 40 items…

Four methods for determining the dimensionality of a set of test items were compared: (1) linear factor analysis; (2) residual analysis; (3) nonlinear factor analysis; and (4) Bejar's method. Five artificial test data sets (for 40 items and 1500 examinees) were generated, consistent with the three-parameter logistic model and the assumption of…

The question of whether test factor structure is indicative of the test item hierarchy was examined. Data from 1,000 subjects on two sets of five bivalued Law School Admission Test items, which were analyzed with latent trait methods of Bock and Lieberman and of Christoffersson in Psychometrika, were analyzed with an ordering-theoretic method to…

A Monte Carlo study was conducted to estimate the small sample standard errors and statistical bias of psychometric statistics commonly used in the analysis of achievement tests. The statistics examined in this research were: (1) the index of item difficulty; (2) the index of item discrimination; (3) the corrected item-total point-biserial…