This paper discusses the limitations of Classical Test Theory, the purpose of Item Response Theory/Latent Trait Measurement models, and the step-by-step calculations in the Rasch measurement model. The paper explains how Item Response Theory (IRT) transforms person abilities and item difficulties into the same metric for test-independent and…

This paper describes structural equation modeling (SEM) in comparison with another overarching analysis within the general linear model (GLM) analytic family: canonical correlation analysis. The uninitiated reader can gain an understanding of SEM's basic tenets and applications. Latent constructs discovered via a measurement model are explored and…

Item response theory models arose from the inherent limitations of classical test theory methods of test analysis. A brief description of those limitations and the corresponding enhancements provided by item response models is provided. Further, an examination of the popular Rasch one-parameter latent trait model is undertaken. Specific…

In this paper are described some features of the intensive use of math software, primarily DERIVE, in the context of modeling in an introductory university course in differential equations. Different aspects are detailed: changes in the curriculum that included not only course contents, but also the sequence of introduction to various topics and…

This paper aims to describe a Bayesian approach to modeling and estimating cognitive models both in terms of statistical machinery and actual instrument development. Such a method taps the knowledge of experts to provide initial estimates for the probabilistic relationships among the variables in a multivariate latent variable model and refines…

Stochastic models are developed in this article to examine the rate of test misgrading in educational and psychological measurement. The estimation of inadvertent grading errors can serve as a basis for quality control in measurement. Limitations of traditional Poisson models have been reviewed to highlight the need to introduce new models using…

This handbook explains how to do Rasch measurement. The emphasis is on practice, but theoretical explanations are also provided. The Forward contains an introduction to the topic of Rasch measurement. Chapters 2, 4, 5, and 7 use a small problem to illustrate the application of Rasch measurement in detail, and methodological issues are considered…

For meaningful learning of mathematics, a learning set is required which demands that all things accepted as true should be demonstrable in terms of a paradigm appropriate to the child's cognitive development: preparatory, concrete-particular, concrete-general, formal-abstract. Future teachers should experience all paradigms to become aware that…

Paper presented at the 4th International Congress for Logic, Methodology and Philosophy of Science, August 29-September 4, 1971, Bucharest, Rumania. (RS)

Four methods of finding the range of values of the solution of a problem when the data are known to lie within given bounds are illustrated. (MS)

An allocation model is proposed for instructional systems which have instructional programs that can be structured in terms of behavioral objectives, instructional activities, and required achievement levels. The model assumes that the relevant characteristics of students and teachers are known and that the instructional resources needed for an…

The Rasch model is an item analysis model with logistic item characteristic curves of equal slope, i.e. with constant item discriminating powers. The proposed goodness of fit test is based on a comparison between difficulties estimated from different scoregroups and over-all estimates. (Author)

A mathematical expression of the classic zone and sector phenomena in the distribution of residential neighborhood characteristics in urban areas is developed. (Author/JB)

The time-series process postulated is a more general form of the integrated moving average model than for which estimation and testing procedures were formerly available. (Author)