Rasch Measurement and the R Statistics Environment

Rasch measurement has been slow to penetrate into the mainstream of statistical thinking despite positive comments from recognized authority figures such as Otis Dudley Duncan (1984) and Leo Goodman (1990).

But there are promising signs. One is the article "Using the open-source statistical language R to analyze the dichotomous Rasch model" by Y. Li in Behavioral Research Methods, 2006, 38(3), 532-41.

Li's Figure 2, showing the likelihood function for a 3-item test. This is the only graphical Figure in the article.

Its Abstract states: "R, an open-source statistical language and data analysis tool, is gaining popularity among psychologists currently teaching statistics. R is especially suitable for teaching advanced topics, such as fitting the dichotomous Rasch model - a topic that involves transforming complicated mathematical formulas into statistical computations. This article describes R's use as a teaching tool and a data analysis software program in the analysis of the Rasch model in item response theory. It also explains the theory behind, as well as an educator's goals for, fitting the Rasch model with joint maximum likelihood estimation. This article also summarizes the R syntax for parameter estimation and the calculation of fit statistics. The results produced by R is compared with the results obtained from MINISTEP and the output of a conditional logit model. The use of R is encouraged because it is free, supported by a network of peer researchers, and covers both basic and advanced topics in statistics frequently used by psychologists."

Li's article is a competent presentation of Rasch estimation with R. His example dataset is the familiar Knox Cube Test. So his work is a springboard for statisticians looking for a familiar entry point into the somewhat specialized Rasch world.

Li's article also states that "R's pedagogical value makes it well suited for the underlying logic of ... statistical methods. R's design philosophy emphasize data visualization ... These design characteristics not only help students understand the critical abstract theoretical concepts ,,,, they also help students connect abstract statistical concepts with computations."

This is the next step for those following along Li's path. Number crunching is a necessary first step, but picturing the latent variable and conceptualizing what the measures mean are the direction in which the path leads. Let us hope that a subsequent paper on Rasch and R will capitalize on these ideas and include the construction of maps and the underlying measurement concepts which are the motivation behind Rasch models.

Courtesy of William P. Fisher, Jr.

Duncan, O.D. (1984) Rasch measurement: Further examples and discussion. In Charles F. Turner and Elizabeth Martin, editors, Surveying Subjective Phenomena, volume 2, chapter 12, pages 367-403, Russell Sage Foundation, New-York.

Goodman, L.A. (1990) "Total-score models and Rasch-type models for the analysis of a multidimensional contingency table, or a set of multidimensional contingency tables, with specified and/or unspecified order for response categories," Sociological Methodology, Vol. 20, edited by Clifford C. Clogg, Oxford: Basil Blackwell.

Rasch Measurement and the R Statistics Environment. William P. Fisher, Jr. … Rasch Measurement Transactions, 2007, 21:1 p. 1087

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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