Rasch and Continuous Variables

Question: Can Rasch analyze continuous response-level data, such as time and distance?

Answer: There are Rasch models for continuous observations, but processes are rarely truly continuous. Rasch is formulated in terms of distinguishable qualitative advances. How much better, faster, more accurate, does a performance need to be for it to be noticeably better? Think of the same thing in human weight. Our weight varies all day long, so it is not until it has changed by 2 kilos that we really notice a difference. The basic approach in Rasch is to start by categorizing really big increments. If those analyze successfully, we can then reduce the size of the increments until we reach the level where further reduction introduces more randomness than information into the data.

There are several indicators of over-categorization. One is that the model polytomous category probability curves start to look a mess, instead of an advancing range of hills. Another is that, as the number of categories increase, the sample-person "test" reliability falls far behind the value predicted by the Spearman-Brown Prophecy Formula. Going from 2 categories (one decision per item) to 3 categories (two decisions per item) is somewhat like doubling the test length, but not so efficient. So given the reliability, R(m), for an m-category rating scale, we would predict the reliability for an (m+1) category rating scale to be appreciably better, in the range:

R(m) < R(m+1) < m*R(m) / (m-1+R(m))

We can keep track of the reliability as we increase the number of categories. When reliability not longer shows a reasonable increase (or starts to decrease) we have over-categorized.

Rasch and Continuous Variables. John M. Linacre … Rasch Measurement Transactions, 2007, 21:1 p. 1088

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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