A measurement ideal is that each respondent uses the rating scale in the same way. But this doesn't always happen. Does allowing for personal idiosyncrasies solve the problem?
I asked 62 hikers to rate the difficulty of 20 mountains on the Appalachian Trail, using a 5-point rating scale, from 1=easy to 5=extremely hard. The respondents rated each of the 20 mountains in comparison to some other "standard" mountain of the respondent's choice. It was clear from the comments of the hikers that they were answering this item idiosyncratically. One hiker said that, compared to the Rocky Mountains, the mountains on the Appalachian Trail were easy, and so he never used the 4 and 5 ratings. Another hiker said that there is no such thing as an easy mountain, and never used the 1 and 2 ratings.
When I modelled all the hikers to use the rating scale in the same way, I found that 13 of the hikers showed noticeable misfit, with infit or outfit greater than 1.4 (see Figure). This motivated me to hope that the misfit was caused by each hiker defining a separate rating scale.
In a new calibration, in which the 13 misfitting hikers were modelled to have their own rating scales, there was some overall improvement in fit and statistical separations improved slightly, but most misfit was still unexplained. It looks like the real solution to personal idiosyncrasies is to rewrite my questionnaire.
Modeling person response styles. Bowles R. Rasch Measurement Transactions, 2000, 14:1 p.739
|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|
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