Ratio scale of measures: twice as much

Question: I want to say that person A has twice the ability of person B. How can I do that with logit (or user-scaled) measures?

 

To say that "one person is twice as good as another" requires a reference point. Think of the same thing with mountains. Mountain A is twice as high as Mountain B. The reference point is "sea level".

 

Constructing a reference point: A useful approach is to add to the data a dummy person whose performance is at your hypothesized reference point. Include in the data ratings for this dummy person against real items. Weight the dummy person at 0 with PWEIGHT=

 

Similarly a dummy item at the item's reference point. Include in the data ratings for this dummy item against real persons.  Weight the dummy person at 0 with IWEIGHT=

 

You can now use the person or item at the reference point as the basis for your "twice as much" statements.

 

For further convenience, you can anchor the dummy person at 0 with PAFILE= or the dummy item at 0 with IAFILE=, but not both at the same time.


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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 with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind 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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