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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