Ratio scale of logit measures

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, e.g., 999=Reference Person. Include in the data ratings for this dummy person against real items, raters, tasks, etc.


Similarly a dummy rater at the raters's reference point, 999=Reference rater. Include in the data ratings for this dummy rater against real persons, tasks, etc.


Downweight the dummy ratings in the data using "R0.0001".




R0.0001, 999, 19,1,1,1   ; reference person (give the reference batter at least 20 ratings against different raters, etc.)

R0.0001, 1, 99,1,1,1   ; reference rater (give the reference pitcher at least 20 ratings against different persons, etc.)


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


You can take this a step further for convenience. Anchor the Dummy person and Dummy rater both at 0 logits.  Then make sure that an unanchored facet is non-centered

Noncenter=3 ; facet 3, items

or include a dummy facet that can be non-centered:


Noncenter=5 ; dummy facet for non-centering





5, Dummy facet

1=Dummy element



5,1   ; Facet 5 has element number 1 for every observation


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