[Rasch] Re: Rasch-Poisson

Mike Linacre (RMT) rmt at rasch.org
Sat May 23 18:58:40 EST 2009

Thank you for your further questions, Anthony:

You asked: What's the equation that I wrote in my previous email then?
P (X=1| b) = e^b/ (e^b+e^d)

Reply: This is an alternative way of writing the Rasch dichotomous model. 
It is an algebraic transformation of:
P (X=1| b) = e^(b-d)/ (1+e^(b-d))

You asked: Is there any way to get ratio scale measures with winsteps (or 
by hand) according to that equation?

Reply: there is some ambiguity about the term "ratio scale".

If you mean a Steven's "ratio scale", then any additive scale is a ratio 
scale provided that a point on the additive scale is defined as the origin 
(zero point), e.g., absolute zero on a temperature scale, or the end of a 
rule on a length scale. So, if you can define a zero point on a Rasch logit 
scale, then it becomes a Stevens' ratio scale relative to that zero point,

If you mean a "scale of ratios", so that, for example, 2 is twice 1, 3 is 
twice 2, 4 is twice 3, etc. then numbers on an additive scale (such as 
Rasch measures) are converted to a "scale of ratios" by exponentiating the 
numbers. Georg Rasch used a "scale of ratios" in his original formulation 
of his models for measurement.

You asked: How can one convert an interval scale logit measure of say, 1.5 
to a ratio measure according to the equation in my email? Will  it be again 
in logits?

Reply: assuming you mean a "scale of ratios", then e^1.5 = 4.5 is an 
"odds-units" ratio measure corresponding to 1.5 logits (log-odds-units) 
additive units.

You asked: Is Poisson a mathematician?
Thank you, Trevor, for answering this ....

Mike L.

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  22:4 Spring 2009

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