[Rasch] shift of person parameter scale

Rense Lange rense.lange at gmail.com
Sat May 4 10:28:30 EST 2013

Nothing wrong with rescaling person measures using multiplication and addition both - everybody does it. I just wanted to stress that one should not use multiplied item locations directly for equating, etc. (shifts up/down are fine - because person estimates can easily be adjusted). 

Intuitively, this is because when the item parms are multiplied non-trivially, the observed (raw) data of the equating sample that you are going to use do NOT naturally come so multiplied (I don't know how one would do this to observations)


On May 3, 2013, at 7:08 PM, Tom Conner <connert at msu.edu> wrote:

> Doesn't linear transformation involve both multiplication and addition/substraction?
> On 5/3/13 7:49 PM, Rense Lange wrote:
>> To be sure: multiplications shouldn't be done to Rasch calibrated item parameters (adding - subtracting something is fine). Except, perhaps, to display them in the same metric as the (transformed) person measures.  But, don't multiply if you want to use the items later for anchoring, say.
>> Right?
>> Rense Lange
>> On May 3, 2013, at 6:04 PM, Mike Linacre <mike at winsteps.com> wrote:
>>> Thank you for your question, Felix.
>>> You have a "Fahrenheit-to-Celsius" situation, equivalent to http://www.rasch.org/rmt/rmt223d.htm . You can subtract 0.5 from all the person and item location estimates, then multiply all the resulting estimates by 1.0/1.2. Also adjust discrimination parameters by 1.2/1.0.  Verify that these values are correct by computing some raw scores based on the rescaled estimates and comparing them with the original observed scores.
>>> OK?
>>> Mike L.
>>> On 5/3/2013 7:02 AM, Fischer, Felix wrote:
>>>> I have been told that it is possible to shift item parameters of IRT models in order to achieve a certain distribution of person-estimates for a given sample. Practically I have a graded response model estimated in a larger sample including a representative sample. now, I want to shift the parameters that the distribution of the person estimates of the representative sample is normalized (has mean = 0 and sd = 1). Actually, the distribution is slightly different, eg mean = 0.5 and sd = 1.2. 
>>>> Is anyone aware how to change the item-parameters? Or is there any reference where I could look up the procedure?
>>>> Best, Felix
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> -- 
> Tom Conner
> Professor Emeritus
> Department of Sociology
> Michigan State University
> "What if there were no hypothetical questions?"
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