[Rasch] Rasch and Missing data

Agustin Tristan ici_kalt at yahoo.com
Sat Jul 5 02:58:43 EST 2008

Hello Thomas, 
You write:
" the score out of the three easy items can't be compared to the score on the three hardest items. You have to convert raw scores to linear measures first to derive comparable measures."
The explanation concerning raw score and true measures is very difficult to maintain when you see the results of any Rasch analysis program if there are no missing answers. If you have 3 correct answers in a test of 30 dichotomous items, even if you have the 3/30 hardest and me the 3/30 most easy, you and me will have the same measure (same raw score by the way), but we shall have different fit. If I see the output of a Rasch analysis, you will have 3/30 as me, you will have a measure say -2.0 as me! Measure alone will not reflect the difference of items we did answer.
Probably the idea is related to have 3/20 (and 10 missing) and me 3/30 (without missing), evidently your "3" is not equal to my "3" in this case as we answered a different set of items. The explanation has to be different in the first case where we both had 3/30, and so your "3" difficult items produce the same measure as my "3" easy items.

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--- On Fri, 7/4/08, Thomas Salzberger <Thomas.Salzberger at wu-wien.ac.at> wrote:

From: Thomas Salzberger <Thomas.Salzberger at wu-wien.ac.at>
Subject: Re: [Rasch] Rasch and Missing data
To: rasch at acer.edu.au
Date: Friday, July 4, 2008, 11:46 AM

At 18:25 04.07.2008, Anthony James wrote:


The person has a score of 25 (out of 30) with no missing response. Let's assume you have 6 items with six response categories (scored 0 to 5).
If there is one response missing, the score is (in your example) 21 - but the 21 is not out of 30 but out of 25.

Even with the same max score you may not be able to compare raw scores. If you have two persons with three missings each (one persons misses the three easiest items, the other person misses the three hardest), they both have a theoretical score range of 0 to 15 but still the score out of the three easy items can't be compared to the score on the three hardest items. You have to convert raw scores to linear measures first to derive comparable measures. 
Raw score suffiency still holds in the sense that given a particular set of three items answered, the raw score contains all the information available.

It should be noted that it also depends on the type of missing. If it is missing not at random things will be more complicated.

Dear all,<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

It is generally argued that RM is robust to missing data because the total score is the sufficient statistic for parameter estimation.

But, missing data affects total score too. Suppose that in a complete data set the total score of a person is 25 out of 30. If this dataset is affected by ¡missingness¢ then the total score of this person would be say, 21 out of 30. If his measure when there¢s no missing data is say, 2 logits (based on 25/30) his measure from the ¡missingness  struck¢ dataset would be say, 1.5 logits because some of his correct answers are missing and  his raw score diminishes (21/30). So the measure we get is not equivalent to what we would have got when all data were present.



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