[Rasch] Rasch and Missing data

Thomas Salzberger Thomas.Salzberger at wu-wien.ac.at
Sat Jul 5 02:46:18 EST 2008

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.
>Rasch mailing list
>Rasch at acer.edu.au

Liebe Gruesse
Thomas Salzberger
Dr. Thomas Salzberger
Österreichische Gesellschaft für Absatzwirtschaft
c/o Department of Marketing, Institute for Marketing Management
University of Economics and Business Administration (WU-Wien)
Augasse 2-6 / A-1090 Wien / Austria, Europe
Email: Thomas.Salzberger at wu-wien.ac.at
Tel: (+43-1-) 31336 4406
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