[Rasch] Negative pt-bis and fit of 1.0? How can this be?

David Andrich david.andrich at uwa.edu.au
Wed Mar 7 12:33:49 EST 2012

Yes, Mark has explained it. The usual tests of fit have very little power if there is no person separation and little item separation. In that case a correct and incorrect score are more or less equally likely and so there is no evidence of unlikely responses (misfit). The connection between a traditional test theory statistic and power of the test of fit is the simple traditional reliability index (coefficient alpha), or in the case of some missing data, the index based on Rasch model estimates (which I call person separation but can be called Rasch model reliability). I consider that no fit statistics should be reported without this statistic also being reported, and a comment as to whether it is large enough to have power in detecting misfit. The usual number of 0.75 and above seems mandatory. In the program RUMM for example, we interpret this number as evidence of the power of the test of fit, with a colour coding from Excellent, Good, Reasonable, Low, and Too Low. 
Hope this helps


David Andrich, BSc MEd W.Aust., PhD Chic, FASSA
Chapple Professor 
david.andrich at uwa.edu.au
Graduate School of Education
The University of Western Australia
M428, 35 Stirling Highway, 
Western Australia , 6009

Telephone: +61 8 6488 1085
Fax: +61 8 6488 1052
CRICOS Code: 00126G
Pearson Psychometric Laboratory

-----Original Message-----
From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Stuart Luppescu
Sent: Wednesday, 7 March 2012 5:53 AM
To: rasch at acer.edu.au
Subject: Re: [Rasch] Negative pt-bis and fit of 1.0? How can this be?

On Tue, 2012-03-06 at 15:36 -0600, Stuart Luppescu wrote:
> Are you saying that if I just generated 1's and 0's randomly and tried
> to calibrate them they would all fit? Hmmm. I'm going to have to try
> that.... 

Very interesting, indeed! Of course, you get 0 reliability and
point-biserials near 0, but all the fit statistics are very close to
1.0! Mark Moulton gets a beer next time I see him for providing the
instructional moment of the day.

Stuart Luppescu -=- slu .at. ccsr.uchicago.edu        
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