Antw: [Rasch] Fit & Dimensionality

Moritz Heene heene at
Thu Jul 10 18:37:51 EST 2008

Dear Antony,

This problem is similar to the question whether the 2-PL model is unidimensional. So do intersecting item response curves (ICCs) imply that a test is multidimensional? Not necessarily because differences in item slopes could have been caused by different random error components among the items. So the test would still be unidimensional. But unidimensionality only holds if all error components/vectors are orthogonal to each other and to the underlying trait. Unfortunately, most of the 2-PL proponents deftly avoid to test this strong assumption which is rarely met (s. Masters, 1988; Tuerlinckx & De Boeck, 2001a, 2001b; see also Lumsden, 1978).



Lumsden, J. (1978). Tests are perfectly reliable. British Journal of Mathematical and Statistical Psychology, 31(1), 19-26.

Masters, G. N. (1988). Item discrimination: When more is worse. Journal of Educational Measurement, 25(1), 15-29.

Tuerlinckx, F., & De Boeck, P. (2001). The Effect of Ignoring Item Interactions on the Estimated Discrimination Parameters in Item Response Theory. Psychological Methods, 6(2), 181-195.

Tuerlinckx, F., & De Boeck, P. (2001). Non-modeled item interactions lead to distorted discrimination parameters: A case study. Methods of Psychological Research Online, 6(2), 159-174.

Dr. Moritz Heene 
Ludwig Maximilian University Munich
Department Psychology
Methodology and Psychological Assessment
Leopoldstrasse 13
80802 Munich, Germany
Tel.: +49 89 / 2180 5192 
Fax: +49 89 / 2180 5235

>>> Anthony James <luckyantonio2003 at> 09.07.2008 09:03 >>>
Hi all,
I have found something interesting:
"...a Rasch model fit impressively supports unidimensionality of a
test,2 but in reverse, a Rasch model misfit does not necessarily contradict
unidimensionality. The appropriateness of the scoring rule has merely been invalidated
in the latter case" (p.381).
This is very different to what I have learned.
Any ideas?
It is here: 


More information about the Rasch mailing list