[Rasch] Comparison Rasch 3-parm IRT

Mike Linacre mike at winsteps.com
Fri Sep 13 14:55:13 EST 2013

Thank you for your questions about Rasch and 3-PL reliability, Ricardo.

In general, the information in a response that fits the dichotomous 
Rasch model contains more statistical information than an equivalent 
response that fits the 3-PL model. This is because of the information 
that is lost due to the lower asymptote, c parameter. For example, 
suppose that the c parameter is 0.99, then there is almost no 
information in the response. If the item-sample targeting is at 70% 
success and c=2, we expect a 3-PL response to contain around 67% of the 
information in a Rasch response.

Rasch Reliability = 0.70. Measure S.D. = 0.79.  So, according to 
Spearman(1910), RMSE (average S.E.) = 0.43
3PL Reliability=0.56. Theta S.D. = 0.79.  So, according to 
Spearman(1910), RMSE (average S.E.) = 0.52

Do these average S.E.s look like those reported by your software, 
Ricardo? If so, your 3-PL responses have (0.43/0.52)^2 = 68% of the 
information in your Rasch responses, and we expect that the average 
person is scoring around 70% on the test.

Hope this helps ....

Mike L.

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