[Rasch] Bias in JMLE

Mike Linacre (RMT) rmt at rasch.org
Sat Aug 2 18:29:06 EST 2008

Thank you for your questions, Anthony.

In the psychometric literature, the terms "bias" and "inconsistency" are 
usually used in the context of the estimation of the difficulties of 
dichotomous items in a fixed length test administered to a sample of persons.

If the sample size is infinite, and the resulting item estimates are their 
true values, then the estimates are consistent.
If the sample size is finite, and the expectations of the possible item 
estimates are their true values, then the estimates are unbiased.

JMLE estimates are inconsistent and biased. They are less central than the 
true values. For instance, if the test consists of two dichotomous items, 
then, with an infinite sample, the JMLE estimate of the difference between 
the two item difficulties will be twice the true value.

Ben Wright and Graham Douglas discovered that the multiplier (L-1)/L is an 
approximate correction for JMLE item bias, where L is the test length. For 
a two-item test this correction would be (2-1)/2 = 0.5 . It is implemented 
in Winsteps with STBIAS=YES. There is much more about this in Winsteps Help 
at http://www.winsteps.com/winman/index.htm?ebiascorrection.htm

Mike L.

At 8/1/2008, you wrote:
>It is documented in the literature that JMLE is biased.
>What  does this mean?
>What is meant by bias or inconsistency in JMLE?
>Is the correction factor K-1/K is multiplied by JMLE estimates?

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  21:4 Spring 2008
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