At the 3^rd Rasch day I wrongly stated that Winsteps isn't appropriate for test equating using concurrent estimation. To clarify: concurrent estimation will not result in bias if you use CML estimation or specify different distributions for different populations in MMLE: Hanson & Beguin (2002) remarking on the study of Kim & Cohen (1998):

Bilog was also used for concurrent estimation, although this is not strictly appropriate in the case in which the groups taking the two forms are not randomly equivalent, because BILOG cannot estimate the correct specified model in which separate latent variable distributions are assumed for the groups of examinees taking the two forms.

Kolen and Brennan cite Mars (2000) on this for MMLE (p.167), but later they then state it again (p. 388), without evidence or citations or referring to the estimation method, which misled me into generalising. Winsteps by default uses JMLE, and doesn’t support MMLE.

Thank you to Anton Beguin for clearing this up for me.

Hanson, B.A. & Béguin, A.A. (2002) Obtaining a Common Scale for Item Response Theory Item Parameters Using Separate Versus Concurrent Estimation in the Common-Item Equating Design. Applied Psychological Measurement, Vol. 26, No. 1, 3-24

Kolen, M.J. & Brennan, R.L. (2004) Test Equating, Scaling and Linking New York: Springer

	1. 15-02-2008 08:22
	Thank for this email, Chris.    Winsteps would implement CMLE (and I will probably include it in a future upgrade to Winsteps), but the problems with CMLE are:  a) long test length (loss of computational precision)  b) missing data (only a few, well defined, missing data patterns allowed)  The more complex the concurrent equating situation, the more difficult to implement with CMLE.    MMLE for concurrent equating has the problem that sample distributions have to be specified in advance when often that is a finding, not an assumption. This is noticeable in educational and medicals applications when the sample distribution is truncated to "only high- (or low-) performers on the screening test take the full test", etc.    Cordially,  Mike L. Registered Report

Chris Wheadon

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