[Rasch] Comparison Rasch 3-parm IRT

Ricardo Primi rprimi at mac.com
Fri Sep 13 11:50:12 EST 2013

Dear List members

I have a question about comparison of Rasch model.  vs  IRT  3 param model. I am working in the development of a national test for entering teaching profession in Brazil. I recently analyzed data of a pre-test item bank and calibrated the items/persons using the Rasch model  (centering the scale on the persons side: UPMEAN = 0) and also in XCALIBRE using the 3-parameter model (MML with a Bayesian prior of mean 0 and SD 1, that is, also centered on persons). So I had two estimates for each one of the same group or persons. Unidimensinality was ok (done using parallel analysis in psych). Item had generally lower discrimination and c around .20. M and SD of both measures and theta estimates were very similar (0 and .79). Correlation between the two was very high: .97. I then compared information functions from the two calibrations. I transformed information > standard errors > local reliability – LR (Daniel, 1999): LR = 1 - (  (se ** 2) / variance of theta ). I saw that the rash local reliabilities (information) for the persons measures were higher (M=.70) than the 3-parm (M=.56). My question: Is this possible ? Is it because of a and c ? Is there some error in this procedure that I missed ?

I attached the plot of the LR. I computed model and real local reliabilities for the rasch measures and both are higher then IRT counterparts ..

Thank you in advance from your inputs ..

Ricardo Primi
USF, Brazil (www.labape.com.br)

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