itemPar2PL {difR}R Documentation

Item parameter estimation for DIF detection using 2PL model


Fits the 2PL model and returns related item parameter estimates, standard errors and covariances between item parameters.





numeric: the data matrix.


itemPar2PL permits to get item parameter estimates from the 2PL model. The output is ordered such that it can be directly used with the general itemParEst command, as well as the methods of Lord (difLord) and Raju (difRaju) and Generalized Lord's (difGenLord) to detect differential item functioning.

The data is a matrix whose rows correspond to the subjects and columns to the items.

Missing values are allowed but must be coded as NA values. They are discarded for item parameter estimation.

The 2PL model is fitted using marginal maximum likelihood by means of the functions from the ltm package (Rizopoulos, 2006).


A matrix with one row per item and five columns: the estimates of item discrimination a and difficulty b parameters, the related standard errors se(a) and se(b), and the covariances cov(a,b), in this order.


The 2PL model is fitted under the linear parametrization in ltm, the covariance matrix is extracted with the vcov() function, and final standard errors and covariances are derived by the Delta method. See Rizopoulos (2006) for further details, and the Note.pdf document in the difR package for mathematical details.


Sebastien Beland
Collectif pour le Developpement et les Applications en Mesure et Evaluation (Cdame)
Universite du Quebec a Montreal,
David Magis
Department of Psychology, University of Liege
Research Group of Quantitative Psychology and Individual Differences, KU Leuven,
Gilles Raiche
Collectif pour le Developpement et les Applications en Mesure et Evaluation (Cdame)
Universite du Quebec a Montreal,


Magis, D., Beland, S., Tuerlinckx, F. and De Boeck, P. (2010). A general framework and an R package for the detection of dichotomous differential item functioning. Behavior Research Methods, 42, 847-862. doi: 10.3758/BRM.42.3.847

Rizopoulos, D. (2006). ltm: An R package for latent variable modelling and item response theory analyses. Journal of Statistical Software, 17, 1–25. doi: 10.18637/jss.v017.i05

See Also

itemPar1PL, itemPar3PL, itemPar3PLconst, itemParEst, difLord, difRaju,



## Not run: 

 # Loading of the verbal data

 # Getting item parameter estimates
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[Package difR version 5.1 Index]