itemPar1PL {difR}R Documentation

Item parameter estimation for DIF detection using Rasch (1PL) model


Fits the Rasch (1PL) model and returns related item parameter estimates.


itemPar1PL(data, engine = "ltm", discr = 1)



numeric: the data matrix.


character: the engine for estimating the 1PL model, either "ltm" (default) or "lme4".


either NULL or a real positive value for the common discrimination parameter (default is 1). Not used if engine is "lme4". See Details.


itemPar1PL permits to get item parameter estimates from the Rasch or 1PL 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 estimation engine is set by the engine argument. By default (engine="ltm"), the Rasch model is fitted using marginal maximum likelihood, by means of the function rasch from the ltm package (Rizopoulos, 2006). The other option, engine="lme4", permits to fit the Rasch model as a generalized linear mixed model, by means of the glmer function of the lme4 package (Bates and Maechler, 2009).

With the "ltm" engine, the common discrimination parameter is set equal to 1 by default. It is possible to fix another value through the argumentdiscr. Alternatively, this common discrimination parameter can be estimated (though not returned) by fixing discr to NULL. See the functionalities of rasch command for further details.


A matrix with one row per item and two columns, the first one with item parameter estimates and the second one with the related standard errors.


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,


Bates, D. and Maechler, M. (2009). lme4: Linear mixed-effects models using S4 classes. R package version 0.999375-31.

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

itemPar2PL, itemPar3PL, itemPar3PLconst, itemParEst, difLord, difRaju,



## Not run: 

 # Loading of the verbal data
 # Getting item parameter estimates ('ltm' engine)
 itemPar1PL(verbal[, 1:24])

 # Estimating the common discrimination parameter instead
 itemPar1PL(verbal[, 1:24], discr = NULL)

 # Getting item parameter estimates ('lme4' engine) 
 itemPar1PL(verbal[, 1:24], engine = "lme4")
## End(Not run)

[Package difR version 5.1 Index]