itemPar3PLconst {difR}R Documentation

Item parameter estimation for DIF detection using constrained 3PL model


Fits the 3PL model with constrained pseudo-guessing values and returns related item parameter estimates.


itemPar3PLconst(data, c=rep(0,ncol(data)))



numeric: the data matrix.


numeric value or vector of constrained pseudo-guessing parameters. See Details.


itemPar3PLconst permits to get item parameter estimates from the 3PL model for which the pseudo-guessing parameters are constrained to some fixed values. 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 output is similar to that of itemPar2PL method to fit the 2PL model; an additional column is included and holds the fixed pseudo-guessing parameter values.

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 argument c can be either a single numeric value or a numeric vector of the same length of the number of items. In the former case, the pseudo-guessing parameters are considered to be all identical to the given c value; otherwise c is directly used to constraint these parameters.

The constrained 3PL 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 six columns: the item discrimination a and difficulty estimates b, the corresponding standard errors se(a) and se(b), the covariances cov(a,b) and the constrained pseudo-guessing values c.


The constrained 3PL model is fitted under the linear parametrization in tpm, 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, itemPar2PL, itemPar3PL, itemParEst, difLord, difRaju,



## Not run: 

 # Loading of the verbal data

 # Constraining all pseudo-guessing parameters to be equal to 0.05
 itemPar3PLconst(verbal[,1:24], c = 0.05)

 # Constraining pseudo-guessing values to  0.1 for the first 10 items,
 # and to 0.05 for the remaining ones
 itemPar3PLconst(verbal[,1:24], c = c(rep(0.1, 10), rep(0.05, 14)))
## End(Not run)

[Package difR version 5.1 Index]