itemParEst {difR}R Documentation

Item parameter estimation for DIF detection

Description

Fits a specified logistic IRT model and returns related item parameter estimates.

Usage

 itemParEst(data, model, c=NULL, engine="ltm")
 

Arguments

data numeric: the data matrix.
model character: the IRT model to be fitted (either "1PL", "2PL" or "3PL").
c optional numeric value or vector giving the values of the constrained pseudo-guessing parameters. See Details.
engine character: the engine for estimating the 1PL model, either "ltm" (default) or "lme4".

Details

itemParEst permits to get item parameter estimates of some prespecified logistic IRT model, together with estimates of the standard errors and the covariances between item parameters, if any. The output is ordered such that it can be directly used with 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 not allowed.

If the model is not the 1PL model, or if engine is equal to "ltm", the selected IRT model is fitted using marginal maximum likelihood by means of the functions from the ltm package (Rizopoulos, 2006). Otherwise, the 1PL model is fitted as a generalized linear mixed model, by means of the glmer function of the lme4 package (Bates and Maechler, 2009). The 3PL model can be fitted either unconstrained or by fixing the pseudo-guessing values. In the latter case the argument c holds either a numeric vector of same length of the number of items, with one value per item pseudo-guessing parameter, or a single value which is duplicated for all the items. If c is different from NULL then the 3PL model is always fitted (whatever the value of model).

Each row of the output matrix corresponds to one item of the data set; the number of columns depends on the fitted model. At most, nine columns are produced, with the unconstrained 3PL model. The order of the columns is the following: first, the estimates of item discrimination a, difficulty b and pseudo-guessing c; second, the corresponding standard errors se(a), se(b) and se(c); finally, the covariances between the item parameters, cov(a,b), cov(a,c) and cov(b,c).

If the 2PL model is fitted, only five columns are displayed: a, b, se(a), se(b) and cov(a,b). In case of the 1PL model, only b and se(b) are returned. If the constrained 3PL is considered, the output matrix holds six columns, the first five being identical to those from the 2PL model, and the last one holds the fixed pseudo-guessing parameters.

Value

A matrix with one row per item and at most nine columns, with item parameter estimates, standard errors and covariances, if any. See Details.

Author(s)

Sebastien Beland
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
sebastien.beland.1@hotmail.com
David Magis
Research Group of Quantitative Psychology and Individual Differences
Katholieke Universiteit Leuven
David.Magis@psy.kuleuven.be, http://ppw.kuleuven.be/okp/home/
Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
raiche.gilles@uqam.ca, http://www.er.uqam.ca/nobel/r17165/

References

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

Rizopoulos, D. (2006). ltm: An R package for latent variable modelling and item response theory analyses. Journal of Statistical Software, 17, 1-25. URL: http://www.jstatsoft.org/v17/i05/

See Also

itemPar1PL, itemPar2PL, itemPar3PL, itemPar3PLconst, difLord, difRaju, difGenLord

Examples

# Loading of the verbal data
data(verbal)

# Estimation of the item parameters (1PL model, "ltm" engine)
items.1PL<-itemParEst(verbal[,1:24],model="1PL")

# Estimation of the item parameters (1PL model, "lme4" engine)
# (remove #)
# items.1PL<-itemParEst(verbal[,1:24],model="1PL", engine="lme4")

# Estimation of the item parameters (2PL model)
items.2PL<-itemParEst(verbal[,1:24],model="2PL")

# Estimation of the item parameters (3PL model)
# items.3PL<-itemParEst(verbal[,1:24],model="3PL")

# Constraining all pseudo-guessing values to be equal to 0.05
items.3PLc<-itemParEst(verbal[,1:24],model="3PL",c=0.05)

[Package difR version 1.1 Index]