itemPar3PL: Item parameter estimation for DIF detection using 3PL model

In difR: Collection of Methods to Detect Dichotomous and Polytomous Differential Item Functioning (DIF)

Item parameter estimation for DIF detection using 3PL model

Description

Fits the 3PL model and returns related item parameter estimates.

Usage

itemPar3PL(data)

Arguments

data	numeric: the data matrix.

Details

itemPar3PL permits to get item parameter estimates from the 3PL 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 output consists of nine columns which are displayed in the following order. The first three columns hold the estimates of item discrimination a, difficulty b and pseudo-guessing c parameters. In the next three columns one can find the related standard errors se(a), se(b) and se(c). Eventually, the last three columns contain the covariances between item parameters, respectively cov(a,b), cov(a,c) and cov(b,c).

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 3PL model is fitted using marginal maximum likelihood by means of the functions from the ltm package (Rizopoulos, 2006).

Value

A matrix with one row per item and nine columns. See Details.

Note

The 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.

Author(s)

David Magis
Data science consultant at IQVIA Belux
Brussels, Belgium
Sebastien Beland
Faculte des sciences de l'education
Universite de Montreal (Canada)
[e-mail]
Gilles Raiche
Universite du Quebec a Montreal
[e-mail]

References

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v017.i05")}

See Also

itemPar1PL, itemPar2PL, itemPar3PLconst, itemParEst, difLord, difRaju,

difGenLord

Examples

## Not run: 

 # Loading of the verbal data
 data(verbal)

 # Getting item parameter estimates
 itemPar3PL(verbal[,1:24])
 
## End(Not run)
 

difR documentation built on June 8, 2025, 1:03 p.m.