equateIRT-package {equateIRT}

IRT Equating Methods

Description

This package computes direct, chain and average (bisector) equating coefficients with standard errors using IRT methods for dichotomous items. The IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Test scoring can be performed by true score equating and observed score equating methods. DIF detection can be performed using a Wald-type test.

Details

Package:	equateIRT
Type:	Package
Version:	2.5.0
Date:	2024-07-30
License:	GPL-3

Direct equating coefficients and their standard errors between forms presenting common items can be computed using function direc. The equating methods implemented are "mean-mean", "mean-geometric mean", "mean-sigma", "Haebara" and "Stocking-Lord". Estimates of item parameters and their covariance matrix can be imported from the R packages ltm and mirt or from the IRT programs IRTPRO and flexMIRT using functions import.ltm, import.mirt, import.irtpro and import.flexmirt. Item parameter estimates from other software can be imported as well by the user. Data should be previously organized using function modIRT. Function alldirec computes all direct equating coefficients (with standard errors) between all pairs of a list of forms. Function chainec computes chain equating coefficients (and standard errors) given direct equating coefficients between forms directly linked. Average equating coefficients with standard errors can be calculated using function bisectorec, that implements the (weighted) bisector method. Once the equating coefficients are obtained, the computation of equated scores can be performed using function score, which implements true score equating and observed score equating. Standard errors of equated scores are also provided. Three simulated datasets are available for illustrative purposes. These datasets contain item parameter coefficients and their covariance matrix. In particular, est3pl concerns a three-parameter logistic model, est2pl regards a two-parameter logistic model, and estrasch refers to a Rasch model. The estimates included in est2pl are obtained from the dataset data2pl, also contained in the package. Function dif.test performs a Wald-type test for the detection of DIF (Battauz, 2018). The stability of the equating transformations can be assessed using function sd.test, which tests if the equating coefficients that link the same two forms are equal, and function id.test, which tests if the equating coefficients that link a form to itself through a chain of forms return the identity equating.

Author(s)

Michela Battauz

Maintainer: Michela Battauz <[e-mail]>

References

Battauz, M. (2013). IRT Test Equating in Complex Linkage Plans. Psychometrika, 78, 464–480.

Battauz, M. (2015). equateIRT: An R Package for IRT Test Equating. Journal of Statistical Software, 68, 1–22.

Battauz, M. (2019). On Wald tests for differential item functioning detection. Statistical Methods and Applications. 28, 103–118.

Battauz, M. (2022). Testing for differences in chain equating. Statistica Neerlandica, 1–12.

Cai L. (2013). FlexMIRT version 2: Flexible Multilevel Multidimensional Item Analysis and Test Scoring [Computer Software]. Chapel Hill, NC: Vector Psychometric Group.

Cai, L., du Toit, S. H. C., Thissen, D. (2011). IRTPRO: Flexible, multidimensional, multiple categorical IRT modeling [Computer software]. Chicago: Scientific Software International.

Chalmers, R. P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48, 1–29.

Holland, P.W. and Strawderman, W.E. (2011). How to average equating functions if you must. In A.A. von Davier (Ed.), Statistical models for test equating, scaling, and linking (pp. 89–107). New York: Springer.

Kolen, M.J. and Brennan, R.L. (2014). Test equating, scaling, and linking: methods and practices, 3rd ed., New York: Springer.

Ogasawara, H. (2000). Asymptotic standard errors of IRT equating coefficients using moments. Economic Review (Otaru University of Commerce), 51, 1–23.

Ogasawara, H. (2001a). Item response theory true score equatings and their standard errors. Journal of Educational and Behavioral Statistics, 26, 31–50.

Ogasawara, H. (2001b). Standard Errors of Item Response Theory Equating/Linking by Response Function Methods. Applied Psychological Measurement, 25, 53–67.

Ogasawara, H. (2003). Asymptotic standard errors of IRT observed-score equating methods. Psychometrika, 68, 193–211.

Rizopoulos, D. (2006). ltm: an R package for latent variable modelling and item response theory analyses. Journal of Statistical Software, 17, 1–25.