equateMultiple-package: Equating of Multiple Forms

In equateMultiple: Equating of Multiple Forms

Equating of Multiple Forms

Description

The EquateMultiple package implements IRT-based methods to equate simultaneously many forms calibrated separately. This package estimates the equating coefficients to convert the item parameters and the ability values to the scale of the base form. It can be applied to a large number of test forms, as well as to 2 forms. The computation of the equated scores is also implemented.

Details

This package implements the methods proposed in Haberman (2009), Battauz (2017) and Battauz and Leoncio (2023). Function multiec computes the equating coefficients to convert the item parameters and the ability values to the scale of the base form. The methods implemented are: multiple mean-geometric mean (Haberman, 2009), multiple mean-mean, multiple item response function, multiple test response function (Battauz, 2017), and likelihood-based linking (Battauz and Leoncio, 2023). The function provides the equating coefficients, estimates of item parameters on a common scale and the standard errors of the equating coefficients and item parameters on a common scale. Equated scores can be computed using true score equating and observed score equating methods. Standard errors of equated scores are also provided.

Author(s)

Michela Battauz [aut, cre], Waldir Leoncio [ctb]

Maintainer: Michela Battauz <[e-mail]>

References

Battauz, M. (2017). Multiple equating of separate IRT calibrations. Psychometrika, 82, 610–636. doi:10.1007/s11336-016-9517-x.

Battauz, M., Leoncio, W. (2023). A Likelihood Approach to Item Response Theory Equating of Multiple Forms Applied Psychological Measurement, 47, 200-220. doi: 10.1177/01466216231151702.

Haberman, S. J. (2009). Linking parameter estimates derived from an item response model through separate calibrations. ETS Research Report Series, 2009, i-9. doi:10.1002/j.2333-8504.2009.tb02197.x.

See Also

equateIRT

Examples

data(est2pl)
# prepare the data
mods <- modIRT(coef = est2pl$coef, var = est2pl$var, display = FALSE)
# Estimation of the equating coefficients with the multiple mean-mean method
eqMM <- multiec(mods = mods, base = 1, method = "mean-mean")
summary(eqMM)

# Estimation of the equating coefficients with the 
# multiple mean-geometric mean method (Haberman, 2009)
eqMGM <- multiec(mods = mods, base = 1, method = "mean-gmean")
summary(eqMGM)

# Estimation of the equating coefficients with the multiple item response function method
eqIRF <- multiec(mods = mods, base = 1, method = "irf")
summary(eqIRF)

# Estimation of the equating coefficients with the multiple item response function method
# using as initial values the estimates obtained with the multiple mean-geometric mean method
eqMGM <- multiec(mods = mods, base = 1, method = "mean-gmean", se = FALSE)
eqIRF <- multiec(mods = mods, base = 1, method = "irf", start = eqMGM)
summary(eqIRF)

# Estimation of the equating coefficients with the multiple test response function method
eqTRF <- multiec(mods = mods, base = 1, method = "trf")
summary(eqTRF)

# Estimation of the equating coefficients with the likelihood-based method
eqLIK <- multiec(mods = mods, base = 1, method = "lik")
summary(eqLIK)

# scoring using the true score equating method and equating coefficients 
# obtained with the multiple item response function method
score(eqIRF)

equateMultiple documentation built on June 8, 2025, 11:39 a.m.