multiec: Multiple Equating Coefficients

In equateMultiple: Equating of Multiple Forms

Multiple Equating Coefficients

Description

Calculates the equating coefficients between multiple forms.

Usage

multiec(mods, base = 1, method = "mean-mean", se = TRUE, nq = 30, start = NULL, 
	iter.max = 100000, obsinf = TRUE, trace = TRUE)

Arguments

mods	an object of the class modIRT containing item parameter coefficients and their covariance matrix of the forms to be equated.
base	integer value indicating the base form.
method	the method used to compute the equating coefficients. This should be one of "mean-mean", "mean-gmean", "irf", "trf" or "lik" (see details).
se	logical; if TRUE the standard errors of the equating coefficients and the item parameters on a common scale are computed.
nq	number of quadrature points used for the Gauss-Hermite quadrature for methods "irf" or "trf".
start	initial values. This can be a vector containing the A and B equating coefficients excluding the base form, or an object of class mlteqc returned by function multiec. Used only with methods "irf", "trf" and "lik".
iter.max	maximum number of iterations allowed. Used only with methods "irf", "trf" and "lik".
obsinf	logical; if TRUE the standard errors are computed using the observed information matrix. Used only with method "lik", see Battauz and Leoncio (2023).
trace	logical; if TRUE tracing information is produced.

Details

The methods implemented for the computation of the multiple equating coefficients are the multiple mean-mean method ("mean-mean"), the multiple mean-geometric mean method ("mean-gmean"), the multiple item response function method ("irf"), the multiple test response function method ("trf"), and likelihood-based equating ("lik").

Value

An object of class mlteqc with components

A	A equating coefficients.
B	B equating coefficients.
se.A	standard errors of A equating coefficients.
se.B	standard errors of B equating coefficients.
varAB	covariance matrix of equating coefficients.
as	discrimination parameters on a common scale \hat a_j^*.
bs	difficulty parameters on a common scale \hat b_j^*.
se.as	standard errors of discrimination parameters on a common scale.
se.bs	standard errors of difficulty parameters on a common scale.
tab	data frame containing item parameter names (Item), item parameter estimates of all the forms (e.g. T1, ..., T3), and item parameter estimates of all the forms converted in the scale of the base form (e.g. T3.as.T1).
varFull	list of covariance matrices of the item parameter estimates of every form.
partial	partial derivatives of equating coefficients with respect to the item parameters.
itmp	number of item parameters of the IRT model.
method	the equating method used.
basename	the name of the base form.
convergence	An integer code. 0 indicates successful convergence. Returned only with methods "irf", "trf" and "lik".

Author(s)

Michela Battauz, Waldir Leoncio [ctb]

References

Battauz, M. (2017). Multiple equating of separate IRT calibrations. Psychometrika, 82, 610–636.

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.

See Also

score.mlteqc, modIRT

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)

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