equateMultiple (version 1.1.1)

multiec: 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)

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".

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.

Author

Michela Battauz, Waldir Leoncio [ctb]

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").

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)