direc: Direct Equating Coefficients

In equateIRT: IRT Equating Methods

Direct Equating Coefficients

Description

Calculates direct equating coefficients and standard errors using IRT methods.

Usage

direc(mods, which, mod1, mod2, method = "mean-mean", suff1 = ".1", suff2 = ".2",
   D = 1, quadrature = TRUE, nq = 30, items.select = NULL)

Arguments

mods	an object of the class modIRT containing item parameter coefficients and their covariance matrix of the forms to be equated.
which	which forms to equate. Can be specified by name or number.
mod1	deprecated; please use mods instead. An object of the class modIRT containing item parameter coefficients and their covariance matrix of the first form.
mod2	deprecated; please use mods instead. An object of the class modIRT containing item parameter coefficients and their covariance matrix of the second form.
method	the equating method to be used. This should be one of "mean-mean", "mean-gmean", "mean-sigma", "Haebara" or "Stocking-Lord".
suff1	suffix to identify the first form to be equated.
suff2	suffix to identify the second form to be equated.
D	constant D of the IRT model used to estimate item parameters. See below for more details.
quadrature	logical; if TRUE the Gauss-Hermite quadrature is used to approximate the integral in the function that is minimized in the Haebara and Stocking-Lord methods. If FALSE the integral is replaced with a sum over 40 equally spaced values ranging from -4 to 4 with an increment of 0.05 and weights equal to one for all values.
nq	number of quadrature points used for the Gauss-Hermite quadrature if quadrature is TRUE.
items.select	optional character vector including the names of the items to use for equating.

Details

Equating coefficients perform the conversion from the scale of the first form to the scale of the second form.

In the three-parameter logistic model the probability of a positive response on item i is

π_i = c_i + (1 - c_i) * exp{D a_i (θ - b_i)} / [1 + exp{D a_i (θ - b_i)}],

where a_i is the item discrimination parameter, b_i is the item difficulty parameter, c_i is the item guessing parameter and θ is the latent ability. The constant D can be specified using argument D of the direc function. The two-parameter logistic model can be obtained by setting c_i equal to zero, the one-parameter logistic model can be obtained by setting c_i equal to zero and a_i costant across items, while the Rasch model can be obtained by setting c_i equal to zero and a_i equal to 1.

The type of IRT model does not need to be specified as it is obtained from arguments mod1 and mod2.

Value

An object of class eqc with components

tab1	item parameters of the first form.
tab2	item parameters of the second form.
tab	Data frame containing item names (Item), item parameters of the first form (e.g. test1), item parameters of the second form (e.g. test2), and item parameters of the first form converted in the scale of the second form (e.g. test1.as.test2).
var12	covariance matrix of item parameters of the first and the second form (only items used for equating).
varFull	list of covariance matrices of the item parameters (one matrix for each form)
partial	partial derivatives of equating coefficients A and B with respect to item parameters.
A	equating coefficient A.
B	equating coefficient B.
varAB	covariance matrix of the equating coefficients.
commonitem	list of length 2 containing the names of common item parameters and the names of the common items selected for equating.
suffixes	suffixes used to identify the forms.
ni	number of common items.
nis	number of common items selected for equating.
forms	names of equated forms.
method	the equating method used.
itmp	number of item parameters of the IRT model.

Author(s)

Michela Battauz

References

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

Kolen, M.J. and Brennan, R.L. (2014). Test equating, scaling, and linking: methods and practices, 3nd 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. (2001). Standard Errors of Item Response Theory Equating/Linking by Response Function Methods. Applied Psychological Measurement, 25, 53–67.

See Also

eqc, itm, modIRT, summary.eqc

Examples

# three-parameter logistic model
# direct equating coefficients between forms 1 and 2 using the Stocking-Lord method
data(est3pl)
test <- paste("test", 1:5, sep = "")
mod3pl <- modIRT(coef = est3pl$coef, var = est3pl$var, names = test, display = FALSE)
l12 <- direc(mods = mod3pl, which = c("test1", "test2"), method = "Stocking-Lord")
summary(l12)

# two-parameter logistic model
# direct equating coefficients between forms 1 and 5 using the Haebara method
data(est2pl)
test <- paste("test", 1:5, sep = "")
mod2pl <- modIRT(coef = est2pl$coef, var = est2pl$var, names = test, display = FALSE)
l15 <- direc(mods = mod2pl, which = c(1,5), method = "Haebara")
summary(l15)

# Rasch model
# direct equating coefficients between forms 5 and 4 using the mean-mean method
data(estrasch)
test <- paste("test", 1:5, sep = "")
modrasch <- modIRT(coef = estrasch$coef, var = estrasch$var, names = test, 
	display = FALSE)
l54 <- direc(mods = modrasch, which = c(5,4), method = "mean-mean")
summary(l54)

equateIRT documentation built on Aug. 8, 2022, 5:08 p.m.