The R Package equateMultiple: A Tutorial"

In equateMultiple: Equating of Multiple Forms

Functionalities

The equateMultiple package computes:

• Equating coefficients between multiple forms.
• Item parameter estimates on a common scale (based on the item parameter estimates from different forms).
• Standard errors of the equating coefficients and the item parameter estimates on a common scale.

Data preparation

Data preparation follows the same steps of the equateIRT package.

Load the package equateMultiple and the data

library("equateMultiple")
data("data2pl", package = "equateIRT")

Estimate a two parameter logistic model for 5 data sets with the R package mirt

library("mirt")
m1 <- mirt(data2pl[[1]], SE = TRUE)
m2 <- mirt(data2pl[[2]], SE = TRUE)
m3 <- mirt(data2pl[[3]], SE = TRUE)
m4 <- mirt(data2pl[[4]], SE = TRUE)
m5 <- mirt(data2pl[[5]], SE = TRUE)

Create an object of class modIRT

mlist<- list(m1, m2, m3, m4, m5)
test <- paste("test", 1:5, sep = "")
mods <- modIRT(est.mods = mlist, names = test, display = FALSE)

The linkage plan

lplan<-linkp(mods = mods)
lplan

Multiple equating coefficients

Estimation of the equating coefficients using the multiple mean-mean method. Form 1 is the base form.

eqMM <- multiec(mods = mods, method = "mean-mean")
summary(eqMM)

Estimation of the equating coefficients using the multiple mean-geometric mean method.

eqMGM <- multiec(mods = mods, method = "mean-gmean")
summary(eqMGM)

Estimation of the equating coefficients using the multiple item response function method.

eqIRF<-multiec(mods = mods, method = "irf")
summary(eqIRF)

Estimation of the equating coefficients using the multiple item response function method. The initial values are the estimates obtained with the multiple mean-geometric mean method.

eqMGM <- multiec(mods = mods, method = "mean-gmean", se = FALSE)
eqIRF<-multiec(mods = mods, method = "irf", start = eqMGM)
summary(eqIRF)

Estimation of the equating coefficients using the multiple test response function method.

eqTRF<-multiec(mods = mods, method = "trf")
summary(eqTRF)

Estimation of the equating coefficients using the likelihood-based method.

eqLIK <- multiec(mods = mods, method = "lik")
summary(eqLIK)

It is possible to change the base form, that is the form whose item parameter estimates are left unchanged. All other item parameter estimates are converted to the scale of the base form.

eqLIK <- multiec(mods = mods, method = "lik", base = 5)
summary(eqLIK)

Item parameter estimates on a common scale

The package computes estimates of the item parameters on the scale of the base form, obtained using all estimates available for the same item across all the forms. Their standard errors are also computed. They can be extracted as follows (using the multiple item response function method).

item.common(eqIRF)

Equated scores

Equated scores with the true score equating method

scTSE<-score(eqIRF)
round(scTSE,3)

Equated scores with the observed score equating method, avoiding computation of standard errors

scOSE<-score(eqIRF, method = "OSE", se = FALSE)
round(scOSE,3)

equateMultiple documentation built on Oct. 15, 2024, 5:06 p.m.