The R Package equateMultiple: A Tutorial"

In equateMultiple: Equating of Multiple Forms

Functionalities

The equateMultiple package computes:

• Equating coefficients between multiple forms.
• Synthetic item parameters (sort of mean of the item parameter estimates from different forms).
• Standard errors of the equating coefficients and the synthetic item parameters.

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 ltm

library("ltm")
m1 <- ltm(data2pl[[1]] ~ z1)
m2 <- ltm(data2pl[[2]] ~ z1)
m3 <- ltm(data2pl[[3]] ~ z1)
m4 <- ltm(data2pl[[4]] ~ z1)
m5 <- ltm(data2pl[[5]] ~ z1)

Extract the item parameter estimates and the covariance matrices

estm1 <- import.ltm(m1, display = FALSE)
estm2 <- import.ltm(m2, display = FALSE)
estm3 <- import.ltm(m3, display = FALSE)
estm4 <- import.ltm(m4, display = FALSE)
estm5 <- import.ltm(m5, display = FALSE)
estm1$coef[1:3, ]
estm1$var[1:3, 1:3]

Create a list of coefficients and covariance matrices

estc <- list(estm1$coef, estm2$coef, estm3$coef, estm4$coef, estm5$coef)
estv <- list(estm1$var, estm2$var, estm3$var, estm4$var, estm5$var)
test <- paste("test", 1:5, sep = "")

Create an object of class modIRT

mods <- modIRT(coef = estc, var = estv, names = test, display = FALSE)
coef(mods$test1)[1:5]

The linkage plan

lplan<-linkp(coef = estc)
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, base = 1, method = "mean-mean")
summary(eqMM)

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

eqMGM <- multiec(mods = mods, base = 1, method = "mean-gmean")
summary(eqMGM)

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

eqIRF<-multiec(mods = mods, base = 1, 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, base = 1, method = "mean-gmean", se = FALSE)
eqIRF<-multiec(mods = mods, base = 1, method = "irf", start = eqMGM)
summary(eqIRF)

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

eqTRF<-multiec(mods = mods, base = 1, method = "trf")
summary(eqTRF)

Synthetic item parameters

The synthetic item parameters and their standard errors can be extracted as follows (using the multiple item response function method).

eqIRF$as
eqIRF$bs
eqIRF$se.as
eqIRF$se.bs

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. 17, 2022, 5:08 p.m.