chainec {equateIRT}

Chain Equating Coefficients

Description

Calculates chain (indirect) equating coefficients and standard errors using IRT methods.

Usage

chainec(r = NULL, direclist, f1 = NULL, f2 = NULL, pths = NULL)

Arguments

r

length of the chain, that is the number of forms used for equating including extremes. It should be at least 3. It does not need to be specified if argument pths is not NULL.

direclist

an object of the class eqclist return by function alldirec containing direct equating coefficients between pairs of forms.

f1

the name of the first form of the chain.

f2

the name of the last form of the chain.

pths

vector, matrix or data frame containing the path used for equating. The number of columns is equal to r and the number of rows is equal to the equatings that have to be performed. If NULL all the chain equating coefficients of length r will be computed.

Details

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

Value

An object of class ceqclist consisting in a list with length equal to the number of chain equating coefficients computed. Each component of the list is an object of class ceqc with components

tab1

item parameters of the first form.

tab2

item parameters of the last form.

tab

Data frame containing item names (Item), item parameters of the first form (e.g. test1), item parameters of the last form (e.g. test3), and item parameters of the first form converted in the scale of the last form (e.g. test1.as.test3).

varAll

covariance matrix of item parameters of all forms used in the chain.

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 r-1 containing the names of common item parameters between adjacent forms.

ni

vector containing number of common items between pairs of adjacent forms.

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. (2013). IRT Test Equating in Complex Linkage Plans. Psychometrika, 78, 464–480.

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, 3rd ed., New York: Springer

See Also

alldirec, eqc, itm, summary.ceqc, summary.ceqclist

Examples

# the following code can be used to start from item response data

## Not run: 
library("mirt")
data("data2pl")

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)

mlist<- list(m1,m2,m3,m4,m5)
test <- paste("test", 1:5, sep = "")
mod2pl <- modIRT(est.mods = mlist, names = test, display = FALSE)

direclist2pl <- alldirec(mods = mod2pl, method = "Haebara")

# compute chain equating coefficients for path 1,2,3,4
pth1 <- paste("test", 1:4, sep = "")
chainec1 <- chainec(direclist = direclist2pl, pths = pth1)
summary(chainec1)

## End(Not run)

# ===========================================================================
# the following code uses item parameter estimates previously obtained

# three-parameter logistic model
# direct equating coefficients 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)
direclist3pl <- alldirec(mods = mod3pl, method = "Stocking-Lord")
# compute all chain equating coefficients of length 4
chainec4 <- chainec(r = 4, direclist = direclist3pl)
summary(chainec4)
summary(chainec4$test1.test2.test3.test4)
# compute all chain equating coefficients of length 4 
# where the first form is test1
chainec4.1 <- chainec(r = 4, direclist = direclist3pl, f1 = "test1")
summary(chainec4.1)
# compute all chain equating coefficients of length 4 
# where the first form is test1 and the last form is test4
chainec4.14 <- chainec(r = 4, direclist = direclist3pl, f1 = "test1", f2 = "test4")
summary(chainec4.14)


# two-parameter logistic model
# direct equating coefficients using the "Haebara" method
data(est2pl)
test<-paste("test", 1:5, sep = "")
mod2pl <- modIRT(coef = est2pl$coef, var = est2pl$var, names = test, display = FALSE)
direclist2pl <- alldirec(mods = mod2pl, method = "Haebara")
# compute chain equating coefficients of a given path
pth <- paste("test", c(1,5,4), sep = "")
chainec154 <- chainec(direclist = direclist2pl, pths = pth)
summary(chainec154)


# Rasch model
# direct equating coefficients 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)
direclistrasch <- alldirec(mods = modrasch, method = "mean-mean", all = TRUE)
# compute chain equating coefficients of two given paths
pth1 <- paste("test", 1:3, sep = "")
pth2 <- paste("test", c(1,5,4), sep = "")
pths <- rbind(pth1, pth2)
chainec1 <- chainec(direclist = direclistrasch, pths = pths)
summary(chainec1)