bisectorec function

Bisector Equating Coefficients

Calculates average equating coefficients using the bisector method and standard errors given a set of direct and chain equating coefficients.

bisectorec(ecall, mods = NULL, weighted = TRUE, unweighted = TRUE)

Arguments

• ecall: list of objects of class eqc or ceqc

  returned by functions direc and chainec.

• mods: an object of class modIRT containing item parameter coefficients and their covariance matrix of the forms to be equated. From version 2.0 it can be NULL

• weighted: logical; if TRUE weighted bisector coefficients are computed.

• unweighted: logical; if TRUE unweighted bisector coefficients are computed.

Returns

An object of class meqc with components - coef: data frame containing link, path, coefficient A, coefficient B, standard error of coefficient A (seA), standard error of coefficient B (seB) and weights of direct, chain and bisector equating coefficients.

• method: the equating method used.

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.

Holland, P.W. and Strawderman, W.E. (2011). How to average equating functions if you must. In A.A. von Davier (Ed.), Statistical models for test equating, scaling, and linking (pp. 89--107). New York: Springer.

Author(s)

Michela Battauz

See Also

chainec, convert, direc, eqc, summary.meqc

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)
# compute chain equating coefficients for path 1,5,4
pth2 <- c(paste("test", c(1,5,4), sep = ""))
chainec2 <- chainec(direclist = direclist2pl, pths = pth2)
# create a list of objects of class ceqc
ecall <- c(chainec1, chainec2)
# compute bisector and weighted bisector coefficients
allec <- bisectorec(ecall = ecall, weighted = TRUE, unweighted = TRUE)
summary(allec)
## 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 chain equating coefficients for path 1,2,3,4,5
pth3 <- paste("test", 1:5, sep = "")
chainec3 <- chainec(direclist = direclist3pl, pths = pth3)
# create a list of objects of class eqc or ceqc
ecall <- c(chainec3, direclist3pl["test1.test5"])
# compute bisector and weighted bisector coefficients
allec <- bisectorec(ecall = ecall, weighted = TRUE, unweighted = TRUE)
summary(allec)

# 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 for path 1,2,3,4
pth1 <- paste("test", 1:4, sep = "")
chainec1 <- chainec(direclist = direclist2pl, pths = pth1)
# compute chain equating coefficients for path 1,5,4
pth2 <- c(paste("test", c(1,5,4), sep = ""))
chainec2 <- chainec(direclist = direclist2pl, pths = pth2)
# compute chain equating coefficients for path 1,2,3,4,5
pth3 <- paste("test", 1:5, sep = "")
chainec3 <- chainec(direclist = direclist2pl, pths = pth3)
# create a list of objects of class eqc or ceqc
ecall <- c(chainec1, chainec2, chainec3, direclist2pl["test1.test5"])
# compute bisector and weighted bisector coefficients
allec <- bisectorec(ecall = ecall, weighted = TRUE, unweighted = TRUE)
summary(allec)

# 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 for path 1,2,3,4
pth1 <- paste("test", 1:4, sep = "")
chainec1 <- chainec(direclist = direclistrasch, pths = pth1)
# compute chain equating coefficients for path 1,5,4
pth2 <- c(paste("test", c(1,5,4), sep = ""))
chainec2 <- chainec(direclist = direclistrasch, pths = pth2)
# create a list of objects of class eqc or ceqc
ecall <- c(chainec1, chainec2)
# compute bisector and weighted bisector coefficients
allec <- bisectorec(ecall = ecall, weighted = TRUE, unweighted = TRUE)
summary(allec)