convert function

Item Parameters Conversion

Converts item and person parameters using equating coefficients.

convert(A, B, coef = NULL, person.par = NULL)

Arguments

• A: equating coefficient A.
• B: equating coefficient B.
• coef: vector of item parameters return by function modIRT.
• person.par: vector of person parameters estimates.

Details

Difficulty parameters $b$ are converted using transformation $b*A+B$; discrimination parameters $a$ are converted using transformation $a/A$; guessing parameters c are not transformed.

Person parameters $\theta$ are converted using transformation $\theta*A+B$.

Returns

A list with components - coef: vector of item parameters transformed.

• person.par: vector of person parameters transformed

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, 3rd ed., New York: Springer

Author(s)

Michela Battauz

See Also

itm, modIRT

Examples

# conversion using direct coefficients
# 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(mod1 = mod3pl[1], mod2 = mod3pl[2], method = "Stocking-Lord")
convert(A = l12$A, B = l12$B, coef = coef(mod3pl$test1))
# the conversion of item parameters is obtained also using
itm(l12)

# conversion using bisector coefficients
# 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)
# 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)
eqc14<-eqc(allec, link = "test1.test4", path = "bisector")
convert(A = eqc14$A, B = eqc14$B, coef = coef(mod2pl$test1), person.par = seq(-3, 3, 0.5))