alldirec function

Direct Equating Coefficients Between All Pairs of a List of Forms

Calculates direct equating coefficients and standard errors using IRT methods between all pairs of a list of forms.

alldirec(mods, method = "mean-mean", all = FALSE, quadrature = TRUE, nq = 30, 
        direction = "both")

Arguments

• mods: an object of the class modIRT containing item parameter coefficients and their covariance matrix of the forms to be equated.
• method: the equating method to be used. This should be one of "mean-mean", "mean-gmean", "mean-sigma", "Haebara" or "Stocking-Lord".
• all: logical; if FALSE forms that do not have common items will not appear in the output.
• quadrature: logical; if TRUE the Gauss-Hermite quadrature is used to approximate the integral in the function that is minimized in the Haebara and Stocking-Lord methods. If FALSE the integral is replaced with a sum over 40 equally spaced values ranging from -4 to 4 with an increment of 0.05 and weights equal to one for all values.
• nq: number of quadrature points used for the Gauss-Hermite quadrature if quadrature is TRUE
• direction: a character string specifying the direction used to equate pair of forms. If "back" newer forms are equated to older forms, if "forward" older forms are equated to newer forms, if "both" (the default) equating is performed in both directions. Form A is considered to be newer than Form B if it is listed after Form B in mods.

Returns

An object of class eqclist consisting in a list with length equal to the number of pairs of forms equated. Each component of the list is an object of class eqc returned by function direc.

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

Ogasawara, H. (2000). Asymptotic standard errors of IRT equating coefficients using moments. Economic Review (Otaru University of Commerce), 51 , 1--23.

Ogasawara, H. (2001). Standard Errors of Item Response Theory Equating/Linking by Response Function Methods. Applied Psychological Measurement, 25 , 53--67.

Author(s)

Michela Battauz

See Also

direc, eqc, itm, modIRT, summary.eqclist

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")
summary(direclist2pl)
summary(direclist2pl$test2.test1)
## 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")
summary(direclist3pl)
summary(direclist3pl$test1.test2)

# 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")
summary(direclist2pl)
summary(direclist2pl$test1.test5)

# 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)
summary(direclistrasch)
summary(direclistrasch$test5.test4)