# Bisector Equating Coefficients Calculates average equating coefficients using the bisector method and standard errors given a set of direct and chain equating coefficients. ```r 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 ```r # 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) ```

bisectorec function