# Chain Equating Coefficients Calculates chain (indirect) equating coefficients and standard errors using IRT methods. ```r 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. ## Returns 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. ## 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 ## Author(s) Michela Battauz ## See Also `alldirec`, `eqc`, `itm`, `summary.ceqc`, `summary.ceqclist` ## 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) 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) ```

chainec function