# 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. ```r 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 ```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") 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) ```

alldirec function