# Standard error of equating difference This function calculates the standard error of equating diference (SEED) as described in Von Davier et al. (2004). ```r SEED(eq1, eq2) ``` ## Arguments - `eq1`: An object of class `ker.eq` which contains one of the two estimated equated functions to be used for the SEED. - `eq2`: An object of class `ker.eq` which contains one of the two estimated equated functions to be used for the SEED. ## Details The SEED can be used as a measure to choose whether to support or not a certain equating function on another another one. For instance, when $h_X$ and $h_Y$ tends to infinity, then the (gaussian kernel) $\hat{e}_Y(x)$ equating function tends to the linear equating function (see Theorem 4.5 in Von Davier et al, 2004 for more details). Thus, one can calculate the measure $$ SEED_Y(x)=\sqrt{Var(\hat{e}_Y(x)-\widehat{Lin}_Y(x))}SEED_Y(x)={Var(\hat{e}_Y(x)-\widehat{Lin}_Y(x))}^{1/2} $$ to decide between $\hat{e}_Y(x)$ and $\widehat{Lin}_Y(x)$. ## Returns A two column matrix with the values of `SEEYx` for each `x` in the first column and the values of `SEEXy` for each `y` in the second column ## References Gonzalez, J. (2014). SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating. **Journal of Statistical Software, 59(7),** 1-30. Von Davier, A., Holland, P., and Thayer, D. (2004). **The Kernel Method of Test Equating**. New York, NY: Springer-Verlag. ## Author(s) Jorge Gonzalez jorge.gonzalez@mat.uc.cl ## See Also `ker.eq` ## Examples ```r #Example: Figure7.7 in Von Davier et al, (2004) data(Math20EG) mod.gauss<-ker.eq(scores=Math20EG,kert="gauss", hx = NULL, hy = NULL,degree=c(2, 3),design="EG") mod.linear<-ker.eq(scores=Math20EG,kert="gauss", hx = 20, hy = 20,degree=c(2, 3),design="EG") Rx<-mod.gauss$eqYx-mod.linear$eqYx seed<-SEED(mod.gauss,mod.linear)$SEEDYx plot(0:20,Rx,ylim=c(-0.8,0.8),pch=15) abline(h=0) points(0:20,2*seed,pch=0) points(0:20,-2*seed,pch=0) #Example Figure 10.4 in Von Davier (2011) mod.unif<-ker.eq(scores=Math20EG,kert="unif", hx = NULL, hy = NULL,degree=c(2, 3),design="EG") mod.logis<-ker.eq(scores=Math20EG,kert="logis", hx = NULL, hy = NULL,degree=c(2, 3),design="EG") Rx1<-mod.logis$eqYx-mod.gauss$eqYx Rx2<-mod.unif$eqYx-mod.gauss$eqYx seed1<-SEED(mod.logis,mod.gauss)$SEEDYx seed2<-SEED(mod.unif,mod.gauss)$SEEDYx plot(0:20,Rx1,ylim=c(-0.2,0.2),pch=15,main="LK vs GK",ylab="",xlab="Scores") abline(h=0) points(0:20,2*seed1,pch=0) points(0:20,-2*seed1,pch=0) plot(0:20,Rx2,ylim=c(-0.2,0.2),pch=15,main="UK vs GK",ylab="",xlab="Scores") abline(h=0) points(0:20,2*seed2,pch=0) points(0:20,-2*seed2,pch=0) ```

SEED function