SEED | R Documentation |
This function calculates the standard error of equating diference (SEED) as described in Von Davier et al. (2004).
SEED(eq1, eq2)
eq1 |
An object of class |
eq2 |
An object of class |
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)={Var(\hat{e}_Y(x)-\widehat{Lin}_Y(x))}^{1/2}
to decide between \hat{e}_Y(x) and \widehat{Lin}_Y(x).
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
Jorge Gonzalez jorge.gonzalez@mat.uc.cl
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.
ker.eq
#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)
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