SEED {SNSequate}

Standard error of equating difference

Description

This function calculates the standard error of equating diference (SEED) as described in Von Davier et al. (2004).

Usage

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))}

to decide between \hat{e}_Y(x) and \widehat{Lin}_Y(x).

Value

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

Author(s)

Jorge Gonzalez [e-mail]

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.

See Also

ker.eq

Examples

#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)