KernelChainedEquate: Apply kernel chained equating

In CambridgeAssessmentResearch/KernEqWPS: Kernel Equating Without Pre-Smoothing

Apply kernel chained equating

Description

Chained equating via an anchor test is done by successively applying the KernelEquateFromScoresEG function between.

Usage

KernelChainedEquate(dx, dy, hX = NA, hY = NA, hA = NA)

Arguments

dx	Data frame with variables "x" and "a" representing scores for individual candidates on form X and on the anchor test.
dy	Data frame with variables "y" and "a" representing scores for individual candidates on form Y and on the anchor test.
hX	Bandwidth for form X. By default a plug-in estimator from Andersson and von Davier (2014) is used.
hY	Bandwidth for form Y. By default a plug-in estimator from Andersson and von Davier (2014) is used.
hA	Bandwidth for the anchor form. By default a plug-in estimator from Andersson and von Davier (2014) is used which will differ across populations. If a value is specified then the same bandwidth will be used in both populations.

Value

The function returns a list with the following elements:

chainedFunc

A function that translates any vector of scores on form X into equivalent scores on form Y.

EqTable

A data frame combining the sorted unique scores on form X in the data and their equated values on form Y (chained kernel).

References

Andersson, B., & von Davier, A. A. (2014). Improving the bandwidth selection in kernel equating. Journal of Educational Measurement, 51(3), 223-238.

Examples

#Simulate two data sets with roughly equivalent relationship to underlying "true" scores but a difference in means
n1=8000
n2=5500
t1=rnorm(n1,0.5,1)
t2=rnorm(n2,0,1)
x=round(pmin(100,pmax(0,50+20*(0.9*t1+rnorm(n1,0,sqrt(1-0.9^2))))))
a1=round(pmin(20,pmax(0,10+4*(0.7*t1+rnorm(n1,0,sqrt(1-0.7^2))))))
cor(cbind(x,t1,a1))
y=round(pmin(100,pmax(0,50+20*(0.9*t2+rnorm(n2,0,sqrt(1-0.9^2))))))
a2=round(pmin(20,pmax(0,10+4*(0.7*t2+rnorm(n2,0,sqrt(1-0.7^2))))))
cor(cbind(y,t2,a2))
KernelChainedEquate(data.frame(x=x,a=a1),data.frame(y=y,a=a2))

CambridgeAssessmentResearch/KernEqWPS documentation built on Feb. 23, 2024, 9:34 p.m.