FindAVDBandwidth: Method to estimate appropriate bandwidth using the Andersson...

In CambridgeAssessmentResearch/KernEqWPS: Kernel Equating Without Pre-Smoothing

Method to estimate appropriate bandwidth using the Andersson and von Davier plug-in formula.

Description

The formula for suggesting an appropriate bandwidth is very simple and can easily be seen by looking at the function code.

Usage

FindAVDBandwidth(scores, fX)

Arguments

scores	Vector of possible scores.
fX	Number of people achieving each score. Weighted numbers are also acceptable but must add up to the overall sample size. Must be same length as scores.

Value

The function returns a single value representing the suggested bandwidth.

References

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

Examples

#EXAMPLE OF FINDING BANDWIDTH TO EQUATE FIRST AND SECOND HALVES OF MATHS TEST
x1=rowSums(mathsdata[,1:62])
y1=rowSums(mathsdata[,63:124])
summary(x1)
summary(y1)
tabx1=table(x1)
taby1=table(y1)

RoughHx=FindAVDBandwidth(as.numeric(names(tabx1)),as.vector(tabx1))
RoughHx

RoughHy=FindAVDBandwidth(as.numeric(names(taby1)),as.vector(taby1))
RoughHy

eq1=KernelEquateFromScoresEG(x1,y1,hX=RoughHx,hY=RoughHy)
plot(sort(unique(x1)),eq1$yx,type='l')

#prove that above code is the same as the default method of equating
eq2=KernelEquateFromScoresEG(x1,y1)
lines(sort(unique(x1)),eq2$yx,lty=2,col="purple")

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