LevineObservedEquate: Apply Levine Observed Score equating to data from a NEAT...

In CambridgeAssessmentResearch/KernEqWPS: Kernel Equating Without Pre-Smoothing

Apply Levine Observed Score equating to data from a NEAT design.

Description

Apply Levine Observed Score equating to data from a NEAT design.

Usage

LevineObservedEquate(dx, dy, ws = NA, internal = FALSE)

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.
ws	Vector of two elements denoting the relative weights of the dx population and the dy population in the synthetic population where equating takes place.
internal	Logical input denoting whether the anchor test in internal or external (default) to the tests being equated.

Value

The function returns a list with the following elements:

lys

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.

muSx

Estimated mean on form X within the synthetic population.

sigmaSx

Estimated standard deviation on form X within the synthetic population.

muSy

Estimated mean on form Y within the synthetic population.

sigmaSy

Estimated standard deviation on form Y within the synthetic population.

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))
LevineObservedEquate(data.frame(x=x,a=a1),data.frame(y=y,a=a2))
#equated scores should be close to identity

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