CircleArcTuckerEquate: Apply circle-arc method based on Tucker equating

In CambridgeAssessmentResearch/KernEqWPS: Kernel Equating Without Pre-Smoothing

Apply circle-arc method based on Tucker equating

Description

Circle-arc equating via an anchor test is done by using the Tucker method to estimate the means on each from in the synthetic population.

Usage

CircleArcTuckerEquate(dx, dy, ws = NA, maxX, maxY, minX = 0, minY = 0)

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.
maxX	Maximum score on form X (or upper point for circle arc method).
maxY	Maximum score on form Y (or upper point for circle arc method).
minX	Minimum score on form X (or lower point for circle arc method). Default of zero.
minY	Minimum score on form Y (or lower point for circle arc method). Default of zero.

Value

The function returns a list with the following elements:

yxFunc

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

EqTable

A data frame showing the equivalent score on form Y for every integer score between minX and maxxX on form X.

meanX

Estimated mean form X score in synthetic population.

meanY

Estimated mean form X score in synthetic population.

Examples

#demonstrate method on a 30 item test with an internal 5 item anchor
#define 30 rasch item difficulties as equally spread
itedifs=rep(seq(-2,2,length=5),6)

#simulate population one item scores (and then form scores)
n1=300
t1=rnorm(n1,0.5,1)
ites1=0+(plogis(t1%*%t(rep(1,30))-rep(1,length(t1))%*%t(itedifs))>matrix(runif(n1*30),nrow=n1))
scoresX1=rowSums(ites1[,1:30])
scoresA1=rowSums(ites1[,26:30])
#simulate parallel tests in population two
n2=3000
t2=rnorm(n2,0,1)
ites2=0+(plogis(t2%*%t(rep(1,30))-rep(1,length(t2))%*%t(itedifs))>matrix(runif(n2*30),nrow=n2))
scoresY2=rowSums(ites2[,1:30])
scoresA2=rowSums(ites2[,26:30])

circ_eq=CircleArcTuckerEquate(data.frame(x=scoresX1,a=scoresA1),data.frame(y=scoresY2,a=scoresA2),NA,30,30)
circ_eq

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