EquateNN: Experimental technique to equate using a pre-trained neural...

In CambridgeAssessmentResearch/KernEqWPS: Kernel Equating Without Pre-Smoothing

Experimental technique to equate using a pre-trained neural network

Description

This function is designed to work in the NEAT equating design. It assumes all scores are integers and that it is an EXTERNAL anchor test.

Usage

EquateNN(
  dx,
  dy,
  anchortargettable,
  maxx = NA,
  maxy = NA,
  maxa = NA,
  WeightsList = EquateNNWeights
)

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.
anchortargettable	Table giving distribution of anchor test scores in the target population.
maxx	Maximum score available on form X (calculated from the data by default).
maxy	Maximum score available on form Y (calculated from the data by default).
maxa	Maximum score available on anchor test (calculated from the data by default).
WeightsList	A list of neural network parameters used in calculations. Changing this from the default value is not recommended.

Value

The function returns a list with two elements.

CNNEqFunc

A function that translates any vector of scores on form X (from 0-maxx) into equivalent scores on form Y.

EqTable

A data frame combining scores from 0-maxx in the data and their equated values on form Y.

Examples

#example where we simulate scores on two parallel tests in two populations using classical test theory
n1=400
n2=300
t1=rnorm(n1,0.5,1)
t2=rnorm(n2,0,1)
dx1=data.frame(x=round(pmin(100,pmax(0,50+20*(0.9*t1+rnorm(n1,0,sqrt(1-0.9^2)))))),
	a=round(pmin(20,pmax(0,10+4*(0.7*t1+rnorm(n1,0,sqrt(1-0.7^2)))))))
dy1=data.frame(y=round(pmin(100,pmax(0,50+20*(0.9*t2+rnorm(n2,0,sqrt(1-0.9^2))))))
	,a=round(pmin(20,pmax(0,10+4*(0.7*t2+rnorm(n2,0,sqrt(1-0.7^2)))))))
NNeq1=EquateNN(dx1,dy1,table(dy1$a))
chainedeq1=KernelChainedEquate(dx1, dy1)$EqTable
pseeq1=PSEObservedEquate(dx1, dy1, target = "y")$EqTable
plot(chainedeq1$x,chainedeq1$equiyx,type='l')#chained equating function
lines(pseeq1$x,pseeq1$equiyx,lty=3,col="red")#PSE estimated equating function
lines(NNeq1$EqTable$x,NNeq1$EqTable$yx,lty=2)#NN estimated equating function
lines(0:100,0:100,col="blue",lty=3,lwd=4)#true equating function (identity as set up to be parallel tests)

#example using some real data (but no criterion equate to compare to)
dx2=data.frame(x=rowSums(mathsdata[1:250,1:35]),a=rowSums(mathsdata[1:250,41:50]))
summary(dx2)
dy2=data.frame(y=rowSums(mathsdata[251:500,51:90]),a=rowSums(mathsdata[251:500,41:50]))
summary(dy2)
NNeq2=EquateNN(dx2,dy2,table(dy1$a))
chainedeq=KernelChainedEquate(dx2, dy2)$EqTable
plot(chainedeq$x,chainedeq$equiyx,type='l')#chained equating function
lines(NNeq2$EqTable$x,NNeq2$EqTable$yx,lty=2)#NN estimated equating function

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