SampleItemsToHitTarget: Function to find a set of items within a test with given...

In CambridgeAssessmentResearch/KernEqWPS: Kernel Equating Without Pre-Smoothing

Function to find a set of items within a test with given available maximum score

Description

This function finds a random selection of indices within a matrix of items scores so that the sum of the maximum scores available on these items meets a predefined total. This is done using brute computing power to solve an extremely simple version of the famous Knapsack problem where all the values we need to consider (the maximum item scores) are (fairly) small integers. The function will print the number of selected items with each number of marks in the chosen solution.

Usage

SampleItemsToHitTarget(itemat, targtot, chooseclosestproportional = TRUE)

Arguments

itemat	Matrix of item scores.
targtot	The target sum of maximum scores on selected items.
chooseclosestproportional	Logical value indicating whether the proportion of items with each number of available marks be chosen so as to match the proportions for the overall test as closely as possible (default=TRUE).

Value

The function returns a vector denoting which items should be included.

Examples

library(KernEqWPS)
summary(mathsdata)
maxes=apply(mathsdata,2,max,na.rm=TRUE)
sum(maxes)
#make form X with 50 marks
itesX=SampleItemsToHitTarget(as.matrix(mathsdata),50)
formX=mathsdata[,itesX]
#note difference in selected item totals if we set chooseclosestproportional=FALSE
SampleItemsToHitTarget(as.matrix(mathsdata),50,chooseclosestproportional=FALSE)
#make form Y with 50 marks from the remainder
remain=mathsdata[,-itesX]
itesY=SampleItemsToHitTarget(as.matrix(remain),50)
formY=remain[,itesY]
#make form A with 10 marks from the remainder
remain=remain[,-itesY]
itesA=SampleItemsToHitTarget(as.matrix(remain),10)
formA=remain[,itesA]

length(itesX)
length(itesY)
length(itesA)

#check
x=rowSums(formX)
y=rowSums(formY)
a=rowSums(formA)
summary(x)
summary(y)
summary(a)
cor(cbind(x,y,a))

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