PEN1: Calulate PEN1 criterion for match of continuized and original...

In CambridgeAssessmentResearch/KernEqWPS: Kernel Equating Without Pre-Smoothing

Calulate PEN1 criterion for match of continuized and original score distributions

Description

This function calculates the penalty term for a given bandwidth against a given distribution. The definition of PEN1 can be found in Liang and von Davier (2014). The values of PEN1 are not of much interest in their own right. Finding the bandwidth that minimises this penalty (using optPEN1) can potentially be useful as identifying a plausible bandwidth to use in subsequent kernel equating.

Usage

PEN1(h, scores, fX)

Arguments

h	Bandwith being considered.
scores	Vector of possible scores.
fX	Number of people achieving each score (weighted numbers, probabilities or proportions also acceptable). Must be same length as scores.

Value

The function returns the value of PEN1 for the given bandwidth.

References

Liang, T., & von Davier, A. A. (2014). Cross-validation: An alternative bandwidth-selection method in kernel equating. Applied Psychological Measurement, 38(4), 281-295.

Examples

x1=rowSums(mathsdata)#make some scores
tab=tabulate(x1+1)#count how many people got each integer score
cbind(0:max(x1),tab)#look at the table
PEN1(0.5,0:max(x1),tab)#calculate PEN1 for a given bandwidth
optPEN1(0:max(x1),tab)#optimise PEN1

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