MDIAweights: Function to find weights that can be applied to a data set so...

In CambridgeAssessmentResearch/KernEqWPS: Kernel Equating Without Pre-Smoothing

Function to find weights that can be applied to a data set so that means of columns match assigned targets.

Description

Method is from Haberman, 1984.

Usage

MDIAweights(datamatrix, targets, tol = 1e-06, maxiter = 100, starttheta = NA)

Arguments

datamatrix	Numeric matrix (or something that can be quickly converted into one e.g. a data frame).
targets	Vector indicating the desired mean value for each column after weighting.
tol	Numeric input relating to required proximity of weighted means to target means in order for algorithm to be considered converged (default 1e-6).
maxiter	Numeric input denoting the maximum number of iterations that will be applied to find the weights (default 100).
starttheta	Starting parameter vector to begin iterative process (by default a vector of zeros).

Value

The function returns a list with the following elements:

wts

A vector of weights.

iter

The number of iterations taken to converge. If this is equal to maxiter then convergenece may not have been achieved.

FinalWeightedMeans

The weighted means on each column in the data matrix.

theta

Parameters used for weighting.

References

Haberman, S. J. (1984). Adjustment by minimum discriminant information. The Annals of Statistics, 12(3), 971-988.

Examples

#try weighting one population (with a logistic distribution)
#to match E(x), E(x^2),E(x^3),E(x^4), E(x^5), E(x^6) and E(x^7) of another (with a normal distribution)
x1=rnorm(50000,100,30)
summary(x1)
x2=rlogis(50000,120,25)
summary(x2)
MDIAx2=MDIAweights(cbind(x2,x2^2,x2^3,x2^4,x2^5,x2^6,x2^7),c(mean(x1),mean(x1^2),mean(x1^3),mean(x1^4),mean(x1^5),mean(x1^6),mean(x1^7)))
MDIAx2$iter
sum(MDIAx2$wts)
summary(MDIAx2$wts)
summary(MDIAx2$wts/mean(MDIAx2$wts))
c(mean(x1),sum(MDIAx2$wts*x2))
c(mean(x1^2),sum(MDIAx2$wts*x2^2))
c(mean(x1^3),sum(MDIAx2$wts*x2^3))
c(mean(x1^4),sum(MDIAx2$wts*x2^4))
c(mean(x1^5),sum(MDIAx2$wts*x2^5))
c(mean(x1^6),sum(MDIAx2$wts*x2^6))
c(mean(x1^7),sum(MDIAx2$wts*x2^7))
#see if it worked visually
dat1=data.frame(x=c(x1,x2)
	,pop=as.factor(c(rep(1,length(x1)),rep(2,length(x2))))
	,wts=c(rep(1/length(x1),length(x1)),MDIAx2$wts))
library(ggplot2)
ggplot(data=dat1,aes(x=x,fill=pop))+geom_density(alpha=0.5)#unweighted
ggplot(data=dat1,aes(x=x,fill=pop,weight=wts))+geom_density(alpha=0.5)#weighted

CambridgeAssessmentResearch/KernEqWPS documentation built on July 6, 2024, 5:55 a.m.