fabCI (version 0.2)

multifabCIhom: Multigroup FAB t-intervals for the homoscedastic model

Description

Computation of 1-alpha FAB t-intervals for homoscedastic multigroup data.

Usage

multifabCIhom(y, g, alpha = 0.05, prop = 0.5)

Arguments

y

a numeric vector of data

g

a group membership vector, of the same length as y

alpha

the type I error rate, so 1-alpha is the coverage rate

prop

the proportion of groups to obtain the sample variance estimate

Author

Chaoyu Yu

Details

For each group j, this function computes an estimate of the parameters in a hierarchical model for means using data from other groups, and uses this information to construct a FAB t-interval for group j. These intervals have 1-alpha frequentist coverage, assuming within-group normality and that the within group variance is the same across groups.

Examples

## -- simulate the data
mu = 0; sigma2 = 10; tau2 = 1; p =100; 
theta = rnorm(p,mu,sqrt(tau2))
ns = round(runif(p,2,18))
Y=c()
for(i in 1:p){
 d2 = rnorm(ns[i],theta[i],sqrt(sigma2))
 d1 = rep(i,ns[i])
 d = cbind(d1,d2)
 Y = rbind(Y,d)}
y = Y[,2]
g = Y[,1]

## -- FAB t-intervals
FCI = multifabCIhom(y,g)  

## -- UMAU t-intervals 
ybar<-tapply(y,g,mean) ; ssd<-tapply(y,g,sd) ; n<-table(g) 
qtn<-cbind( qt(.025,n-1),  qt(.975,n-1) ) 
UCI<-sweep(sweep(qtn,1,ssd/sqrt(n),"*"),1,ybar,"+") 

mean( (UCI[,2]-UCI[,1])/(FCI[,2]-FCI[,1]) , na.rm=TRUE)