Question

Give an example in R language about construct simultaneous confidence intervals based on T² and Bonferroni correction.

Answer 1

Forming Simultaneous Confidence Intervals in R

With the definitions and equations out of the way, we can explore how to build the simulatenous confidence intervals in R. The investr is the only package I’ve found that performs the Bonferroni and Working-Hotelling procedures. Of course, not being satisified with just using a package and calling it a day as I often am, we will build a custom function that creates intervals using both procedures to verify our understanding.

Start by loading the necessary packages and the delivery dataset.

library(robustbase)
## Warning: package 'robustbase' was built under R version 3.3.1
library(investr)
## Warning: package 'investr' was built under R version 3.3.1
library(ggplot2)
library(gridExtra)
data("delivery")
Fit linear models with each predictor variable.

dist.lm <- lm(delTime ~ distance, data = delivery)
prod.lm <- lm(delTime ~ n.prod, data = delivery)
Using the plotFit function from the investr package, plot the Bonferroni and Working-Hotelling confidence intervals. Setting the argument adjust to Scheffe instructs the function to build Working-Hotelling intervals.

par(mfrow=c(2,2))

plotFit(dist.lm, interval = 'confidence', adjust = 'Scheffe', main = 'Working-Hotelling DelTime ~ Distance')
plotFit(prod.lm, interval = 'confidence', adjust = 'Scheffe', main = 'Working-Hotelling DelTime ~ Products')

plotFit(dist.lm, interval = 'confidence', k = 0.95, adjust = 'Bonferroni', main = 'Bonferroni DelTime ~ Distance')
plotFit(prod.lm, interval = 'confidence', k = 0.95, adjust = 'Bonferroni', main = 'Bonferroni DelTime ~ Products')