Why does the results of the bootstrapping methods differs if it is being used the same seed?

Question

I want to generate 95% confidence intervals from the R2 of a linear model. While developing the code and using the same seed for both approaches, I figured it out that doing the bootstrap manually doesn't give me the same results as using the boot function from the boot package. I am wondering now if I am doing something wrong? or why is this happening?

On the other hand, in order to calculate the 95% CI I was trying to use the confint function, but I'm getting an error "$ operator is invalid for atomic vectors". Any solution to avoid this error?

Here is a reproducible example to explain my concerns

#creating the dataframe
a <- rpois(n = 100, lambda = 10)
b <- rnorm(n = 100, mean = 5, sd = 1)
DF<- data.frame(a,b)

#bootstrapping manually
set.seed(123)
x=length(DF$a) 
B_manually<- data.frame(replicate(100, summary(lm(a~b, data = DF[sample(x, replace = T),]))$r.squared))
names(B_manually)[1]<- "r_squared"

#Bootstrapping using the function "Boot" from Boot library
set.seed(123)
library(boot)
B_boot <- boot(DF, function(data,indices)
  summary(lm(a~b, data[indices,]))$r.squared,R=100)

head(B_manually) == head(B_boot$t)
r_squared
1     FALSE
2     FALSE
3     FALSE
4     FALSE
5     FALSE
6     FALSE
#Why does the results of the manually vs boot function approach differs if I'm using the same seed?

# 2nd question (Using the confint function to determine the 95 CI gives me an error)
confint(B_manually$r_squared, level = 0.95, method = "quantile")
confint(B_boot$t, level = 0.95, method = "quantile")
#Error: $ operator is invalid for atomic vectors

#NOTE: I already used the boot.ci to determine the 95 confidence interval, as well as the 
#quantile function to determine the CI, but the results of these CI differs from each others
#and just wanted to compare with the confint function.
quantile(B_function$t, c(0.025,0.975))
boot.ci(B_function, index=1,type="perc")

Thanks in advance for any help!

Answer 1

The boot package does not use replicate with sample to generate the indices. Check the importance.array function under the source code for boot. It basically generates all the indices at one go. So there's no reason to assume that you will end up with the same indices or same result. Take a step back, the purpose of bootstrap is to use random sampling methods to obtain a estimate of your parameters, you should get similar estimates from different implementation of bootstrap.

For example, you can see the distribution of R^2 is very similar:

set.seed(111)
a <- rpois(n = 100, lambda = 10)
b <- rnorm(n = 100, mean = 5, sd = 1)
DF<- data.frame(a,b)

set.seed(123)
x=length(DF$a) 
B_manually<- data.frame(replicate(999, summary(lm(a~b, data = DF[sample(x, replace = T),]))$r.squared))

library(boot)
B_boot <- boot(DF, function(data,indices)
  summary(lm(a~b, data[indices,]))$r.squared,R=999)

par(mfrow=c(2,1))
hist(B_manually[,1],breaks=seq(0,0.4,0.01),main="dist of R2 manual")
hist(B_boot$t,breaks=seq(0,0.4,0.01),main="dist of R2 boot")

The function confint you are using, is meant for a lm object, and works on estimating a confidence interval for the coefficient, see help page. It takes the standard error of the coefficient and multiply it by the critical t-value to give you confidence interval. You can check out this book page for the formula. The objects from your bootstrapping are not lm objects and this function doesn't work. It is not meant for any other estimates.