通过自举计算相关系数

Question

I'm looking at the correlation between the day of the year that 5 species of bird started moulting their feathers and the numbers of days it took these 5 species to complete the moulting of their feathers.

I've tried to simulate my data in the code below. For each of the 5 species, I have start day for 10 individuals and the durations for 10 individuals. For each species, I calculated the mean start day and mean duration then calculated the correlation across these 5 species.

What I want to do is bootstrap the mean start date and bootstrap the mean duration for each species. I want to repeat this 10,000 times and calculate the correlation coefficient after each repeat. I then want to extract the 0.025, 0.5 and 0.975 quantiles of the 10,000 correlation coefficients.

I got as far as simulating the raw data, but my code quickly got messy once I tried to bootstrap. Can anyone help me with this?

# speciesXX_start_day is the day of the year that 10 individuals of birds started moulting their feathers
# speciesXX_duration is the number of days that each individuals bird took to complete the moulting of its feathers
species1_start_day <- as.integer(rnorm(10, 10, 2))
species1_duration <- as.integer(rnorm(10, 100, 2))

species2_start_day <- as.integer(rnorm(10, 20, 2))
species2_duration <- as.integer(rnorm(10, 101, 2))

species3_start_day <- as.integer(rnorm(10, 30, 2))
species3_duration <- as.integer(rnorm(10, 102, 2))

species4_start_day <- as.integer(rnorm(10, 40, 2))
species4_duration <- as.integer(rnorm(10, 103, 2))

species5_start_day <- as.integer(rnorm(10, 50, 2))
species5_duration <- as.integer(rnorm(10, 104, 2))

start_dates <- list(species1_start_day, species2_start_day, species3_start_day, species4_start_day, species5_start_day)
start_duration <- list(species1_duration, species2_duration, species3_duration, species4_duration, species5_duration)

library(plyr)

# mean start date for each of the 5 species
starts_mean <- laply(start_dates, mean)

# mean duration for each of the 5 species
durations_mean <- laply(start_duration, mean)

# correlation between start date and duration
cor(starts_mean, durations_mean)

Answer 1

R allows you to resample datasets with the sample function. In order to bootstrap you can just take random samples (with replacement) of your original dataset and then recalculate the statistics for each subsample. You can save the intermediate results in a datastructure so that you can process the data afterwards.

A possible example solution for your specific problem is added below. We take 10000 subsamples of size 3 for each of the species, calculate the statistics and then save the results in a list or vector. After the bootstrap we are able to process all the data:

nrSamples = 10000;
listOfMeanStart = list(nrSamples)
listOfMeanDuration = list(nrSamples)
correlations <- vector(mode="numeric", length=nrSamples)

for(i in seq(1,nrSamples))
{
  sampleStartDate = sapply(start_dates,sample,size=3,replace=TRUE)
  sampleDurations = sapply(start_duration,sample,size=3,replace=TRUE)

  listOfMeans[[i]] <- apply(sampleStartDate,2,mean) 
  listOfMeanDuration[[i]] <- apply(sampleDurations,2,mean)
  correlations[i] <- cor(listOfMeans[[i]], listOfMeanDuration[[i]])
}

quantile(correlations,c(0.025,.5,0.975))