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Bootstrapping Example

Jonathan Bakdash and Laura Marusich

2024-08-14

Source: vignettes/repro_bootstrapping.Rmd
repro_bootstrapping.Rmd

Reproducible Example of Bootstrapping

Below we illustrate a reproducible example of bootstrapping with rmcorr. Note, only the estimated confidence interval changes with bootstrapping. We also show how to extract the sampling distribution for bootstrapped rmcorr effect size.
- set.seed() is used to make the results reproducible.
- nreps is set to only 100 to run this example quickly. Ideally, it should be > 500.

Rmcorr effect size with Bootstrapped 95% Confidence Inverval 

set.seed(532) 
boot.blandrmc <- rmcorr(Subject, PaCO2, pH, bland1995,
                        CIs = "bootstrap",
                        nreps = 100, 
                        bstrap.out = T)
#> Warning in rmcorr(Subject, PaCO2, pH, bland1995, CIs = "bootstrap", nreps =
#> 100, : 'Subject' coerced into a factor
boot.blandrmc
#> 
#> Repeated measures correlation
#> 
#> r
#> -0.5067697
#> 
#> degrees of freedom
#> 38
#> 
#> p-value
#> 0.0008471081
#> 
#> 95% confidence interval
#> -0.726023 -0.05893805

Sampling Distribution of Bootstrapped Effects

In this graph, the x-axis is the bootstrapped rmcorr effect sizes and the y-axis frequency. The red line is the mean of the sampling distribution and blue line is the median of the sampling distribution. Because these two values are calculated from the bootstrap sampling distribution, note that they slightly differ from the non-bootstrapped point estimated effect size.

boot.rmcorr.samplingdist <- round(boot.blandrmc$resamples, digits = 2)
boot.rmcorr.mean <- mean(boot.blandrmc$resamples)
boot.rmcorr.median <- median(boot.blandrmc$resamples)

x.vals <- sprintf("%.2f", seq(-0.80, 0.00, by = 0.10))

hist(boot.rmcorr.samplingdist, 
     main = "Sampling Distribution of Bootstrapped Effect Sizes",
     xaxt = "n",
     xlab = "Effect Size",
     las = 1)
abline(v = boot.rmcorr.mean,   col = "red",  lwd = 2)
abline(v = boot.rmcorr.median, col = "blue", lwd = 2)
axis(1, 
     at = as.numeric(x.vals),
     labels = x.vals) 

#Compare point-est effect for bootstrap vs. non-bootstrap model
#Boostrapped effect sizes
#Mean
boot.rmcorr.mean
#> [1] -0.5073347
#Median
boot.rmcorr.median
#> [1] -0.5304375

#Non-bootstrapped 
blandrmc <- rmcorr(Subject, PaCO2, pH, bland1995)
#> Warning in rmcorr(Subject, PaCO2, pH, bland1995): 'Subject' coerced into a
#> factor

blandrmc$r
#> [1] -0.5067697