# Bootstrapping Example

#### Jonathan Bakdash and Laura Marusich

#### 2024-07-26

### 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