overlapping (version 2.5)

boot.overlap: Nonparametric Bootstrap to estimate the overlapping area

Description

Resampling via non-parametric bootstrap to estimate the overlapping area between two or more kernel density estimations from empirical data.

Usage

boot.overlap( x, B = 1000, pairsOverlap = FALSE, ... )

Value

It returns a list containing the following components:

OVboot_stats

a data frame \(q \times 3\) where each row contains the following statistics: estOV, estimated overlapping area, \(\hat{\eta}\); bias, difference between the expected value over the bootstrap samples and the observed overlapping area: \(E(\hat{\eta}^*)-\hat{\eta}\); se, bootstrap standard error \(\sigma_{\hat{\eta}}\).

OVboot_dist

a matrix with B rows (bootstrap replicates) and \(q\) columns (depending on the number of elements of x); each column is a boostrap distribution of the corresponding overlapping measure.

Arguments

x

a list of numerical vectors to be compared (each vector is an element of the list).

B

integer, number of bootstrap draws.

pairsOverlap

logical, if TRUE, available only when the list x contains more than two elements, it returns the overlapped area relative to each pair of distributions.

...

options, see function overlap for details.

Author

Massimiliano Pastore

Details

If the list x contains more than two elements (i.e., more than two distributions) it computes the bootstrap overlapping measure between all the \(q\) paired distributions. For example, if x contains three elements then \(q = 3\); if x contains four elements then \(q = 6\).

References

Pastore, M. (2018). Overlapping: a R package for Estimating Overlapping in Empirical Distributions. The Journal of Open Source Software, 3 (32), 1023. tools:::Rd_expr_doi("https://doi.org/10.21105/joss.01023")

Pastore, M., Calcagnì, A. (2019). Measuring Distribution Similarities Between Samples: A Distribution-Free Overlapping Index. Frontiers in Psychology, 10:1089. tools:::Rd_expr_doi("https://doi.org/10.3389/fpsyg.2019.01089")

Examples

set.seed(1)
x <- list(Y1=rnorm(100), Y2=rnorm(90,1,3))
## bootstrapping
out <- boot.overlap( x, B = 20, pairsOverlap = TRUE )
out$OVboot_stats

# bootstrap quantile intervals
quantile( out$OVboot_dist, probs = c(.05, .9) )

# plot of bootstrap distributions
Y <- data.frame( values = c(out$OVboot_dist) )
ggplot( Y, aes( values )) + geom_density()

# missing data
x$Y1[1:10] <- NA
out <- boot.overlap( x, B = 20, pairsOverlap = TRUE )
out$OVboot_stats

# ++++++++++++++++++++++++
set.seed(20150605)
x <- list(X1=rnorm(100), X2=rt(50,8), X3=rchisq(80,2))

## bootstrapping
out <- boot.overlap( x, B = 10, pairsOverlap = TRUE )
out$OVboot_stats

# bootstrap quantile intervals
apply( out$OVboot_dist, 2, quantile, probs = c(.05, .9) )

# plot of bootstrap distributions
Y <- stack( data.frame( out$OVboot_dist ))
ggplot( Y, aes( values )) + facet_wrap( ~ind ) + geom_density()