# bootstrap: Partial Bootstrap Analysis In dimensio: Multivariate Data Analysis

## Description

Checks analysis with partial bootstrap resampling.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```bootstrap(object, ...) ## S4 method for signature 'numeric' bootstrap(object, do, n, ...) ## S4 method for signature 'integer' bootstrap(object, do, n, ...) ## S4 method for signature 'BootstrapVector' summary( object, level = 0.95, type = c("student", "normal"), probs = c(0.25, 0.75), na.rm = FALSE, ... ) ## S4 method for signature 'CA' bootstrap(object, n = 30) ## S4 method for signature 'PCA' bootstrap(object, n = 30) ```

## Arguments

 `object` A `numeric` or an `integer` vector or a `CA` or `PCA` object (see below). `...` Currently not used. `do` A `function` that takes `object` as an argument and returns a single numeric value. `n` A non-negative `integer` giving the number of bootstrap replications. `level` A length-one `numeric` vector giving the confidence level. Must be a single number between 0 and 1. If `NULL`, no confidence interval are computed. `type` A `character` string giving the type of confidence interval to be returned. It must be one "`student`" (default) or "`normal`". Any unambiguous substring can be given. Only used if `level` is not `NULL`.“ `probs` A `numeric` vector of probabilities with values in [0,1] (see `stats::quantile()`). If `NULL`, quantiles are not computed. `na.rm` A `logical` scalar: should missing values be removed from `object` before the sample statistics are computed?

## Value

If `object` is a `numeric` or an `integer` vector, `bootstrap()` returns a `BootstrapVector` object (i.e. a `numeric` vector of the `n` bootstrap values of `do`).

If `object` is a `CA` or a `PCA` object, `bootstrap()` returns a `BootstrapCA` or a `BootstrapPCA` object.

`summary()` returns a `numeric` vector with the following elements:

`min`

Minimum value.

`mean`

Mean value.

`max`

Maximum value.

`lower`

Lower bound of the confidence interval.

`upper`

Upper bound of the confidence interval.

`Q*`

Sample quantile to `*` probability.

## Methods (by class)

• `numeric`: Samples randomly from the elements of `object` with replacement.

• `integer`: Samples observations from a multinomial distribution.

N. Frerebeau

## References

Greenacre, Michael J. Theory and Applications of Correspondence Analysis. London: Academic Press, 1984.

Lebart, L., Piron, M. and Morineau, A. Statistique exploratoire multidimensionnelle: visualisation et inférence en fouille de données. Paris: Dunod, 2006.

Other resampling methods: `jackknife()`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60``` ```library(ggrepel) ## Random samples from x with replacement x <- rnorm(20) # numeric boot <- bootstrap(x, do = mean, n = 100) # Sample mean summary(boot) ## Sample observations from a multinomial distribution x <- sample(1:100, 100, TRUE) # integer boot <- bootstrap(x, do = median, n = 100) summary(boot) ## Partial bootstrap on CA ## Data from Lebart et al. 2006, p. 170-172 color <- data.frame( brun = c(68, 15, 5, 20), chatain = c(119, 54, 29, 84), roux = c(26, 14, 14, 17), blond = c(7, 10, 16, 94), row.names = c("marron", "noisette", "vert", "bleu") ) ## Compute correspondence analysis X <- ca(color) ## Plot results plot(X) + ggrepel::geom_label_repel() ## Bootstrap (30 replicates) Y <- bootstrap(X, n = 30) ## Get replicated coordinates get_replications(Y, margin = 1) get_replications(Y, margin = 2) ## Plot with ellipses plot_rows(Y) + ggplot2::stat_ellipse() plot_columns(Y) + ggplot2::stat_ellipse() ## Partial bootstrap on PCA ## Compute principal components analysis data(iris) X <- pca(iris) ## Plot results plot_columns(X) + ggrepel::geom_label_repel() ## Bootstrap (30 replicates) Y <- bootstrap(X, n = 30) ## Plot with ellipses plot_columns(Y) + ggplot2::stat_ellipse() ```