mimic: Modify a dataset to mimic another dataset

Description

Modifies a dataset x so that it shares sample summary statistics with a target dataset x2.

Usage

mimic(x, x2, idempotent = TRUE, ...)

Value

An object of class c("anscombe", "matrix", "array") with plot and print methods. This returned dataset has the following summary statistics in common with x2.

The sample means of each variable.
The sample variances of each variable.
The sample correlation matrix.
The estimated regression coefficients from least squares linear regressions of each variable on each other variable.

The target and new summary statistics are returned as attributes old_stats and new_stats. If x2 is supplied then it is returned as a attribute old_data.

Arguments

x, x2: Numeric matrices or data frames. Each column contains observations on a different variable. Missing observations are not allowed. get_stats(x2) sets the target summary statistics. If x2 is missing then set_stats is called with d = ncol(x) and any additional arguments supplied via .... This can be used to set target summary statistics (means, variances and/or correlations).
idempotent: A logical scalar. If idempotent = TRUE then mimic(x, x) returns x, apart from a change of class. If idempotent = FALSE then the returned dataset may be a rotated version of the original dataset, with the same summary statistics. See Details.
...: Additional arguments to be passed to set_stats.

Details

The input dataset x is modified by shifting, scaling and rotating it so that its sample mean and covariance matrix match those of the target dataset x2.

The rotation is based on the square root of the sample correlation matrix. If idempotent = FALSE then this square root is based on the Cholesky decomposition this matrix, using chol. If idempotent = TRUE the square root is based on the spectral decomposition of this matrix, using the output from eigen. This is a minimal rotation square root, which means that if the input data x already have the exactly/approximately the required summary statistics then the returned dataset is exactly/approximately the same as the target dataset x2.

Examples

Run this code

### 2D examples

# The UK and a dinosaur
got_maps <- requireNamespace("maps", quietly = TRUE)
got_datasauRus <- requireNamespace("datasauRus", quietly = TRUE)
if (got_maps && got_datasauRus) {
  library(maps)
  library(datasauRus)
  dino <- datasaurus_dozen_wide[, c("dino_x", "dino_y")]
  UK <- mapdata("UK")
  new_UK <- mimic(UK, dino)
  plot(new_UK)
}

# Trump and a dinosaur
if (got_datasauRus) {
  library(datasauRus)
  dino <- datasaurus_dozen_wide[, c("dino_x", "dino_y")]
  new_dino <- mimic(dino, trump)
  plot(new_dino)
}

## Examples of passing summary statistics

# The default is zero mean, unit variance and no correlation
new_faithful <- mimic(faithful)
plot(new_faithful)

# Change the correlation
mat <- matrix(c(1, -0.9, -0.9, 1), 2, 2)
new_faithful <- mimic(faithful, correlation = mat)
plot(new_faithful)

### A 3D example

new_randu <- mimic(datasets::randu, datasets::trees)
# The samples summary statistics are equal
get_stats(new_randu)
get_stats(datasets::trees)