# lol.sims.mean_diff: Mean Difference Simulation In lolR: Linear Optimal Low-Rank Projection

## Description

A function for simulating data in which a difference in the means is present only in a subset of dimensions, and equal covariance.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```lol.sims.mean_diff( n, d, rotate = FALSE, priors = NULL, K = 2, md = 1, subset = c(1), offdiag = 0, s = 1 ) ```

## Arguments

 `n` the number of samples of the simulated data. `d` the dimensionality of the simulated data. `rotate` whether to apply a random rotation to the mean and covariance. With random rotataion matrix `Q`, `mu = Q*mu`, and `S = Q*S*Q`. Defaults to `FALSE`. `priors` the priors for each class. If `NULL`, class priors are all equal. If not null, should be `|priors| = K`, a length `K` vector for `K` classes. Defaults to `NULL`. `K` the number of classes. Defaults to `2`. `md` the magnitude of the difference in the means in the specified subset of dimensions. Ddefaults to `1`. `subset` the dimensions to have a difference in the means. Defaults to only the first dimension. `max(subset) < d`. Defaults to `c(1)`. `offdiag` the off-diagonal elements of the covariance matrix. Should be < 1. `S_{ij} = offdiag` if `i != j`, or 1 if `i == j`. Defaults to `0`. `s` the scaling parameter of the covariance matrix. S_ij = scaling*1 if i == j, or scaling*offdiag if i != j. Defaults to `1`.

## Value

A list of class `simulation` with the following:

 `X` `[n, d]` the `n` data points in `d` dimensions as a matrix. `Y` `[n]` the `n` labels as an array. `mus` `[d, K]` the `K` class means in `d` dimensions. `Sigmas` `[d, d, K]` the `K` class covariance matrices in `d` dimensions. `priors` `[K]` the priors for each of the `K` classes. `simtype` The name of the simulation. `params` Any extraneous parameters the simulation was created with.

## Details

For more details see the help vignette: `vignette("sims", package = "lolR")`

Eric Bridgeford

## Examples

 ```1 2 3``` ```library(lolR) data <- lol.sims.mean_diff(n=200, d=30) # 200 examples of 30 dimensions X <- data\$X; Y <- data\$Y ```

lolR documentation built on July 8, 2020, 7:35 p.m.