# muqie3D: Three-dimensional Quantile In Yamm: Multivariate Methods Based on Projections and Related Concepts

## Description

This function plots the collection of all MUltivariate QuantIlE points in three dimensions (`muqie3D`) over all unit-length direction vectors `u`, which projects the `yamm`-centred multivariate data onto the chosen vector `u` to obtain a univariate set. The `muqie3D` point is merely the vector `u` rescaled to have length equal to the quantile of the univariate set.

## Usage

 ```1 2 3``` ```muqie3D (xdata, dm=c(1,2,3), probs=0.5, nsegs=30, nprojs=2000, reltol=0.001, plot.it=FALSE, full.return=FALSE) ```

## Arguments

 `xdata` The data as a matrix or dataframe with the number of columns greater than or equal to three, with each row being viewed as one multivariate observation. `dm` A numeric vector with three entries representing the selected columns of the data considered. The default value is c(1,2,3), which means the first three columns of data are chosen if the dimension of data is more than three. `probs` The quantile of the data after projected to obtain a univariate set. `nsegs` The number of the three-dimensional unit-length direction vectors `u`, which is computed by dividing a unit sphere into `nsegs` equal sectors. `nprojs` The number of projections for the dataset when computing `yamm`. The default value is 2000. `reltol` The tolerance of the optimisation process in the function `yamm`. The default value is 0.001. `plot.it` Logical. If `TRUE`, the function `muqie` will produce a three-dimensional quantile plot. `full.return` Logical. If `TRUE`, the function `muqie` will return a list of full results. See “Value”.

## Value

If `full.results` = `TRUE`, it returns a list comprising of

 `ans ` A data matrix with four rows. The first three rows represent the x-, y- and z-coordinates of the projection vector `u` respectively. The last row is univariate quantile of the projected data matrix. `uvd ` A data matrix after projecting the `yamm`-centred multivariate data onto a set of projection vectors `u`. `cdata ` The `yamm`-centred multivariate data matrix. `yamm ` The yamm value of the multivariate data. See `yamm` for more details.

If `full.results` = `FALSE` (default), it will only return `ans`.

## References

Chen, F. and Nason, Guy P. (2020) A new method for computing the projection medi an, its influence curve and techniques for the production of projected quantile plots. PLOS One, (to appear)

`yamm`

## Examples

 ```1 2 3 4``` ```data(beetle) # # Compute the 0.7-quantile for the first three columns of the beetle data. muqie3D(beetle, dm=c(1,3,6), probs=0.7) ```

Yamm documentation built on April 14, 2020, 6:49 p.m.