# maximum.dist: Computes the Maximum Distance In StatMatch: Statistical Matching or Data Fusion

 maximum.dist R Documentation

## Computes the Maximum Distance

### Description

This function computes the Maximum distance (or L^Inf norm) between units in a dataset or between observations in two distinct datasets.

### Usage

```maximum.dist(data.x, data.y=data.x, rank=FALSE)
```

### Arguments

 `data.x` A matrix or a data frame containing variables that should be used in the computation of the distance. Only continuous variables are allowed. Missing values (`NA`) are not allowed. When only `data.x` is supplied, the distances between rows of `data.x` are computed. `data.y` A numeric matrix or data frame with the same variables, of the same type, as those in `data.x` (only continuous variables are allowed). Dissimilarities between rows of `data.x` and rows of `data.y` will be computed. If not provided, by default it is assumed `data.y=data.x` and only dissimilarities between rows of `data.x` will be computed. `rank` Logical, when `TRUE` the original values are substituted by their ranks divided by the number of values plus one (following suggestion in Kovar et al. 1988). This rank transformation permits to remove the effect of different scales on the distance computation. When computing ranks the tied observations assume the average of their position (`ties.method = "average"` in calling the `rank` function).

### Details

This function computes the L^Inf distance also know as minimax distance. In practice the distance between two records is the maximum of the absolute differences on the available variables:

d(i,j) =max(|x_1i-x_1j|,|x_2i-x_2j|,...,|x_Ki-x_Kj|)

When `rank=TRUE` the original values are substituted by their ranks divided by the number of values plus one (following suggestion in Kovar et al. 1988).

### Value

A `matrix` object with distances between rows of `data.x` and those of `data.y`.

### Author(s)

Marcello D'Orazio mdo.statmatch@gmail.com

### References

Kovar, J.G., MacMillan, J. and Whitridge, P. (1988). “Overview and strategy for the Generalized Edit and Imputation System”. Statistics Canada, Methodology Branch Working Paper No. BSMD 88-007 E/F.

`rank`,

### Examples

```
md1 <- maximum.dist(iris[1:10,1:4])
md2 <- maximum.dist(iris[1:10,1:4], rank=TRUE)

md3 <- maximum.dist(data.x=iris[1:50,1:4], data.y=iris[51:100,1:4])
md4 <- maximum.dist(data.x=iris[1:50,1:4], data.y=iris[51:100,1:4], rank=TRUE)

```

StatMatch documentation built on March 18, 2022, 6:55 p.m.