# mahalanobis.dist: Computes the Mahalanobis Distance In StatMatch: Statistical Matching or Data Fusion

 mahalanobis.dist R Documentation

## Computes the Mahalanobis Distance

### Description

This function computes the Mahalanobis distance among units in a dataset or between observations in two distinct datasets.

### Usage

```mahalanobis.dist(data.x, data.y=NULL, vc=NULL)
```

### Arguments

 `data.x` A matrix or a data frame containing variables that should be used in the computation of the distance between units. Only continuous variables are allowed. Missing values (`NA`) are not allowed. When only `data.x` is supplied, the distances between rows of `data.x` is 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. `vc` Covariance matrix that should be used in distance computation. If it is not supplied (`vc = NULL`) it is estimated from the input data. In particular, when `vc = NULL` and only `data.x` is supplied then the covariance matrix is estimated from `data.x` (i.e. `vc = var(data.x)`). On the contrary when `vc = NULL` and both `data.x` and `data.y` are available then the covariance matrix is estimated on the joined data sets (i.e. `vc = var(rbind(data.x, data.y))`).

### Details

The Mahalanobis distance is calculated by means of:

d(i,j) = ((x_i - x_j)^T * S^(-1) * (x_i - x_j) )^(1/2)

The covariance matrix S is estimated from the available data when `vc=NULL`, otherwise the one supplied via the argument `vc` is used.

### Value

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

### Author(s)

Marcello D'Orazio mdo.statmatch@gmail.com

### References

Mahalanobis, P C (1936) “On the generalised distance in statistics”. Proceedings of the National Institute of Sciences of India 2, pp. 49-55.

`mahalanobis`

### Examples

```
md1 <- mahalanobis.dist(iris[1:6,1:4])
md2 <- mahalanobis.dist(data.x=iris[1:6,1:4], data.y=iris[51:60, 1:4])

vv <- var(iris[,1:4])
md1a <- mahalanobis.dist(data.x=iris[1:6,1:4], vc=vv)
md2a <- mahalanobis.dist(data.x=iris[1:6,1:4], data.y=iris[51:60, 1:4], vc=vv)

```

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