# Contrast matrices

### Description

Return a matrix of contrasts for factor coding.

### Usage

1 2 3 4 5 | ```
contr.cum(n)
contr.diff(n)
contr.2nd(n)
contr.orth(n)
``` |

### Arguments

`n` |
A vector of levels for a factor, or the number of levels. |

### Details

These functions are used for creating contrast matrices for use in
fitting regression models. The columns of the
resulting matrices contain contrasts which can be used for coding a
factor with `n`

levels.

`contr.cum`

gives a coding corresponding to successive differences
between factor levels.

`contr.diff`

gives a coding that correspond to the cumulative sum
of the value for each level. This is not meaningful in a model where the
intercept is included, therefore `n`

columns ia always returned.

`contr.2nd`

gives contrasts corresponding to 2nd order differences
between factor levels. Returns a matrix with `n-2`

columns.

`contr.orth`

gives a matrix with `n-2`

columns, which are
mutually orthogonal and orthogonal to the matrix `cbind(1,1:n)`

### Value

A matrix with `n`

rows and `k`

columns, with
`k`

=`n`

for `contr.diff`

`k`

=`n-1`

for `contr.cum`

`k`

=`n-2`

for `contr.2nd`

and `contr.orth`

.

### Author(s)

Bendix Carstensen

### See Also

`contr.treatment`

### Examples

1 2 3 4 5 | ```
contr.cum(6)
contr.2nd(6)
contr.diff(6)
contr.orth(6)
``` |