# Contrasts

##### Functions to Construct Contrasts

These are substitutes for similarly named functions in the

- Keywords
- models, regression

##### Usage

```
contr.Treatment(n, base = 1, contrasts = TRUE)
contr.Sum(n, contrasts = TRUE)
contr.Helmert(n, contrasts = TRUE)
```

##### Arguments

- n
- a vector of levels for a factor, or the number of levels.
- base
- an integer specifying which level is considered the baseline level.
Ignored if
`contrasts`

is`FALSE`

. - contrasts
- a logical indicating whether contrasts should be computed.

##### Details

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

levels.
The returned value contains the computed contrasts. If the argument `contrasts`

is `FALSE`

then a square matrix is returned.
Several aspects of these contrast functions are controlled by options set via the `options`

command:
[object Object],[object Object],[object Object],[object Object],[object Object]
Note that there is no replacement for `contr.poly`

in the `base`

package (which produces
orthogonal-polynomial contrasts) since this function already constructs easy-to-read contrast names.

##### Value

- A matrix with
`n`

rows and`k`

columns, with`k = n - 1`

if`contrasts`

is`TRUE`

and`k = n`

if`contrasts`

is`FALSE`

.

##### References

Fox, J. and Weisberg, S. (2011)
*An R Companion to Applied Regression*, Second Edition, Sage.

##### See Also

##### Examples

```
# contr.Treatment vs. contr.treatment in the base package:
lm(prestige ~ (income + education)*type, data=Prestige,
contrasts=list(type="contr.Treatment"))
## Call:
## lm(formula = prestige ~ (income + education) * type, data = Prestige,
## contrasts = list(type = "contr.Treatment"))
##
## Coefficients:
## (Intercept) income education
## 2.275753 0.003522 1.713275
## type[T.prof] type[T.wc] income:type[T.prof]
## 15.351896 -33.536652 -0.002903
## income:type[T.wc] education:type[T.prof] education:type[T.wc]
## -0.002072 1.387809 4.290875
lm(prestige ~ (income + education)*type, data=Prestige,
contrasts=list(type="contr.treatment"))
## Call:
## lm(formula = prestige ~ (income + education) * type, data = Prestige,
## contrasts = list(type = "contr.treatment"))
##
## Coefficients:
## (Intercept) income education
## 2.275753 0.003522 1.713275
## typeprof typewc income:typeprof
## 15.351896 -33.536652 -0.002903
## income:typewc education:typeprof education:typewc
## -0.002072 1.387809 4.290875
```

*Documentation reproduced from package car, version 2.0-13, License: GPL (>= 2)*