# model.matrix

##### Construct Design Matrices

`model.matrix`

creates a design (or model) matrix, e.g., by
expanding factors to a set of dummary variables (depending on the
contrasts) and expanding interactions similarly.

- Keywords
- models

##### Usage

`model.matrix(object, …)`# S3 method for default
model.matrix(object, data = environment(object),
contrasts.arg = NULL, xlev = NULL, …)

##### Arguments

- object
- an object of an appropriate class. For the default
method, a model formula or a
`terms`

object. - data
- a data frame created with
`model.frame`

. If another sort of object,`model.frame`

is called first. - contrasts.arg
- A list, whose entries are values (numeric
matrices or character strings naming functions) to be used
as replacement values for the
`contrasts`

replacement function and whose names are the names of columns of`data`

containing`factor`

s. - xlev
- to be used as argument of
`model.frame`

if`data`

is such that`model.frame`

is called. - …
- further arguments passed to or from other methods.

##### Details

`model.matrix`

creates a design matrix from the description
given in `terms(object)`

, using the data in `data`

which
must supply variables with the same names as would be created by a
call to `model.frame(object)`

or, more precisely, by evaluating
`attr(terms(object), "variables")`

. If `data`

is a data
frame, there may be other columns and the order of columns is not
important. Any character variables are coerced to factors. After
coercion, all the variables used on the right-hand side of the
formula must be logical, integer, numeric or factor. If `contrasts.arg`

is specified for a factor it overrides the
default factor coding for that variable and any `"contrasts"`

attribute set by `C`

or `contrasts`

. In an interaction term, the variable whose levels vary fastest is the
first one to appear in the formula (and not in the term), so in
`~ a + b + b:a`

the interaction will have `a`

varying
fastest. By convention, if the response variable also appears on the
right-hand side of the formula it is dropped (with a warning),
although interactions involving the term are retained.

##### Value

The design matrix for a regression-like model with the specified formula
and data. There is an attribute `"assign"`

, an integer vector with an entry
for each column in the matrix giving the term in the formula which
gave rise to the column. Value `0`

corresponds to the intercept
(if any), and positive values to terms in the order given by the
`term.labels`

attribute of the `terms`

structure
corresponding to `object`

. If there are any factors in terms in the model, there is an attribute
`"contrasts"`

, a named list with an entry for each factor. This
specifies the contrasts that would be used in terms in which the
factor is coded by contrasts (in some terms dummy coding may be used),
either as a character vector naming a function or as a numeric matrix.

##### References

Chambers, J. M. (1992)
*Data for models.*
Chapter 3 of *Statistical Models in S*
eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

##### See Also

`model.frame`

, `model.extract`

,
`terms`

`sparse.model.matrix`

from package
https://CRAN.R-project.org/package=Matrix for creating *sparse* model matrices, which may
be more efficient in large dimensions.

##### Examples

`library(stats)`

```
ff <- log(Volume) ~ log(Height) + log(Girth)
utils::str(m <- model.frame(ff, trees))
mat <- model.matrix(ff, m)
dd <- data.frame(a = gl(3,4), b = gl(4,1,12)) # balanced 2-way
options("contrasts")
model.matrix(~ a + b, dd)
model.matrix(~ a + b, dd, contrasts = list(a = "contr.sum"))
model.matrix(~ a + b, dd, contrasts = list(a = "contr.sum", b = "contr.poly"))
m.orth <- model.matrix(~a+b, dd, contrasts = list(a = "contr.helmert"))
crossprod(m.orth) # m.orth is ALMOST orthogonal
```

*Documentation reproduced from package stats, version 3.3.3, License: Part of R 3.3.3*