model.matrix {stats}R Documentation

Construct Design Matrices


model.matrix creates a design matrix.


model.matrix(object, ...)

## Default S3 method:
model.matrix(object, data = environment(object),
             contrasts.arg = NULL, xlev = NULL, ...)


object an object of an appropriate class. For the default method, a model formula or 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 contrasts suitable for input to the contrasts replacement function and whose names are the names of columns of data containing factors.
xlev to be used as argument of model.frame if data has no "terms" attribute.
... further arguments passed to or from other methods.


model.matrix creates a design matrix from the description given in terms(object), using the data in data which must contain 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 it is a data frame, there may be other columns and the order of columns is not important. Any character variables are coerced to factors, with a warning. After coercion, all the variables used in RHD 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.


The design matrix for a regression 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 terms.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.


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


ff <- log(Volume) ~ log(Height) + log(Girth)
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
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

[Package stats version 2.5.0 Index]