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.
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an object of an appropriate class. For the default
method, a model formula or a
a data frame created with
A list, whose entries are values (numeric
matrices or character strings naming functions) to be used
as replacement values for the
to be used as argument of
further arguments passed to or from other methods.
model.matrix creates a design matrix from the description
terms(object), using the data in
must supply variables with the same names as would be created by a
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.
contrasts.arg is specified for a factor it overrides the
default factor coding for that variable and any
attribute set by
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
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-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
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.
sparse.model.matrix from package
\CRANpkgMatrix for creating sparse model matrices, which may
be more efficient in large dimensions.
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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