Convert predictor matrix to design matrix
D = x2fx(X,model)
D = x2fx(X,model,categ)
D = x2fx(X,model,categ,catlevels)
D = x2fx(X, converts
a matrix of predictors model)X to a design matrix D for
regression analysis. Distinct predictor variables should appear in
different columns of X.
The optional input model controls
the regression model. By default, x2fx returns
the design matrix for a linear additive model with a constant term. model is
one of the following:
'linear' — Constant and
linear terms. This is the default.
'interaction' — Constant,
linear, and interaction terms
'quadratic' — Constant,
linear, interaction, and squared terms
'purequadratic' — Constant,
linear, and squared terms
If X has n columns,
the order of the columns of D for a full quadratic
model is:
The constant term
The linear terms (the columns of X,
in order 1, 2, ..., n)
The interaction terms (pairwise products of the columns
of X, in order (1, 2), (1, 3), ..., (1, n),
(2, 3), ..., (n–1, n))
The squared terms (in order 1, 2, ..., n)
Other models use a subset of these terms, in the same order.
Alternatively, model can be a matrix
specifying polynomial terms of arbitrary order. In this case, model should
have one column for each column in X and one row
for each term in the model. The entries in any row of model are
powers for the corresponding columns of X. For
example, if X has columns X1, X2,
and X3, then a row [0 1 2] in model specifies
the term (X1.^0).*(X2.^1).*(X3.^2). A row of all
zeros in model specifies a constant term,
which can be omitted.
D = x2fx(X, treats
columns with numbers listed in the vector model,categ)categ as
categorical variables. Terms involving categorical variables produce
dummy variable columns in D. Dummy variables are
computed under the assumption that possible categorical levels are
completely enumerated by the unique values that appear in the corresponding
column of X.
D = x2fx(X, accepts
a vector model,categ,catlevels)catlevels the same length as categ,
specifying the number of levels in each categorical variable. In
this case, values in the corresponding column of X must
be integers in the range from 1 to the specified number of levels.
Not all of the levels need to appear in X.
The following converts 2 predictors X1 and X2 (the
columns of X) into a design matrix for a full quadratic
model with terms constant, X1, X2, X1.*X2, X1.^2,
and X2.^2.
X = [1 10
2 20
3 10
4 20
5 15
6 15];
D = x2fx(X,'quadratic')
D =
1 1 10 10 1 100
1 2 20 40 4 400
1 3 10 30 9 100
1 4 20 80 16 400
1 5 15 75 25 225
1 6 15 90 36 225The following converts 2 predictors X1 and X2 (the
columns of X) into a design matrix for a quadratic
model with terms constant, X1, X2, X1.*X2,
and X1.^2.
X = [1 10
2 20
3 10
4 20
5 15
6 15];
model = [0 0
1 0
0 1
1 1
2 0];
D = x2fx(X,model)
D =
1 1 10 10 1
1 2 20 40 4
1 3 10 30 9
1 4 20 80 16
1 5 15 75 25
1 6 15 90 36