of the form y~x it describes the response and
the predictors. The formula can be more complicated, such as
y~log(x)+z etc (see formula for more details).
The response should be a factor representing the response variable,
or any vector that can be coerced to such (such as a logical
variable).
data
data frame containing the variables in the formula
(optional).
weights
an optional vector of observation weights.
theta
an optional matrix of class scores, typically with less
than J-1 columns.
dimension
The dimension of the solution, no greater than
J-1, where J is the number classes. Default is
J-1.
eps
a threshold for small singular values for excluding
discriminant variables; default is .Machine$double.eps.
method
regression method used in optimal scaling. Default is
linear regression via the function polyreg, resulting in
linear discriminant analysis. Other possibilities are mars
and bruto. For Penalized Discriminant analysis
gen.ridge is appropriate.
keep.fitted
a logical variable, which determines whether the
(sometimes large) component "fitted.values" of the fit
component of the returned fda object should be kept. The default is
TRUE if n * dimension < 5000.
...
additional arguments to method.
Value
an object of class "fda". Use predict to extract
discriminant variables, posterior probabilities or predicted class
memberships. Other extractor functions are coef,
confusion and plot.
The object has the following components:
percent.explained
the percent between-group variance explained
by each dimension (relative to the total explained.)
values
optimal scaling regression sum-of-squares for each
dimension (see reference). The usual discriminant analysis
eigenvalues are given by values / (1-values), which are used
to define percent.explained.
means
class means in the discriminant space. These are also
scaled versions of the final theta's or class scores, and can be
used in a subsequent call to fda (this only makes sense if
some columns of theta are omitted—see the references).
theta.mod
(internal) a class scoring matrix which allows
predict to work properly.
dimension
dimension of discriminant space.
prior
class proportions for the training data.
fit
fit object returned by method.
call
the call that created this object (allowing it to be
update-able)
confusion
confusion matrix when classifying the training data.
The method functions are required to take arguments x
and y where both can be matrices, and should produce a matrix
of fitted.values the same size as y. They can take
additional arguments weights and should all have a ...
for safety sake. Any arguments to method can be passed on via
the ... argument of fda. The default method
polyreg has a degree argument which allows
polynomial regression of the required total degree. See the
documentation for predict.fda for further requirements
of method. The package earth is suggested for this
package as well; earth is a more detailed implementation of
the mars model, and works as a method argument.
Author(s)
Trevor Hastie and Robert Tibshirani
References
“Flexible Disriminant Analysis by Optimal Scoring” by Hastie,
Tibshirani and Buja, 1994, JASA, 1255-1270.
“Penalized Discriminant Analysis” by Hastie, Buja and Tibshirani, 1995,
Annals of Statistics, 73-102.
“Elements of Statisical Learning - Data Mining, Inference and
Prediction” (2nd edition, Chapter 12) by Hastie, Tibshirani and
Friedman, 2009, Springer