Flexible discriminant analysis.
fda(formula, data, weights, theta, dimension, eps, method,
keep.fitted, …)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 frame containing the variables in the formula (optional).
an optional vector of observation weights.
an optional matrix of class scores, typically with less
than J-1 columns.
The dimension of the solution, no greater than
J-1, where J is the number classes. Default is
J-1.
a threshold for small singular values for excluding
discriminant variables; default is .Machine$double.eps.
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.
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.
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:
the percent between-group variance explained by each dimension (relative to the total explained.)
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.
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).
(internal) a class scoring matrix which allows
predict to work properly.
dimension of discriminant space.
class proportions for the training data.
fit object returned by method.
the call that created this object (allowing it to be
update-able)
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.
``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
predict.fda,
plot.fda,
mars,
bruto,
polyreg,
softmax,
confusion,
# NOT RUN {
data(iris)
irisfit <- fda(Species ~ ., data = iris)
irisfit
## fda(formula = Species ~ ., data = iris)
##
## Dimension: 2
##
## Percent Between-Group Variance Explained:
## v1 v2
## 99.12 100.00
##
## Degrees of Freedom (per dimension): 5
##
## Training Misclassification Error: 0.02 ( N = 150 )
confusion(irisfit, iris)
## Setosa Versicolor Virginica
## Setosa 50 0 0
## Versicolor 0 48 1
## Virginica 0 2 49
## attr(, "error"):
## [1] 0.02
plot(irisfit)
coef(irisfit)
## [,1] [,2]
## [1,] -2.126479 -6.72910343
## [2,] -0.837798 0.02434685
## [3,] -1.550052 2.18649663
## [4,] 2.223560 -0.94138258
## [5,] 2.838994 2.86801283
marsfit <- fda(Species ~ ., data = iris, method = mars)
marsfit2 <- update(marsfit, degree = 2)
marsfit3 <- update(marsfit, theta = marsfit$means[, 1:2])
## this refits the model, using the fitted means (scaled theta's)
## from marsfit to start the iterations
# }