fda {mda}

Flexible Discriminant Analysis

Description

Flexible discriminant analysis.

Usage

fda(formula, data, weights, theta, dimension, eps, method,
    keep.fitted, ...)

Arguments

formula

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

See Also

predict.fda, plot.fda, mars, bruto, polyreg, softmax, confusion,

Examples

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