Classification Fitting Functional Generalized Linear Models

Computes functional classification using functional (and non functional) explanatory variables by basis representation.

The first item in the data list is called "df" and is a data frame with the response and non functional explanatory variables, as glm.

Functional covariates of class fdata or fd are introduced in the following items in the data list.
basis.x is a list of basis for represent each functional covariate. The basis object can be created by the function: create.pc.basis, pca.fd create.pc.basis, create.fdata.basis o create.basis.
basis.b is a list of basis for represent each functional beta parameter. If basis.x is a list of functional principal components basis (see create.pc.basis or pca.fd) the argument basis.b is ignored.

Usage

classif.glm(
  formula,
  data,
  family = binomial(),
  weights = "equal",
  basis.x = NULL,
  basis.b = NULL,
  type = "1vsall",
  prob = 0.5,
  CV = FALSE,
  ...
)

Arguments

formula

an object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under Details.

data

List that containing the variables in the model.

family

a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See family for details of family functions).

weights

Weights:

if character string ='equal' same weights for each observation (by default) and ='inverse' for inverse-probability of weighting.
if numeric vector of length n, Weight values of each observation.

basis.x

List of basis for functional explanatory data estimation.

basis.b

List of basis for functional beta parameter estimation.

type

If type is"1vsall" (by default) a maximum probability scheme is applied: requires G binary classifiers. If type is "majority" (only for multicalss classification G > 2) a voting scheme is applied: requires G (G - 1) / 2 binary classifiers.

prob

probability value used for binari discriminant.

CV

=TRUE, Cross-validation (CV) is done.

...

Further arguments passed to or from other methods.

Value

Return glm object plus:

formula: formula.
data: List that containing the variables in the model.
group: Factor of length n.
group.est: Estimated vector groups.
prob.classification: Probability of correct classification by group.
prob.group: Matrix of predicted class probabilities. For each functional point shows the probability of each possible group membership.
max.prob: Highest probability of correct classification.

Note

If the formula only contains a non functional explanatory variables (multivariate covariates), the function compute a standard glm procedure.

References

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

McCullagh and Nelder (1989), Generalized Linear Models 2nd ed. Chapman and Hall.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S, New York: Springer. Regression for R. R News 1(2):20-25

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

Examples

if (FALSE) { # \dontrun{
data(phoneme)
ldat <- ldata("df" = data.frame(y = phoneme[["classlearn"]]),
             "x" = phoneme[["learn"]])
a1 <- classif.glm(y ~ x, data = ldat)
summary(a1)
newldat <- ldata("df" = data.frame(y = phoneme[["classtest"]]),
                "x" = phoneme[["test"]])
p1 <- predict(a1,newldat)
table(newldat$df$y,p1)
sum(p1==newldat$df$y)/250
} # }