FADA (version 1.1)

FA: Factor Adjusted Discriminant Analysis 1: Decorrelation of the data

Description

This function decorrelates the training dataset and, optionnally, the test dataset by adjusting data for the effects of latent factors of dependence.

Usage

FA(dta, test=NULL, nbf=NULL, maxnbfactors=12, nfolds=10,grouped=FALSE,
plot.diagnostic=FALSE, min.err = 0.001, verbose=TRUE)

Arguments

dta

A list containing the training dataset with the following components: x is the n x p matrix of explanatory variables, where n stands for the training sample size and p for the number of explanatory variables ; y is a numeric vect

test

A list containing the test dataset, with the same list structure as dta.

nbf

Number of factors. If nbf = NULL, the number of factors is estimated. nbf can also be set to a positive integer value. If nbf = 0, the data are not factor-adjusted.

maxnbfactors

The maximum number of factors. Default is maxnbfactors=12.

nfolds

Number of folds for estimation of lambda parameter in Lasso, which is used to estimate individual probabilities of group membership. Default is nfolds=10. The smallest value is nfolds = 3. To perform Leave-One-Out cross-validatio

grouped

If grouped=TRUE, a group Lasso penalty is applied in the multinomial case so that a selected variable is in the model for all groups or not. Default is grouped=FALSE

plot.diagnostic

If diagnostic.plot=TRUE, the values of the variance inflation criterion are plotted for each number of factors. Default is diagnostic.plot=FALSE. This option might be helpful to manually determine the optimal number of factors.

min.err

Threshold of convergence of the algorithm criterion. Default is min.err=0.001.

verbose

Print out number of factors and values of the objective criterion along the iterations. Default is TRUE.

Value

• Returns a list with the following elements:
• meanclass
  Group means estimated after iterative decorrelation
• fadta
  Decorrelated training data
• fatest
  Decorrelated testing data
• Psi
  Estimation of the factor model parameters: specific variance
• B
  Estimation of the factor model parameters: loadings
• groups
  Recall of group variable of training data

References

Friedman, J., Hastie, T. and Tibshirani, R. (2010), Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33, 1-22.

Friguet, C., Kloareg, M. and Causeur, D. (2009), A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104:488, 1406-1415.

Perthame, E., Friguet, C. and Causeur, D. (2014), Stability of feature selection in classification issues for high-dimensional correlated data, Submitted.

See Also

FADA-package FADA glmnet-package

Examples

data(data.train)
data(data.test)
res = FA(data.train,data.test) #  when the optimal number of factors is unknown

### Not run 
# res0 = FA(data.train,data.test,nbf=2) #  when the number of factors is forced