fitPacs: fitPacs function
In clere: Simultaneous Variables Clustering and Regression

Description Usage Arguments Value See Also Examples

This function implements the PACS (Pairwise Absolute Clustering and Sparsity) methodology of Sharma DB et al. (2013). This methodology proposes to estimate the regression coefficients by solving a penalized least squares problem. It imposes a constraint on Beta (the vector of regression coefficients) that is a weighted combination of the L1 norm and the pairwise L-infinity norm. Upper-bounding the pairwise L-infinity norm enforces the covariates to have close coefficients. When the constraint is strong enough, closeness translates into equality achieving thus a grouping property. For PACS, no software was available. Only an R script was released on Bondell's webpage (http://www4.stat.ncsu.edu/~bondell/Software/PACS/PACS.R.r). Since this R script was running very slowly, we decided to reimplement it in C++ and interfaced it with the present R package clere. This corresponds to the option type=1 in Bondell's script.

1	fitPacs(Y, X, lambda = 0.5, betaInput, epsPACS = 1e-05, nItMax = 1000)

`Y`	[numeric]: The vector of observed responses - size `n`.
`X`	[matrix]: The matrix of predictors - size `n` rows and `p` columns.
`lambda`	[numeric]: A non-negative penalty term that controls simultaneouly clusetering and sparsity.
`betaInput`	[numeric]: A vector of initial guess of the model parameters. The authors suggest to use coefficients obtained after fitting a ridge regression with the shrinkage parameter selected using AIC criterion.
`epsPACS`	[numeric]: A tolerance threshold that control the convergence of the algorithm. The default value fixed in Bondell's initial script is 1e-5.
`nItMax`	[numeric]: Maximum number of iterations in the algorithm.

Object of class Pacs containing all the input parameters plus parameter a0 the intercept and parameter K the dimensionality of the model.

Overview : clere-package
Classes : Clere, Pacs
Methods : plot, clusters, predict, summary
Functions : fitClere, fitPacs Datasets : numExpRealData, numExpSimData, algoComp

   n     <- 100
   p     <-  20
   Beta  <- rep(c(0,2),10)
   eps   <- rnorm(n,sd=3)
   x     <- matrix(rnorm(n*p), nrow = n, ncol = p)
   y     <- as.numeric(10+x%*%Beta+eps)
   bInit <- lm(y~scale(x))$coefficients[-1]
   mod   <- fitPacs(Y=y,X=x,lambda=1.25,betaInput=bInit,epsPACS=1e-5,nItMax=1000)