robregcc_sp: Robust model estimation approach for regression with...

In robregcc: Robust Regression with Compositional Covariates

Description

Fit regression model with compositional covariates for a range of tuning parameter lambda. Model parameters is assumed to be sparse.

Usage

robregcc_sp(
  X,
  y,
  C,
  beta.init = NULL,
  gamma.init = NULL,
  cindex = 1,
  control = list(),
  penalty.index = 3,
  alpha = 1,
  verbose = TRUE
)

Arguments

X	predictor matrix
y	phenotype/response vector
C	conformable sub-compositional matrix
beta.init	initial value of model parameter beta
gamma.init	inital value of shift parameter gamma
cindex	index of control (not penalized) variable in the model
control	a list of internal parameters controlling the model fitting
penalty.index	a vector of length 2 specifying type of penalty for model parameter and shift parameter respectively. 1, 2, 3 corresponding to adaptive, soft and hard penalty
alpha	elastic net penalty
verbose	TRUE/FALSE for showing progress of the cross validation

Value

Method	Type of penalty used
betapath	model parameter estimate along solution path
gammapath	shift parameter estimate along solution path
lampath	sequence of fitted lambda)
k0	scaling factor
cver	error from k fold cross validation
selInd	selected index from minimum and 1se rule cross validation error
beta0	beta estimate corresponding to selected index
gamma0	mean shift estimate corresponding to selected index
residual0	residual estimate corresponding to selected index
inlier0	inlier index corresponding to selected index
betaE	Post selection estimate corresponding to selected index
residualE	post selection residual corresponding to selected index
inlierE	post selection inlier index corresponding to selected index

References

Mishra, A., Mueller, C.,(2019) Robust regression with compositional covariates. In prepration. arXiv:1909.04990.

Examples

library(magrittr)
library(robregcc)

data(simulate_robregcc)
X <- simulate_robregcc$X;
y <- simulate_robregcc$y
C <- simulate_robregcc$C
n <- nrow(X); p <- ncol(X); k <-  nrow(C)

Xt <- cbind(1,X)                         # accounting for intercept in predictor
C <- cbind(0,C)                           # accounting for intercept in constraint
bw <- c(0,rep(1,p))                       # weight matrix to not penalize intercept 

example_seed <- 2*p+1               
set.seed(example_seed) 

# Breakdown point for tukey Bisquare loss function 
b1 = 0.5                    # 50% breakdown point
cc1 =  1.567                # corresponding model parameter
b1 = 0.25; cc1 =  2.937   

# Initialization [PSC analysis for compositional data]
control <- robregcc_option(maxiter=1000,tol = 1e-4,lminfac = 1e-7)
fit.init <- cpsc_sp(Xt, y,alp = 0.4, cfac = 2, b1 = b1, 
cc1 = cc1,C,bw,1,control)  

## Robust model fitting

# control parameters
control <- robregcc_option()
beta.wt <- fit.init$betaR    # Set weight for model parameter beta
beta.wt[1] <- 0
control$gamma = 1            # gamma for constructing  weighted penalty
control$spb = 40/p           # fraction of maximum non-zero model parameter beta
control$outMiter = 1000      # Outer loop iteration
control$inMiter = 3000       # Inner loop iteration
control$nlam = 50            # Number of tuning parameter lambda to be explored
control$lmaxfac = 1          # Parameter for constructing sequence of lambda
control$lminfac = 1e-8       # Parameter for constructing sequence of lambda 
control$tol = 1e-20;         # tolrence parameter for converging [inner  loop]
control$out.tol = 1e-16      # tolerence parameter for convergence [outer loop]
control$kfold = 10           # number of fold of crossvalidation
control$sigmafac = 2#1.345
# Robust regression using adaptive lasso penalty
fit.ada <- robregcc_sp(Xt,y,C,
                       beta.init = beta.wt,  cindex = 1, 
                       gamma.init = fit.init$residuals,
                       control = control, 
                       penalty.index = 1, alpha = 0.95)

# Robust regression using lasso penalty [Huber equivalent]   
fit.soft <- robregcc_sp(Xt,y,C, cindex = 1, 
                        control = control, penalty.index = 2, 
                        alpha = 0.95)


# Robust regression using hard thresholding penalty
control$lmaxfac = 1e2               # Parameter for constructing sequence of lambda
control$lminfac = 1e-3              # Parameter for constructing sequence of lambda
control$sigmafac = 2#1.345
fit.hard <- robregcc_sp(Xt,y,C, beta.init = fit.init$betaf, 
                        gamma.init = fit.init$residuals,
                        cindex = 1, 
                        control = control, penalty.index = 3, 
                        alpha = 0.95)
                        

robregcc documentation built on July 26, 2020, 1:07 a.m.