robregcc_sp {robregcc}

Robust model estimation approach for 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)