robregcc (version 1.0)

robregcc_nsp: Robust model estimation approach for regression with compositional covariates.

Description

Generate solution path for range of lambda in case of where model parameter beta is not assumed to be sparse(nsp).

Usage

robregcc_nsp(X, y, C, intercept = FALSE, gamma.wt = NULL,
  control = list(), penalty.index = 1, verbose = TRUE)

Arguments

X

CLR transformed predictor matrix.

y

model response vector

C

sub-compositional constraint matrix

intercept

true/false to include intercept term in the model

gamma.wt

initial value of shift parameter for weight construction/initialization

control

a list of internal parameters controlling the model fitting

penalty.index

1, 2, 3 corresponding to adaptive, soft and hard 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)

X

predictors

y

response

References

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

Examples

# NOT RUN {
library(robregcc)
library(magrittr)

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

# Predictor transformation due to compositional constraint:
# Equivalent to performing centered log-ratio transform 
Xt <- svd(t(C))$u %>% tcrossprod() %>% subtract(diag(p),.) %>% crossprod(t(X),.)
#
Xm <- colMeans(Xt)
Xt <- scale(Xt,Xm,FALSE)                  # centering of predictors 
mean.y <- mean(y)
y <- y - mean.y                           # centering of response 
Xt <- cbind(1,Xt)                         # 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   

# }
# NOT RUN {
# Initialization [PSC analysis for compositional data]
control <- robregcc_option(maxiter=3000,tol = 1e-6)
fit.init  <- cpsc_nsp(Xt, y,alp=0.4,cfac=2,b1 = b1, cc1 = cc1,C,control)


# Robust procedure
# control parameters
control <- robregcc_option()
control$tol <- 1e-30
control$nlam = 25; 
control$lminfac = 1e-5;
control$outMiter = 10000
control$gamma <- 2
# Robust regression using adaptive elastic net penalty [case III, Table 1]
fit.ada <- robregcc_nsp(Xt,y, C, intercept = FALSE,  
                        gamma.wt = fit.init$residuals,
                        control = control, penalty.index = 1)


# Robust regression using elastic net penalty [case II, Table 1]
control$lminfac = 1e-1;
fit.soft <- robregcc_nsp(Xt,y,C,intercept = FALSE, gamma.wt = NULL,
                         control = control, penalty.index = 2)



# Robust regression using hard-ridge penalty [case I, Table 1]
control$tol <- 1e-30
control$nlam = 25; 
control$lminfac = 1e-1; 
control$outMiter = 10000
fit.hard <- robregcc_nsp(Xt,y,C, intercept = FALSE, 
                         gamma.wt = fit.init$residuals,
                         control = control, penalty.index = 3) 

# }