| Title: | Robust Regression with Compositional Covariates |
|---|---|
| Description: | We implement the algorithm estimating the parameters of the robust regression model with compositional covariates. The model simultaneously treats outliers and provides reliable parameter estimates. Publication reference: Mishra, A., Mueller, C.,(2019) <arXiv:1909.04990>. |
| Authors: | Aditya Mishra [aut, cre], Christian Muller [ctb] |
| Maintainer: | Aditya Mishra <[email protected]> |
| License: | GPL (>= 3.0) |
| Version: | 1.1 |
| Built: | 2024-10-23 06:36:49 UTC |
| Source: | CRAN |
The model uses scaled lasoo approach for model selection.
classo(Xt, y, C, we = NULL, type = 1, control = list())classo(Xt, y, C, we = NULL, type = 1, control = list())
Xt |
CLR transformed predictor matrix. |
y |
model response vector |
C |
sub-compositional matrix |
we |
specify weight of model parameter |
type |
1/2 for l1 / l2 loss in the model |
control |
a list of internal parameters controlling the model fitting |
beta |
model parameter estimate |
Shi, P., Zhang, A. and Li, H., 2016. Regression analysis for microbiome compositional data. The Annals of Applied Statistics, 10(2), pp.1019-1040.
library(robregcc) library(magrittr) data(simulate_robregcc) X <- simulate_robregcc$X; y <- simulate_robregcc$y C <- simulate_robregcc$C n <- nrow(X); p <- ncol(X); k <- nrow(C) # Predictor transformation due to compositional constraint: Xt <- cbind(1,X) # accounting for intercept in predictor C <- cbind(0,C) # accounting for intercept in constraint bw <- c(0,rep(1,p)) # weight matrix to not penalize intercept # Non-robust regression, [Pixu Shi 2016] control <- robregcc_option(maxiter = 5000, tol = 1e-7, lminfac = 1e-12) fit.nr <- classo(Xt, y, C, we = bw, type = 1, control = control)library(robregcc) library(magrittr) data(simulate_robregcc) X <- simulate_robregcc$X; y <- simulate_robregcc$y C <- simulate_robregcc$C n <- nrow(X); p <- ncol(X); k <- nrow(C) # Predictor transformation due to compositional constraint: 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 # Non-robust regression, [Pixu Shi 2016] control <- robregcc_option(maxiter = 5000, tol = 1e-7, lminfac = 1e-12) fit.nr <- classo(Xt, y, C, we = bw, type = 1, control = control)
The model uses scaled lasoo approach for model selection.
classo_path(Xt, y, C, we = NULL, control = list())classo_path(Xt, y, C, we = NULL, control = list())
Xt |
CLR transformed predictor matrix. |
y |
model response vector |
C |
sub-compositional matrix |
we |
specify weight of model parameter |
control |
a list of internal parameters controlling the model fitting |
betapath |
solution path estimate |
beta |
model parameter estimate |
library(robregcc) library(magrittr) data(simulate_robregcc) X <- simulate_robregcc$X; y <- simulate_robregcc$y C <- simulate_robregcc$C n <- nrow(X); p <- ncol(X); k <- nrow(C) # Xt <- cbind(1,X) # accounting for intercept in predictor C <- cbind(0,C) # accounting for intercept in constraint bw <- c(0,rep(1,p)) # weight matrix to not penalize intercept # Non-robust regression control <- robregcc_option(maxiter = 5000, tol = 1e-7, lminfac = 1e-12) fit.path <- classo_path(Xt, y, C, we = bw, control = control)library(robregcc) library(magrittr) data(simulate_robregcc) X <- simulate_robregcc$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 # Non-robust regression control <- robregcc_option(maxiter = 5000, tol = 1e-7, lminfac = 1e-12) fit.path <- classo_path(Xt, y, C, we = bw, control = control)
S3 methods extracting estimated coefficients for objects generated by
robregcc. Robust coeffcient estimate.
coef_cc(object, type = 0, s = 0)coef_cc(object, type = 0, s = 0)
object |
Object generated by |
type |
0/1 residual estimate before/after sanity check |
s |
0/1 no/yes 1se rule |
coefficient estimate
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$residuals, cindex = 1, control = control, penalty.index = 3, alpha = 0.95) coef_cc(fit.ada) coef_cc(fit.soft) coef_cc(fit.hard)library(magrittr) library(robregcc) data(simulate_robregcc) X <- simulate_robregcc$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) coef_cc(fit.ada) coef_cc(fit.soft) coef_cc(fit.hard)
Produce model and its residual estimate based on PCS analysis.
cpsc_sp( X0, y0, alp = 0.4, cfac = 2, b1 = 0.25, cc1 = 2.937, C = NULL, we, type, control = list() )cpsc_sp( X0, y0, alp = 0.4, cfac = 2, b1 = 0.25, cc1 = 2.937, C = NULL, we, type, control = list() )
X0 |
CLR transformed predictor matrix. |
y0 |
model response vector |
alp |
(0,0.5) fraction of data sample to be removed to generate subsample |
cfac |
initial value of shift parameter for weight construction/initialization |
b1 |
tukey bisquare function parameter producing desired breakdown point |
cc1 |
tukey bisquare function parameter producing desired breakdown point |
C |
sub-compositional matrix |
we |
penalization index for model parameters beta |
type |
1/2 for l1 / l2 loss in the model |
control |
a list of internal parameters controlling the model fitting |
betaf |
TModel parameter estimate |
residuals |
residual estimate |
Mishra, A., Mueller, C.,(2019) Robust regression with compositional covariates. In prepration. arXiv:1909.04990.
library(robregcc) library(magrittr) data(simulate_robregcc) X <- simulate_robregcc$X; y <- simulate_robregcc$y C <- simulate_robregcc$C n <- nrow(X); p <- ncol(X); k <- nrow(C) Xt <- cbind(1,X) # include intercept in predictor C <- cbind(0,C) # include intercept in constraint bw <- c(0,rep(1,p)) # weights not penalize intercept example_seed <- 2*p+1 set.seed(example_seed) # Breakdown point for tukey Bisquare loss function b1 = 0.5 # 50% breakdown point cc1 = 1.567 # corresponding model parameter b1 = 0.25; cc1 = 2.937 # Initialization [PSC analysis for compositional data] control <- robregcc_option(maxiter = 1000, tol = 1e-4,lminfac = 1e-7) fit.init <- cpsc_sp(Xt, y,alp = 0.4, cfac = 2, b1 = b1, cc1 = cc1,C,bw,1,control)library(robregcc) library(magrittr) data(simulate_robregcc) X <- simulate_robregcc$X; y <- simulate_robregcc$y C <- simulate_robregcc$C n <- nrow(X); p <- ncol(X); k <- nrow(C) Xt <- cbind(1,X) # include intercept in predictor C <- cbind(0,C) # include intercept in constraint bw <- c(0,rep(1,p)) # weights 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)
S3 methods plotting crossvalidation error using the object obtained from robregcc.
plot_cv(object)plot_cv(object)
object |
robregcc fitted onject |
generate cv error plot
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$residuals, cindex = 1, control = control, penalty.index = 3, alpha = 0.95) plot_cv(fit.ada) plot_cv(fit.soft) plot_cv(fit.hard)library(magrittr) library(robregcc) data(simulate_robregcc) X <- simulate_robregcc$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) plot_cv(fit.ada) plot_cv(fit.soft) plot_cv(fit.hard)
S3 methods plotting solution path of model parameter and mean shift using the object obtained from robregcc.
plot_path(object, ptype = 0)plot_path(object, ptype = 0)
object |
Object generated by |
ptype |
path type 0/1 for Gamma/Beta path respectvely |
plot solution path
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$residuals, cindex = 1, control = control, penalty.index = 3, alpha = 0.95) plot_path(fit.ada) plot_path(fit.soft) plot_path(fit.hard)library(magrittr) library(robregcc) data(simulate_robregcc) X <- simulate_robregcc$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) plot_path(fit.ada) plot_path(fit.soft) plot_path(fit.hard)
S3 methods extracting residuals from the objects generated by
robregcc.
plot_resid(object, type = 0, s = 0)plot_resid(object, type = 0, s = 0)
object |
Object generated by |
type |
0/1 residual estimate before/after sanity check |
s |
0/1 no/yes 1se rule |
plot estimated residual
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$residuals, cindex = 1, control = control, penalty.index = 3, alpha = 0.95) plot_resid(fit.ada) plot_resid(fit.soft) plot_resid(fit.hard)library(magrittr) library(robregcc) data(simulate_robregcc) X <- simulate_robregcc$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) plot_resid(fit.ada) plot_resid(fit.soft) plot_resid(fit.hard)
Robust residuals estimate
## S3 method for class 'robregcc' residuals(object, ...)## S3 method for class 'robregcc' residuals(object, ...)
object |
robregcc fitted onject |
... |
Other argumnts for future usage. |
residuals estimate
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$residuals, cindex = 1, control = control, penalty.index = 3, alpha = 0.95) residuals(fit.ada) residuals(fit.soft) residuals(fit.hard)library(magrittr) library(robregcc) data(simulate_robregcc) X <- simulate_robregcc$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) residuals(fit.ada) residuals(fit.soft) residuals(fit.hard)
The model approach use scaled lasoo approach for model selection.
robregcc_option( maxiter = 10000, tol = 1e-10, nlam = 100, out.tol = 1e-08, lminfac = 1e-08, lmaxfac = 10, mu = 1, nu = 1.05, sp = 0.3, gamma = 2, outMiter = 3000, inMiter = 500, kmaxS = 500, tolS = 1e-04, nlamx = 20, nlamy = 20, spb = 0.3, spy = 0.3, lminfacX = 1e-06, lminfacY = 0.01, kfold = 10, fullpath = 0, sigmafac = 2 )robregcc_option( maxiter = 10000, tol = 1e-10, nlam = 100, out.tol = 1e-08, lminfac = 1e-08, lmaxfac = 10, mu = 1, nu = 1.05, sp = 0.3, gamma = 2, outMiter = 3000, inMiter = 500, kmaxS = 500, tolS = 1e-04, nlamx = 20, nlamy = 20, spb = 0.3, spy = 0.3, lminfacX = 1e-06, lminfacY = 0.01, kfold = 10, fullpath = 0, sigmafac = 2 )
maxiter |
maximum number of iteration for convergence |
tol |
tolerance value set for convergence |
nlam |
number of lambda to be genrated to obtain solution path |
out.tol |
tolernce value set for convergence of outer loop |
lminfac |
a multiplier of determing lambda_min as a fraction of lambda_max |
lmaxfac |
a multiplier of lambda_max |
mu |
penalty parameter used in enforcing orthogonality |
nu |
penalty parameter used in enforcing orthogonality (incremental rate of mu) |
sp |
maximum proportion of nonzero elements in shift parameter |
gamma |
adaptive penalty weight exponential factor |
outMiter |
maximum number of outer loop iteration |
inMiter |
maximum number of inner loop iteration |
kmaxS |
maximum number of iteration for fast S estimator for convergence |
tolS |
tolerance value set for convergence in case of fast S estimator |
nlamx |
number of x lambda |
nlamy |
number of y lambda |
spb |
sparsity in beta |
spy |
sparsity in shift gamma |
lminfacX |
a multiplier of determing lambda_min as a fraction of lambda_max for sparsity in X |
lminfacY |
a multiplier of determing lambda_min as a fraction of lambda_max for sparsity in shift parameter |
kfold |
nummber of folds for crossvalidation |
fullpath |
1/0 to get full path yes/no |
sigmafac |
multiplying factor for the range of standard deviation |
a list of controling parameter.
# default options library(robregcc) control_default = robregcc_option() # manual options control_manual <- robregcc_option(maxiter=1000,tol = 1e-4,lminfac = 1e-7)# default options library(robregcc) control_default = robregcc_option() # manual options control_manual <- robregcc_option(maxiter=1000,tol = 1e-4,lminfac = 1e-7)
Simulate data for the robust regression with compositional covariates
robregcc_sim(n, betacc, beta0, O, Sigma, levg, snr, shft, m, C, out = list())robregcc_sim(n, betacc, beta0, O, Sigma, levg, snr, shft, m, C, out = list())
n |
sample size |
betacc |
model parameter satisfying compositional covariates |
beta0 |
intercept |
O |
number of outlier |
Sigma |
covariance matrix of simulated predictors |
levg |
1/0 whether to include leveraged observation or not |
snr |
noise to signal ratio |
shft |
multiplying factor to model variance for creating outlier |
m |
test sample size |
C |
subcompositional matrix |
out |
list for obtaining output with simulated data structure |
a list containing simulated output.
Mishra, A., Mueller, C.,(2019) Robust regression with compositional covariates. In prepration. arXiv:1909.04990.
## Simulation example: library(robregcc) library(magrittr) ## n: sample size ## p: number of predictors ## o: fraction of observations as outliers ## L: {0,1} => leveraged {no, yes}, ## s: multiplicative factor ## ngrp: number of subgroup in the model ## snr: noise to signal ratio for computing true std_err ## Define parameters to simulate example p <- 80 # number of predictors n <- 300 # number of sample O <- 0.10*n # number of outlier L <- 1 s <- 8 ngrp <- 4 # number of sub-composition snr <- 3 # Signal to noise ratio example_seed <- 2*p+1 # example seed set.seed(example_seed) # Simulate subcomposition matrix C1 <- matrix(0,ngrp,23) tind <- c(0,10,16,20,23) for (ii in 1:ngrp) C1[ii,(tind[ii] + 1):tind[ii + 1]] <- 1 C <- matrix(0,ngrp,p) C[,1:ncol(C1)] <- C1 # model parameter beta beta0 <- 0.5 beta <- c(1, -0.8, 0.4, 0, 0, -0.6, 0, 0, 0, 0, -1.5, 0, 1.2, 0, 0, 0.3) beta <- c(beta,rep(0,p - length(beta))) # Simulate response and predictor, i.e., X, y Sigma <- 1:p %>% outer(.,.,'-') %>% abs(); Sigma <- 0.5^Sigma data.case <- vector("list",1) set.seed(example_seed) data.case <- robregcc_sim(n,beta,beta0, O = O, Sigma,levg = L, snr,shft = s,0, C,out = data.case) data.case$C <- C # We have saved a copy of simulated data in the package # with name simulate_robregcc # simulate_robregcc = data.case; # save(simulate_robregcc, file ='data/simulate_robregcc.rda') X <- data.case$X # predictor matrix y <- data.case$y # model response## Simulation example: library(robregcc) library(magrittr) ## n: sample size ## p: number of predictors ## o: fraction of observations as outliers ## L: {0,1} => leveraged {no, yes}, ## s: multiplicative factor ## ngrp: number of subgroup in the model ## snr: noise to signal ratio for computing true std_err ## Define parameters to simulate example p <- 80 # number of predictors n <- 300 # number of sample O <- 0.10*n # number of outlier L <- 1 s <- 8 ngrp <- 4 # number of sub-composition snr <- 3 # Signal to noise ratio example_seed <- 2*p+1 # example seed set.seed(example_seed) # Simulate subcomposition matrix C1 <- matrix(0,ngrp,23) tind <- c(0,10,16,20,23) for (ii in 1:ngrp) C1[ii,(tind[ii] + 1):tind[ii + 1]] <- 1 C <- matrix(0,ngrp,p) C[,1:ncol(C1)] <- C1 # model parameter beta beta0 <- 0.5 beta <- c(1, -0.8, 0.4, 0, 0, -0.6, 0, 0, 0, 0, -1.5, 0, 1.2, 0, 0, 0.3) beta <- c(beta,rep(0,p - length(beta))) # Simulate response and predictor, i.e., X, y Sigma <- 1:p %>% outer(.,.,'-') %>% abs(); Sigma <- 0.5^Sigma data.case <- vector("list",1) set.seed(example_seed) data.case <- robregcc_sim(n,beta,beta0, O = O, Sigma,levg = L, snr,shft = s,0, C,out = data.case) data.case$C <- C # We have saved a copy of simulated data in the package # with name simulate_robregcc # simulate_robregcc = data.case; # save(simulate_robregcc, file ='data/simulate_robregcc.rda') X <- data.case$X # predictor matrix y <- data.case$y # model response
Fit regression model with compositional covariates for a range of tuning parameter lambda. Model parameters is assumed to be sparse.
robregcc_sp( X, y, C, beta.init = NULL, gamma.init = NULL, cindex = 1, control = list(), penalty.index = 3, alpha = 1, verbose = TRUE )robregcc_sp( X, y, C, beta.init = NULL, gamma.init = NULL, cindex = 1, control = list(), penalty.index = 3, alpha = 1, verbose = TRUE )
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 |
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 |
Mishra, A., Mueller, C.,(2019) Robust regression with compositional covariates. In prepration. arXiv:1909.04990.
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$residuals, cindex = 1, control = control, penalty.index = 3, alpha = 0.95)library(magrittr) library(robregcc) data(simulate_robregcc) X <- simulate_robregcc$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)
A list of response (y), predictors (X) and sub-cpmposition matrix (C).
data(simulate_robregcc)data(simulate_robregcc)
A list with three components:
Compositional predictors.
Outcome with outliers.
Sub-cmposition matrix.
Vector y, response with a certain percentage of observations as outliers.
Matrix X, Compositional predictors.
Similated data
library(robregcc) data(simulate_robregcc) X <- simulate_robregcc$X; y <- simulate_robregcc$y C <- simulate_robregcc$C n <- nrow(X); p <- ncol(X); k <- nrow(C)library(robregcc) data(simulate_robregcc) X <- simulate_robregcc$X; y <- simulate_robregcc$y C <- simulate_robregcc$C n <- nrow(X); p <- ncol(X); k <- nrow(C)