mvr: Estimate coefficients of high-dimensional multivariate...
In xliusufe/pqr: pqr

Description Usage Arguments Value Author(s) References Examples

View source: R/mvr.R

This function provides the coefficient matrix estimator of high-dimensional multivariate regression (MVR) with penalty lasso (mcp or scad). The tuning parameter is selected by BIC (the default), AIC, EBIC, CV, or GCV.

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mvr(Y, X, Z=NULL, method="BIC", ncv=10, penalty="LASSO", isPenColumn=TRUE, 
          lambda=NULL, nlam=50, intercept=TRUE, lam_min=1e-4, eps=1e-6, 
          maxstep=20, gamma_pen=2, dfmax=NULL, alpha=1)

`Y`	The response, a vector of size n or a matrix of size n\times q
`X`	The covariates to be penalized, a matrix with dimension n\times p
`Z`	The covariates without penalization, a matrix with dimension n\times d. The default is `NULL`.
`method`	The method to be applied to select parameters. Either `BIC` (the default), `AIC`, `EBIC`, `CV`, or `GCV`.
`ncv`	The number of cross-validation folds. Default is 10. If `method` is not `CV`, `ncv` is useless.
`penalty`	The penalty to be applied to the model. Either "LASSO" (the default), "SCAD", or "MCP".
`isPenColumn`	A logical value indicating whether the coefficients associating with X_j that affects whole response y is penalized. Default is `TRUE`. If `isPenColumn` is `TRUE`, the coefficients associating with X_j that affects simultaneously whole response y is penalized for each j\in \{1,\cdots,p\}. If `isPenColumn` is `FALSE`, the coefficients associating with X_j that affects single response y_l is penalized for each j\in \{1,\cdots,p\}, where l\in \{1,\cdots,q\}.
`lambda`	A user-specified sequence of lambda values. By default, a sequence of values of length `nlam` is computed, equally spaced on the log scale.
`nlam`	The number of lambda values. Default is 50.
`intercept`	Should intercept(s) be fitted (default=`TRUE`) or set to zero (`FALSE`)?
`lam_min`	The smallest value for lambda, as a fraction of lambda.max. Default is 1e-3.
`eps`	Convergence threshhold. The algorithm iterates until the relative change in any coefficient is less than `eps1`. Default is `1e-4`.
`maxstep`	Maximum number of iterations. Default is `20`.
`gamma_pen`	The tuning parameter of the MCP/SCAD penalty (see details).
`dfmax`	Upper bound for the number of nonzero coefficients. Default is no upper bound. However, for large data sets, computational burden may be heavy for models with a large number of nonzero coefficients.
`alpha`	Tuning parameter for the Mnet estimator which controls the relative contributions from the LASSO, MCP/SCAD penalty and the ridge, or L2 penalty. `alpha=1` is equivalent to LASSO, MCP/SCAD penalty, while `alpha=0` would be equivalent to ridge regression. However, `alpha=0` is not supported; `alpha` may be arbitrarily small, but not exactly 0.

`Bhat`	Estimator of `Bhat`.
`rss`	Residual sum of squares (RSS).
`activeX`	The active set of X. It is a p dimensional vector.
`lambda`	The sequence of regularization parameter values in the path.
`selectedID`	The index of `lambda` corresponding to `lambda_opt`.
`lambda_opt`	The value of `lambda` with the minimum `BIC` value.
`bic`	BIC value used to select variables.
`muhat`	Estimator of intercept μ. It is `NULL` if `intercept` is `FALSE`.
`Chat`	Estimator of coefficients of Z. `Chat` is `NULL` if `Z` is `NULL`.
`Y`	Response Y.
`X`	Design matrix X.

Chao Cheng, Xingdong Feng, Jian Huang and Xu Liu (liu.xu@sufe.edu.cn)

Cheng, C., Feng, X., Huang, J. and Liu, X. (2020). Regularized projection score estimation of treatment effects in high-dimensional quantile regression. Manuscript.

	library(pqr)
	
	#example 1
	n <- 200
	q <- 5
	s <- 3
	p <- 100
	B <- matrix(runif(q*s, 2,3), s)
	X <- matrix(rnorm(n*p),n,p)
	Y <- X[,1:s]%*%B + matrix(rnorm(n*q),n)
	fit <- mvr(Y,X)
	fit$activeX
	fit$Bhat
	which(rowSums(fit$Bhat^2)>0)
	fit$muhat
	
	#example 2
	n <- 200
	q <- 5
	s <- 3
	d <- 3
	p <- 100
	B <- matrix(runif(q*s, 2,3), s)
	C <- matrix(runif(q*d, 1,2), d)
	X <- matrix(rnorm(n*p),n,p)
	Z <- matrix(rnorm(n*d),n)
	Y <- X[,1:s]%*%B + Z%*%C + matrix(rnorm(n*q),n)
	fit <- mvr(Y,X,Z)
	fit$activeX
	fit$Bhat
	which(rowSums(fit$Bhat^2)>0)
	fit$Chat
	fit$muhat