| Title: | Higher Criticism Tuned Regression |
| Version: | 0.1.1 |
| Description: | A novel searching scheme for tuning parameter in high-dimensional penalized regression. We propose a new estimate of the regularization parameter based on an estimated lower bound of the proportion of false null hypotheses (Meinshausen and Rice (2006) <doi:10.1214/009053605000000741>). The bound is estimated by applying the empirical null distribution of the higher criticism statistic, a second-level significance testing, which is constructed by dependent p-values from a multi-split regression and aggregation method (Jeng, Zhang and Tzeng (2019) <doi:10.1080/01621459.2018.1518236>). An estimate of tuning parameter in penalized regression is decided corresponding to the lower bound of the proportion of false null hypotheses. Different penalized regression methods are provided in the multi-split algorithm. |
| Depends: | R (≥ 3.4.0) |
| Imports: | glmnet (≥ 2.0-18), harmonicmeanp (≥ 3.0), MASS, ncvreg (≥ 3.11-1), Rdpack (≥ 0.11-0), stats |
| RdMacros: | Rdpack |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 6.1.1 |
| NeedsCompilation: | no |
| Packaged: | 2019-11-22 21:26:00 UTC; tjiang8 |
| Author: | Tao Jiang [aut, cre] |
| Maintainer: | Tao Jiang <tjiang8@ncsu.edu> |
| Repository: | CRAN |
| Date/Publication: | 2019-11-22 21:50:09 UTC |
Bounding Sequence
Description
Calculates bounding sequence of higher crticism for proportion estimator using p-values
Usage
bounding.seq(p.value, alpha)
Arguments
p.value |
A matrix of p-values from permutation: row is from each permutation; column is from each variable. |
alpha |
Probability of Type I error for bounding sequence, the default value is 1 / sqrt(log(p)), where p is number of p-values in each permutation. |
Value
A bounding value of higher criticism with (1 - alpha) confidence.
References
Jeng XJ, Zhang T, Tzeng J (2019). “Efficient Signal Inclusion With Genomic Applications.” Journal of the American Statistical Association, 1–23.
Examples
set.seed(10)
X <- matrix(runif(n = 10000, min = 0, max = 1), nrow = 100)
result <- bounding.seq(p.value = X)
Estimated Lambda
Description
Estimate upper and lower bound of new tuning region of regularization parameter Lambda.
Usage
est.lambda(cv.fit, pihat, p, cov.num = 0)
Arguments
cv.fit |
An object of either class "cv.glmnet" from glmnet::cv.glmnet() or class "cv.ncvreg" from ncvreg::cv.ncvreg(), which is a list generated by a cross-validation fit. |
pihat |
eatimated proprtion from HCTR::est.prop(). |
p |
Total number of variables, except for covariates. |
cov.num |
Number of covariates in model, default is 0. Covariate matrix, W, is assumed on the left side of variable matrix, X. The column index of covariates are before those of variables. |
Value
A list of (1) lambda.max, upper bound of new tuning region; (2) lambda.min, lower bound of new tuning region.
Examples
set.seed(10)
X <- matrix(rnorm(20000), nrow = 100)
beta <- rep(0, 200)
beta[1:100] <- 5
Y <- MASS::mvrnorm(n = 1, mu = X%*%beta, Sigma = diag(100))
fit <- glmnet::cv.glmnet(x = X, y = Y)
pihat <- 0.01
result <- est.lambda(cv.fit = fit, pihat = pihat, p = ncol(X))
Proportion Estimation
Description
Estimates false null hypothesis Proportion from multiple p-values using higher criticism test estimator.
Usage
est.prop(p.value, cn, adj = TRUE)
Arguments
p.value |
A sequence of p-values from test data, not including p-values from covariates. |
cn |
A value of bounding sequence generated by HCTR::bounding.seq(). |
adj |
A boolean algebra to decide whether to use adjusted Higher Criticism test statistic, the default value is TRUE. |
Value
An estimated proportion of false null hypothesis.
References
Meinshausen N, Rice J (2006). “Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses.” The Annals of Statistics, 34(1), 373–393.
Examples
set.seed(10)
X <- matrix(runif(n = 10000, min = 0, max = 1), nrow = 100)
result <- bounding.seq(p.value = X)
Y <- matrix(runif(n = 100, min = 0, max = 1), nrow = 100)
test <- est.prop(p.value = Y, cn = result)
Final Selection
Description
Returns the index of final selected variables in the final chosen model.
Usage
final.selection(cv.fit, pihat, p, cov.num = 0)
Arguments
cv.fit |
An object of either class "cv.glmnet" from glmnet::cv.glmnet() or class "cv.ncvreg" from ncvreg::cv.ncvreg(), which is a list generated by a cross-validation fit. |
pihat |
eatimated proprtion from HCTR::est.prop(). |
p |
Total number of variables, except for covariates. |
cov.num |
Number of covariates in model, default is 0. Covariate matrix, W, is assumed on the left side of variable matrix, X. The column index of covariates are before those of variables. |
Value
A sequence of index of final selected variables in the final chosen model.
Examples
set.seed(10)
X <- matrix(rnorm(20000), nrow = 100)
beta <- rep(0, 200)
beta[1:100] <- 5
Y <- MASS::mvrnorm(n = 1, mu = X%*%beta, Sigma = diag(100))
fit <- glmnet::cv.glmnet(x = X, y = Y)
pihat <- 0.01
result <- est.lambda(cv.fit = fit, pihat = pihat, p = ncol(X))
lambda.seq <- seq(from = result$lambda.min, to = result$lambda.max, length.out = 100)
# Note: The lambda sequences in glmnet and ncvreg are diffrent.
fit2 <- glmnet::cv.glmnet(x = X, y = Y, lambda = lambda.seq)
result2 <- final.selection(cv.fit = fit2, pihat = 0.01, p = ncol(X))
p-values in high-dimensional linear model
Description
Calculates p-values in high-dimentional linear models using multi-split method
Usage
highdim.p(Y, X, W = NULL, type, B = 100, fold.num)
Arguments
Y |
A numeric response vector, containing nobs variables. |
X |
An input matrix, of dimension nobs x nvars. |
W |
A covariate matrix, of dimension nobs x ncors, default is NULL. |
type |
Penalized regression type, valid parameters include "Lasso", "AdaLasso", "SCAD", and "MCP". |
B |
Multi-split times, default is 100. |
fold.num |
The number of cross validation folds. |
Value
A list of objects containing: (1) harmonic mean p-values; (2) original p-values; (3) index of selected samples; (4) index of selected variables
Examples
set.seed(10)
X <- matrix(rnorm(20000), nrow = 100)
beta <- rep(0, 200)
beta[1:100] <- 5
Y <- MASS::mvrnorm(n = 1, mu = X%*%beta, Sigma = diag(100))
result <- highdim.p(Y=Y, X=X, type = "Lasso", B = 2, fold.num = 10)
Multi-split Adaptive Lasso
Description
Multi-splitted variable selection using Adaptive Lasso
Usage
multi.adlasso(X, Y, covar.num = NULL, fold.num)
Arguments
X |
An input matrix, of dimension nobs x nvars. |
Y |
A numeric response vector, containing nobs variables. |
covar.num |
Number of covariates in model, default is NULL. |
fold.num |
The number of cross validation folds. |
Value
A list of two numeric objects of index of (1) selected and (2) unselected variables.
Multi-split Lasso
Description
Multi-splitted variable selection using Lasso
Usage
multi.lasso(X, Y, p.fac = NULL, fold.num)
Arguments
X |
An input matrix, of dimension nobs x nvars. |
Y |
A numeric response vector, containing nobs variables. |
p.fac |
A sequence of penalty factor applied on each variable. |
fold.num |
The number of cross validation folds. |
Value
A list of two numeric objects of index of (1) selected and (2) unselected variables.
Multi-split MCP
Description
Multi-splitted variable selection using MCP
Usage
multi.mcp(X, Y, p.fac = NULL, fold.num)
Arguments
X |
An input matrix, of dimension nobs x nvars. |
Y |
A numeric response vector, containing nobs variables. |
p.fac |
A sequence of penalty factor applied on each variable. |
fold.num |
The number of cross validation folds. |
Value
A list of two numeric objects of index of (1) selected and (2) unselected variables.
Multi-split SCAD
Description
Multi-splitted variable selection using SCAD
Usage
multi.scad(X, Y, p.fac = NULL, fold.num)
Arguments
X |
An input matrix, of dimension nobs x nvars. |
Y |
A numeric response vector, containing nobs variables. |
p.fac |
A sequence of penalty factor applied on each variable. |
fold.num |
The number of cross validation folds. |
Value
A list of two numeric objects of index of (1) selected and (2) unselected variables.
Permutation p-values
Description
Calculates
Usage
pmpv(Y, X, W = NULL, type, B = 100, fold.num = 10, perm.num = 1000)
Arguments
Y |
A numeric response vector, containing nobs variables. |
X |
An input matrix, of dimension nobs x nvars. |
W |
A covariate matrix, of dimension nobs x ncors, default is NULL. |
type |
Penalized regression type, valid parameters include "Lasso", "AdaLasso", "SCAD", and "MCP". |
B |
Multi-split times, default is 100. |
fold.num |
The number of cross validation folds, default is 10. |
perm.num |
Permutation times, default is 1000. |
Value
A matrix containing harmonic mean p-values from permutation.
Examples
set.seed(10)
X <- matrix(rnorm(20000), nrow = 100)
beta <- rep(0, 200)
beta[1:100] <- 5
Y <- MASS::mvrnorm(n = 1, mu = X%*%beta, Sigma = diag(100))
result <- pmpv(Y=Y, X=X, type = "Lasso", B = 2, fold.num = 10, perm.num = 10)