equSA (version 1.2.1)

MNR: Markov Neighborhood Regression for High-Dimensional Inference.

Description

Construct confidence intervals and assess p-values in high-dimensional linear and generalized linear models.

Usage

MNR(x,y,family='gaussian',penalty='lasso',tune='bic',alpha1=0.1,alpha2=0.05,level=0.95)

Arguments

x

The design matrix, of dimensions \(n\)x\(p\), without an intercept. Each row is an observation vector.

y

The response vector of dimension \(n\)x\(1\). Quantitative for family='gaussian', binary (0-1) for family='binomial'. For family='cox', y should be an object of class Surv, as provided by the function Surv() in the package survival.

family

Response type (see above).

penalty

The penalty to be applied in the regularized likelihood subproblems. 'lasso' (the default), 'MCP', or 'SCAD' are provided. See package SIS for detail.

tune

Method for tuning the regularization parameter of the penalized likelihood subproblems and of the final model selected by (I)SIS. Options include tune='bic', tune='ebic', tune='aic', and tune='cv'.

alpha1

The significance level of correlation screening in the \(\psi\)-learning algorithm, see R package equSA for detail. In general, a high significance level of correlation screening will lead to a slightly large separator set, which reduces the risk of missing important variables in the conditioning set. In general, including a few false variables in the conditioning set will not hurt much the accuracy of the \(\psi\)-partial correlation coefficient, the default value is 0.1.

alpha2

The significance level of \(\psi\)-partial correlation coefficient screening for estimating the adjacency matrix, see equSA, the default value is 0.05.

level

the confidence level required, the default value is 0.95

Value

CI

Estimated confidence intervals for all coefficients.

coef

\(p\)x\(1\) estimated regression coefficients for all variables.

pvalue

\(p\)x\(1\) estimated p-values for all variables.

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References

Liang, F., Xue, J. and Jia, B. (2018). Markov Neighborhood Regression for High-Dimensional Inference. Submitted to J. Amer. Statist. Assoc.

Examples

# NOT RUN {
 
# }
# NOT RUN {
library(equSA)
p <- 500
coef_true <- rep(0,p)
coef_true[1:5] <- c(2,4,-3,-5,10)
coef <- c(1,coef_true)
data <- SimMNR(n = 200, p = 500, coef = coef, family = "gaussian")
MNR(data$x, data$y, family = "gaussian")

# }
# NOT RUN {
# }