dmcp: This function obtains the first derivative function of MCP...

In interep: Interaction Analysis of Repeated Measure Data

This function obtains the first derivative function of MCP (Minimax Concave Penalty)

Description

This function obtains the first derivative function of MCP (Minimax Concave Penalty)

Usage

dmcp(theta, lambda, gamma = 3)

Arguments

theta	a coefficient vector.
lambda	the tuning parameter.
gamma	the regularization parameter in MCP (Minimax Concave Penalty). It balances between the unbiasedness and concavity of MCP.

Details

Rigorously speaking, the regularization parametre \gamma needs to be obtained via a data-driven approach. Published studies suggest experimenting with a few values, such as 1.8, 3, 4.5, 6, and 10, then fixing its value. In our numerical study, we have examined this sequence and found that the results are not sensitive to the choice of value of \gamma, and set the value at 3. In practice, to be prudent, values other than 3 should also be investigated. Similar discussions can be found in the references below.

Value

the first derivative of MCP function.

References

Ren, J., Du, Y., Li, S., Ma, S., Jiang, Y. and Wu, C. (2019). Robust network-based regularization and variable selection for high-dimensional genomic data in cancer prognosis. Genetic epidemiology, 43(3), 276-291 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/gepi.22194")}

Ren, J., Jung, L., Du, Y., Wu, C., Jiang, Y. and Liu, J. (2019). regnet: Network-Based Regularization for Generalized Linear Models. R package, version 0.4.0

Wu, C., Zhang, Q., Jiang, Y. and Ma, S. (2018). Robust network-based analysis of the associations between (epi) genetic measurements. Journal of multivariate analysis, 168, 119-130 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jmva.2018.06.009")}

Ren, J., He, T., Li, Y., Liu, S., Du, Y., Jiang, Y. and Wu, C. (2017). Network-based regularization for high dimensional SNP data in the case–control study of Type 2 diabetes. BMC genetics, 18(1), 44 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1186/s12863-017-0495-5")}

Examples

theta=runif(20,-5,5)
lambda=1
dmcp(theta,lambda,gamma=3)

interep documentation built on May 29, 2024, 8:52 a.m.