interep (version 0.1.0)

interep: fit a generalized estimating equation with given lambda

Description

This function makes predictions for generalized estimating equation with a given value of lambda. Typical usage is to have the cv.interep function compute the optimal lambda, then provide it to the interep function.

Usage

interep(e, z, y, response = "continuous", initiation = NULL,
  alpha.i = 1, lam1, lam2, maxits = 30, corre)

Arguments

e

matrix of environment factors.

z

matrix of omics factors. In the case study, the omics measurements are lipidomics data.

y

the longitudinal response.

response

type of the longitudinal response, the default is continuous.

initiation

the method for iniating the coefficient vector. The default is lasso.

alpha.i

the elastic-net mixing parameter. The program adopts the elastic-net to choose initial values of the coefficient vector. alpha.i is the elastic-net mixing parameter, with 0 \(\le\) alpha.i \(\le\) 1. alpha.i=1 is the lasso penalty, and alpha.i=0 is the ridge penalty. The default is 1. If the user chooses a method other than elastic-net to initialize coefficients, alpha.i will be ignored.

lam1

the tuning parameter lambda1 for individual predictors.

lam2

the tuning parameter lambda2 for interactions.

maxits

the maximum number of iterations that is used in the estimation algorithm. The default value is 30

corre

the working correlation structure that is used in the estimation algorithm. interep provides three choices for the working correlation structure: "AR-1", "independece" and "exchangeable".

Value

coef

the coefficient vector.

Details

When dealing with predictors with both main effects and interactions, this function requires two optimal tuning parameters, \(\lambda_{1}\) and \(\lambda_{2}\); when there are only main effects in the predictors, this function only requires \(\lambda_{1}\),

References

Zhou, F., Wang, W., Jiang, Y. and Wu, C. (2018+). Variable selection for interactions in longitudinal lipidomics studies.

Wu, C., Zhong, P. & Cui, Y. (2018). Additive varying-coefficient model for nonlinear gene-environment interactions. Statistical Applications in Genetics and Molecular Biology, 17(2)

Wu, C., Jiang, Y., Ren, J., Cui, Y. and Ma, S. (2018). Dissecting gene-environment interactions: a penalized robust approach accounting for hierarchical structures. Statistics in Medicine, 37:437<U+2013>456

Wu, C., Shi, X., Cui, Y. and Ma, S. (2015) A penalized robust semiparametric approach for gene-environment interactions. Statistics in Medicine, 34 (30): 4016<U+2013>4030

Wu, C., Cui, Y. and Ma, S. (2014) Integrative analysis of gene-environment interactions under a multi-response partially linear varying coefficient model. Statistics in Medicine, 33 (28): 4988<U+2013>4498

Wu, C. and Cui Y. (2013) A novel method for identifying nonlinear gene-environment interactions in case-control association studies. Human Genetics, 132 (12): 1413<U+2013>1425

Examples

# NOT RUN {
data("dat")
e=dat$e
z=dat$z
y=dat$y
index=dat$index
b = interep(e, z, y, response="continuous", alpha.i=1, lam1=dat$lam1, lam2=dat$lam2,
maxits=50, corre="AR-1")
pos = which(b != 0)
tp = length(intersect(index, pos))
fp = length(pos) - tp
list(tp=tp, fp=fp)

# }