bic.BLMCP {GEInter}

BIC for BLMCP

Description

Selects a point along the regularization path of a fitted BLMCP object according to the BIC.

Usage

bic.BLMCP(
  G,
  E,
  Y,
  weight = NULL,
  lambda1_set = NULL,
  lambda2_set = NULL,
  nlambda1 = 20,
  nlambda2 = 20,
  gamma1 = 6,
  gamma2 = 6,
  max_iter = 200
)

Arguments

G

Input matrix of p genetic (G) measurements consisting of n rows. Each row is an observation vector.

E

Input matrix of q environmental (E) risk factors. Each row is an observation vector.

Y

Response variable. A quantitative vector for continuous response. For survival response, Y should be a two-column matrix with the first column being the log(survival time) and the second column being the censoring indicator. The indicator is a binary variable, with "1" indicating dead, and "0" indicating right censored.

weight

Observation weights.

lambda1_set

A user supplied lambda sequence for group minimax concave penalty (MCP), where each main G effect and its corresponding interactions are regarded as a group.

lambda2_set

A user supplied lambda sequence for MCP accommodating interaction selection.

nlambda1

The number of lambda1 values.

nlambda2

The number of lambda2 values.

gamma1

The regularization parameter of the group MCP penalty.

gamma2

The regularization parameter of the MCP penalty.

max_iter

Maximum number of iterations.

Value

An object with S3 class "bic.BLMCP" is returned, which is a list with the ingredients of the BIC fit.

call

The call that produced this object.

alpha

The matrix of the coefficients for main E effects, each column corresponds to one combination of (lambda1,lambda2).

beta

The coefficients for main G effects and G-E interactions, each column corresponds to one combination of (lambda1,lambda2). For each column, the first element is the first G effect and the second to (q+1) elements are the interactions for the first G factor, and so on.

df

The number of nonzeros for each value of (lambda1,lambda2).

BIC

Bayesian Information Criterion for each value of (lambda1,lambda2).

alpha_estimate

Final alpha estimate using Bayesian Information Criterion.

beta_estimate

Final beta estimate using Bayesian Information Criterion.

lambda_combine

The matrix of (lambda1, lambda2), with the first column being the values of lambda1, the second being the values of lambda2.

References

Mengyun Wu, Yangguang Zang, Sanguo Zhang, Jian Huang, and Shuangge Ma. Accommodating missingness in environmental measurements in gene-environment interaction analysis. Genetic Epidemiology, 41(6):523-554, 2017.
Jin Liu, Jian Huang, Yawei Zhang, Qing Lan, Nathaniel Rothman, Tongzhang Zheng, and Shuangge Ma. Identification of gene-environment interactions in cancer studies using penalization. Genomics, 102(4):189-194, 2013.

See Also

predict, coef and plot methods, and the BLMCP function.

Examples

set.seed(100)
sigmaG=AR(0.3,50)
G=MASS::mvrnorm(150,rep(0,50),sigmaG)
E=matrix(rnorm(150*5),150,5)
E[,2]=E[,2]>0;E[,3]=E[,3]>0
alpha=runif(5,2,3)
beta=matrix(0,5+1,50);beta[1,1:8]=runif(8,2,3)
beta[2:4,1]=runif(3,2,3)
beta[2:3,2]=runif(2,2,3)
beta[5,3]=runif(1,2,3)

# continuous with Normal error
y1=simulated_data(G=G,E=E,alpha=alpha,beta=beta,error=rnorm(150),family="continuous")

# survival with Normal error
y2=simulated_data(G,E,alpha,beta,rnorm(150,0,1),family="survival",0.8,1)

# continuous
fit1<-bic.BLMCP(G,E,y1,weight=NULL,lambda1_set=NULL,lambda2_set=NULL,
nlambda1=10,nlambda2=10,gamma1=6,gamma2=6,max_iter=200)
coef1=coef(fit1)
y1_hat=predict(fit1,E,G)
plot(fit1)


## survival
fit2<-bic.BLMCP(G,E,y2,weight=NULL,lambda1_set=NULL,lambda2_set=NULL,
nlambda1=20,nlambda2=20,gamma1=6,gamma2=6,max_iter=200)
coef2=coef(fit2)
y2_hat=predict(fit2,E,G)
plot(fit2)