bic.PTReg {GEInter}

BIC for PTReg

Description

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

Usage

bic.PTReg(
  G,
  E,
  Y,
  lambda1_set,
  lambda2_set,
  gamma1,
  gamma2,
  max_init,
  h = NULL,
  tau = 0.4,
  mu = 2.5,
  family = c("continuous", "survival")
)

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 family="continuous". For family="survival", 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.

lambda1_set

A user supplied lambda sequence for minimax concave penalty (MCP) accommodating main G effect selection.

lambda2_set

A user supplied lambda sequence for MCP accommodating interaction selection.

gamma1

The regularization parameter of the MCP penalty corresponding to G effects.

gamma2

The regularization parameter of the MCP penalty corresponding to G-E interactions.

max_init

The number of initializations.

h

The number of the trimmed samples if the parameter mu is not given.

tau

The threshold value used in stability selection.

mu

The parameter for screening outliers with extreme absolute residuals if the number of the trimmed samples h is not given.

family

Response type of Y (see above).

Value

An object with S3 class "bic.PTReg" 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.

intercept

Matrix of the intercept estimate, each column corresponds to one combination of (lambda1,lambda2).

df

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

BIC

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

family

The same as input family.

intercept_estimate

Final intercept estimate using Bayesian Information Criterion.

alpha_estimate

Final alpha estimate using Bayesian Information Criterion.

beta_estimate

Final beta estimate using Bayesian Information Criterion.

lambda_combine

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

References

Yaqing Xu, Mengyun Wu, Shuangge Ma, and Syed Ejaz Ahmed. Robust gene-environment interaction analysis using penalized trimmed regression. Journal of Statistical Computation and Simulation, 88(18):3502-3528, 2018.

Examples

sigmaG<-AR(rho=0.3,p=30)
sigmaE<-AR(rho=0.3,p=3)
set.seed(300)
G=MASS::mvrnorm(150,rep(0,30),sigmaG)
EC=MASS::mvrnorm(150,rep(0,2),sigmaE[1:2,1:2])
ED = matrix(rbinom((150),1,0.6),150,1)
E=cbind(EC,ED)
alpha=runif(3,0.8,1.5)
beta=matrix(0,4,30)
beta[1,1:4]=runif(4,1,1.5)
beta[2,c(1,2)]=runif(2,1,1.5)
lambda1_set=lambda2_set=c(0.2,0.25,0.3,0.35,0.4,0.5)


#continuous response with outliers/contaminations in response variable
y1=simulated_data(G,E,alpha,beta,error=c(rnorm(140),rcauchy(10,0,5)),family="continuous")
fit1<-bic.PTReg(G,E,y1,lambda1_set,lambda2_set,gamma1=6,gamma2=6,
max_init=50,tau=0.6,mu=2.5,family="continuous")
coefficients1=coefficients(fit1)
y_predict=predict(fit1,E,G)
plot(fit1)

# survival with Normal error
y2=simulated_data(G,E,alpha,beta,rnorm(150,0,1),family="survival",0.7,0.9)
fit2<-bic.PTReg(G,E,y2,lambda1_set,lambda2_set,gamma1=6,gamma2=6,
max_init=50,tau=0.6,mu=2.5,family="survival")
coefficients2=coefficients(fit2)
y_predict=predict(fit2,E,G)
plot(fit2)