emBayes {emBayes}

fit a model with given tuning parameters

Description

This function performs penalized variable selection based on spike-and-slab quantile LASSO (ssQLASSO) or spike-and-slab LASSO (ssLASSO). Typical usage is to first obtain the optimal spike scale and slab scale using cross-validation, then specify them in the 'emBayes' function.

Usage

emBayes(y, clin = NULL, X, quant, s0, s1, func, error = 0.01, maxiter = 100)

Arguments

y

a vector of response variable.

clin

a matrix of clinical factors. It has default value NULL.

X

a matrix of genetic factors.

quant

value of quantile.

s0

value of the spike scale s_{0}.

s1

value of the slab scale s_{1}.

func

methods to perform variable selection. Two choices are available: "ssLASSO" and "ssQLASSO".

error

cutoff value for determining convergence. The algorithm reaches convergence if the difference in the expected log-likelihood of two iterations is less than the value of error. The default value is 0.01.

maxiter

the maximum number of iterations that is used in the estimation algorithm. The default value is 200.

Details

The current version of emBayes supports two types of methods: "ssLASSO" and "ssQLASSO".

• ssLASSO: spike-and-slab LASSO fits a Bayesian linear regression through the EM algorithm.

• ssQLASSO: spike-and-slab quantile LASSO fits a Bayesian quantile regression (based on asymmetric Laplace distribution) through the EM algorithm.

Users can choose the desired method by setting func="ssLASSO" or "ssQLASSO".

Value

A list with components:

alpha

a vector containing the estimated intercept and clinical coefficients.

intercept

value of the estimated intercept.

clin.coe

a vector of estimated clinical coefficients.

beta

a vector of estimated beta coefficients.

sigma

value of estimated asymmetric Laplace distribution scale parameter \sigma.

theta

value of estimated probability parameter \theta.

iter

value of number of iterations.

ll

a vector of expectation of likelihood at each iteration.

Examples

data(data)
##load the clinical factors, genetic factors, response and quantile data
clin=data$clin
X=data$X
y=data$y
quant=data$quant

##generate tuning vectors of desired range 
t0 <- seq(0.01,0.015,length.out=2)
t1 <- seq(0.1,0.5,length.out=2)

##perform cross-validation and obtain tuning parameters based on check loss
CV <- cv.emBayes(y,clin,X,quant,t0,t1,k=5,func="ssQLASSO",error=0.01,maxiter=200)
s0 <- CV$CL.s0
s1 <- CV$CL.s1

##perform BQLSS under optimal tuning and calculate value of TP and FP for selecting beta 
EM <- emBayes(y,clin,X,quant,s0,s1,func="ssQLASSO",error=0.01,maxiter=200)
fit <- EM$beta
coef <- data$coef
tp <- sum(fit[coef!=0]!=0)
fp <- sum(fit[coef==0]!=0)
list(tp=tp,fp=fp)