icmm {icmm}

Empirical Bayes Variable Selection

Description

Empirical Bayes variable selection via the ICM/M algorithm.

Usage

icmm(Y, X, event, b0.start, b.start, family = "gaussian", 
     ising.prior = FALSE, structure, estalpha = FALSE, 
     alpha = 0.5, maxiter = 100)

Arguments

Y

an (n*1) numeric matrix of responses.

X

an (n*p) numeric design matrix.

event

an (n*1) numeric matrix of status for censored data: 0=censored data, 1=event at time. event is required when family="cox".

b0.start

a starting value of intercept term (optional).

b.start

a (p*1) matrix of starting values for regression coefficients.

family

specification of the model. It can be one of these three models: "gaussian", "binomial", "cox". The default is family="gaussian".

ising.prior

a logical flag for Ising prior utilization. ising.prior=FALSE assumes no prior on structure among predictors. ising.prior=TRUE indicates incorporation of Ising prior to capture structure among predictors in modeling process.

structure

a data frame stores the information of structured predictors (need to specify when ising.prior=TRUE).

estalpha

a logical flag specifying whether to obtain alpha via ICM/M algorithm.

alpha

a scalar value of scale parameter in Laplace density (non-zero part of prior). The default value is 0.5.

maxiter

a maximum values of iterations for ICM/M algorithm.

Details

The main function for empirical Bayes variable selection. Iterative conditional modes/medians (ICM/M) is implemented in this function. The basic problem is to estimate regression coefficients in high-dimensional data (i.e., large p small n) and we assume that most coefficients are zero. This function also allows the prior of structure of covariates to be incorporated in the model.

Value

Return a list including elements

coef

a vector of model coefficients. The first element is an intercept term when specifying family="gaussian" or family="binomial".

iterations

number of iterations of ICM/M.

alpha

a scalar value of alpha.

postprob

a p-vector of local posterior probabilities or zeta.

Author(s)

Vitara Pungpapong, Min Zhang, Dabao Zhang

References

Pungpapong, V., Zhang, M. and Zhang, D. (2015). Selecting massive variables using an iterated conditional modes/medians algorithm. Electronic Journal of Statistics. 9:1243-1266. <doi:10.1214/15-EJS1034>.
Pungpapong, V., Zhang, M. and Zhang, D. (2020). Integrating Biological Knowledge Into Case-Control Analysis Through Iterated Conditional Modes/Medians Algorithm. Journal of Computational Biology. 27(7): 1171-1179. <doi:10.1089/cmb.2019.0319>.

See Also

get.ab, get.alpha, get.beta, get.beta.ising, get.pseudodata.binomial,
get.pseudodata.cox, get.sigma, get.wprior, get.zeta, get.zeta.ising

Examples

# Normal linear regression model
# With no prior on structure among predictors
data(simGaussian)
Y<-as.matrix(simGaussian[,1])
X<-as.matrix(simGaussian[,-1])
# Obtain initial values from lasso
data(initbetaGaussian)
initbeta<-as.matrix(initbetaGaussian)
result<-icmm(Y=Y, X=X, b.start=initbeta, family="gaussian", 
        ising.prior=FALSE, estalpha=FALSE, alpha=0.5, maxiter=100)
result$coef
result$iterations
result$alpha
result$wpost

# With prior on structure among predictors
data(linearrelation)
result<-icmm(Y=Y, X=X, b.start=initbeta, family="gaussian", 
        ising.prior=TRUE, structure=linearrelation, 
        estalpha=FALSE, alpha=0.5, maxiter=100)
result$coef
result$iterations
result$alpha
result$wpost

# Binary logistic regression model
data(simBinomial)
Y<-as.matrix(simBinomial[,1])
X<-as.matrix(simBinomial[,-1])
p<-dim(X)[2]
# Obtain initial values from lasso
data(initbetaBinomial)
initbeta<-as.matrix(initbetaBinomial)
result<-icmm(Y=Y, X=X, b0.start=0, b.start=initbeta, family="binomial", 
        ising.prior=TRUE, structure=linearrelation, estalpha=FALSE, 
        alpha=0.5, maxiter=100)
result$coef
result$iterations
result$alpha
result$wpost

# Cox's model
data(simCox)
Y<-as.matrix(simCox[,1])
event<-as.matrix(simCox[,2])
X<-as.matrix(simCox[,-(1:2)])
# Obtain initial values from lasso
data(initbetaCox)
initbeta<-as.matrix(initbetaCox)
result <- icmm(Y=Y, X=X, event=event, b.start=initbeta, family="cox",
          ising.prior=TRUE, structure=linearrelation, estalpha=FALSE,
          alpha=0.5, maxiter=100)
result$coef
result$iterations
result$alpha
result$wpost