postSelect {ecpc}

Perform posterior selection

Description

Given data and estimated parameters from a previously fit multi-group ridge penalised model, perform posterior selection to find a parsimonious model.

Usage

postSelect(object, X, Y, beta=NULL, intrcpt = 0, penfctr=NULL, 
           postselection = c("elnet,dense","elnet,sparse","BRmarginal,dense",
           "BRmarginal,sparse","DSS"), maxsel = 30, penalties=NULL, 
           model=c("linear","logistic","cox"), tauglobal=NULL, sigmahat = NULL, 
           muhatp = 0, X2 = NULL, Y2 = NULL, silent=FALSE)

Arguments

object

An 'ecpc' object returned by ecpc.

X

Observed data: data of p penalised and unpenalised covariates on n samples; (nxp)-dimensional matrix.

Y

Response data; n-dimensional vector (linear, logistic) or Surv object (Cox survival).

beta

Estimated regression coefficients from the previously fit model.

intrcpt

Estimated intercept from the previously fit model.

penfctr

As in glmnet penalty.factor; p-dimensional vector with a 0 if covariate is not penalised, 1 if covariate is penalised.

postselection

Posterior selection method to be used.

maxsel

Maximum number of covariates to be selected a posteriori, in addition to all unpenalised covariates. If maxsel is a vector, multiple parsimonious models are returned.

penalties

Estimated multi-group ridge penalties for all penalised covariates from the previously fit model; vector of length the number of penalised covariates.

model

Type of model for the response.

tauglobal

Estimated global prior variance from the previously fit model.

sigmahat

(linear model only) estimated variance parameter from the previously fit model.

muhatp

(optional) Estimated multi-group prior means for the penalised covariates from the previously fit model.

X2

(optional) Independent observed data.

Y2

(optional) Independent response data.

silent

Should output messages be suppressed (default FALSE)?

Value

A list with the following elements:

betaPost

Estimated regression coefficients for parsimonious models. If 'maxsel' is a vector, 'betaPost' is a matrix with each column the vector estimate corresponding to the maximum number of selected covariates given in 'maxsel'.

a0

Estimated intercept coefficient for parsimonious models.

YpredPost

If independent test set 'X2' is given, posterior selection model predictions for the test set.

MSEPost

If independent test set 'X2', 'Y2' is given, mean squared error of the posterior selection model predictions.

Examples

#####################
# Simulate toy data #
#####################
p<-300 #number of covariates
n<-100 #sample size training data set
n2<-100 #sample size test data set

#simulate all betas i.i.d. from beta_k~N(mean=0,sd=sqrt(0.1)):
muBeta<-0 #prior mean
varBeta<-0.1 #prior variance
indT1<-rep(1,p) #vector with group numbers all 1 (all simulated from same normal distribution)

#simulate test and training data sets:
Dat<-simDat(n,p,n2,muBeta,varBeta,indT1,sigma=1,model='linear') 
str(Dat) #Dat contains centered observed data, response data and regression coefficients

####################################### 
# Fit ecpc and perform post-selection #
#######################################
fit <- ecpc(Y=Dat$Y,X=Dat$Xctd,groupsets=list(list(1:p)),
            groupsets.grouplvl=list(NULL),
            hypershrinkage=c("none"),
            model="linear",maxsel=c(5,10,15,20),
            Y2=Dat$Y2,X2=Dat$X2ctd)

fitPost <- postSelect(fit, Y=Dat$Y, X=Dat$Xctd, maxsel = c(5,10,15,20))
summary(fit$betaPost[,1]); summary(fitPost$betaPost[,1])