CorReg (version 0.14.3)

CorReg-package: Algorithms for regression with correlated covariates

Description

Sequential linear regression based on a structural equation model (explicit correlations). It permits to face highly correlated datasets.

Examples

require(CorReg)
base=mixture_generator(n=25,p=30,ratio=0.4,sigma_X=0.001,tp1=1,tp2=1,tp3=1)
X_appr=base$X_appr
Y_appr=base$Y_appr
Y_test=base$Y_test
X_test=base$X_test
TrueZ=base$Z#True generative structure (binary matrix)
Trueclust=base$mixmod#classes of the gaussian mixtures (orthogonal covariates only)

mixmod=density_estimation(X=X_appr,nbclustmax=10,detailed=TRUE)
BIC_empty_vect=mixmod$BIC_vect
BIC_empty=sum(BIC_empty_vect)

TrueBIC_vect=BicZ(X=X_appr,Z=TrueZ,Bic_null_vect=BIC_empty_vect)
TrueBIC=sum(TrueBIC_vect)

correl=cor(X_appr)#Correlations matrix will weight initialisation

Zini=Winitial(W=correl,X=X_appr)#generates initial Z for the Markov chain
BIC_ini_vect=BicZ(X=X_appr,Z=Zini,Bic_null_vect=BIC_empty_vect)
Bic_ini=sum(BIC_ini_vect)

#one chain
res=searchZ(X=X_appr,Z=Zini,Maxiter=100,Bic_null_vect=BIC_empty_vect)
#multiple chain
#res=searchZ(X=X_appr,Z=NULL,nbini=20,Maxiter=100,Bic_null_vect=BIC_empty_vect)

hatZ=res$Z_opt
hatBic=res$bic_opt
sum(BicZ(X=X_appr,Z=hatZ,Bic_null_vect=BIC_empty_vect))#same value

readZ(Z=hatZ,crit="R2",X=X_appr,output="all",order=1)# <NA>line : name of subregressed covariate

compZ=compare_struct(trueZ=TrueZ,Zalgo=hatZ)#qualitative comparison
select="lar"#LASSO with the Least Angle Regression algorithm to find the best model
resY=correg(X=X_appr,Y=Y_appr,Z=hatZ,compl=TRUE,expl=TRUE,pred=TRUE,
               select=select,K=10,returning=TRUE)

MSE_complete=MSE_loc(Y=Y_test,X=X_test,intercept=TRUE,A=resY$compl$A)
MSE_explicative=MSE_loc(Y=Y_test,X=X_test,intercept=TRUE,A=resY$expl$A)
MSE_predictive=MSE_loc(Y=Y_test,X=X_test,intercept=TRUE,A=resY$pred$A)

MSE=data.frame(MSE_complete,MSE_explicative,MSE_predictive)
#MSE
#barplot(as.matrix(MSE),main="MSE on validation dataset", sub=paste("select=",select))