CorReg (version 1.0.5)

CorReg-package: Quick tutorial for CorReg package

Description

Sequential linear regression based on a structural equation model(explicit correlations). It permits to face highly correlated datasets. We first search for an explicit model of correlations within the covariates by linear regression, then this structure is interpreted and used to reduce dimension and correlations for the main regression on the response variable.

Details

CorReg: see www.correg.org for article and Phd Thesis about CorReg.

References

coming soon. see http://www.correg.org to read the associated PhD Thesis.

Examples

require(CorReg)
   #dataset generation
   base=mixture_generator(n=15,p=10,ratio=0.4,tp1=1,tp2=1,tp3=1,positive=0.5,
                          R2Y=0.8,R2=0.9,scale=TRUE,max_compl=3,lambda=1)
   X_appr=base$X_appr #learning sample
   Y_appr=base$Y_appr #response variable for the learning sample
   Y_test=base$Y_test #responsee variable for the validation sample
   X_test=base$X_test #validation sample

   TrueZ=base$Z#True generative structure (binary adjacency matrix)

   #density estimation for the MCMC (with Gaussian Mixtures)
   density=density_estimation(X=X_appr,nbclustmax=10,detailed=TRUE)
   Bic_null_vect=density$BIC_vect# vector of the BIC found (1 value per covariate)

   #MCMC to find the structure
   res=structureFinder(X=X_appr,verbose=0,reject=0,Maxiter=900,
               nbini=20,candidates=-1,Bic_null_vect=Bic_null_vect,star=TRUE,p1max=15,clean=TRUE)
   hatZ=res$Z_opt #found structure (adjacency matrix)
   hatBic=res$bic_opt #associated BIC

   #BIC comparison between true and found structure
   bicopt_vect=BicZ(X=X_appr,Z=hatZ,Bic_null_vect=Bic_null_vect)
   bicopt_vrai=BicZ(X=X_appr,Z=TrueZ,Bic_null_vect=Bic_null_vect)
   sum(bicopt_vect);sum(bicopt_vrai)

   #Structure comparison
   compZ=compare_struct(trueZ=TrueZ,Zalgo=hatZ)#qualitative comparison

   #interpretation of found and true structure ordered by increasing R2
   readZ(Z=hatZ,crit="R2",X=X_appr,output="all",order=1)# <NA>line : name of subregressed covariate
   readZ(Z=TrueZ,crit="R2",X=X_appr,output="all",order=1)# <NA>line : name of subregressed covariate

   #Regression coefficients estimation
    select="NULL"#without variable selection (otherwise, choose "lar" for example)
   resY=correg(X=X_appr,Y=Y_appr,Z=hatZ,compl=TRUE,expl=TRUE,pred=TRUE,
               select=select,K=10)

   #MSE computation
   MSE_complete=MSE_loc(Y=Y_test,X=X_test,A=resY$compl$A)#classical model on X
   MSE_marginal=MSE_loc(Y=Y_test,X=X_test,A=resY$expl$A)#reduced model without correlations
   MSE_plugin=MSE_loc(Y=Y_test,X=X_test,A=resY$pred$A)#plug-in model
   MSE_true=MSE_loc(Y=Y_test,X=X_test,A=base$A)# True model


   #MSE comparison
   MSE=data.frame(MSE_complete,MSE_marginal,MSE_plugin,MSE_true)
   MSE#estimated structure
   compZ$true_left;compZ$false_left
   barplot(as.matrix(MSE),main="MSE on validation dataset", sub=paste("select=",select))
  abline(h=MSE_complete,col="red")