CorReg (version 1.1.1)

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

Model-based covariable decorrelation in linear regression (CorReg): application to missing data and to steel industry. C Thery - 2015. see http://www.theses.fr/2015LIL10060 to read the associated PhD Thesis.

Examples

   ## Not run: 
# 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$Z#True generative structure (binary adjacency matrix)
#    #Z_i,j=1 means that Xj linearly depends on Xi
#    
#    #density estimation for the MCMC (with Gaussian Mixtures)
#    density=density_estimation(X=X_appr,nbclustmax=10,detailed=TRUE)
#    Bic_null_vect=density$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")
#    ## End(Not run)