CorReg (version 1.0.5)

correg: Linear regression using CorReg's method, with variable selection.

Description

Computes three regression models: Complete (regression on the wole dataset X), marginal (regression using only independant covariates: X[,colSums(Z)==0]) and plug-in (sequential regression based on the marginal model and then use redundant covariates by plug-in, with a regression on the residuals of the marginal model by the residuals of the sub-regressions). Each regression can be computed with variable selection (for example the lasso).

Usage

correg(X = NULL, Y = NULL, Z = NULL, B = NULL, compl = TRUE,
  expl = FALSE, pred = FALSE, select = "lar", criterion = c("MSE",
  "BIC"), X_test = NULL, Y_test = NULL, intercept = TRUE, K = 10,
  groupe = NULL, Amax = NULL, lambda = 1, alpha = NULL, g = 5)

Arguments

X

The data matrix (covariates) without the intercept

Y

The response variable vector

Z

The structure (adjacency matrix) between the covariates

B

The (d+1)xd matrix associated to Z and that contains the parameters of the sub-regressions

compl

(boolean) to decide if the complete modele is computed

expl

(boolean) to decide if the explicative model is in the output

pred

(boolean) to decide if the predictive model is computed

select

selection method in ("lar","lasso","forward.stagewise","stepwise", "elasticnet", "NULL","ridge","adalasso","clere","spikeslab")

criterion

the criterion used to compare the models

X_test

validation sample

Y_test

response for the validation sample

intercept

boolean. If FALSE intercept will be set to 0 in each model.

K

the number of clusters for cross-validation

groupe

a vector of integer to define the groups used for cross-validation (to obtain a reproductible result)

Amax

the maximum number of non-zero coefficients in the final model

lambda

(optional) parameter for elasticnet (quadratic penalty) if select="elasticnet"

alpha

Coefficients of the explicative model to coerce the predictive step. if not NULL explicative step is not computed.

g

(optional) number of group of variables for clere if select="clere"

Value

• a list that contains:
• compl
  Results associated to the regression on X
• expl
  Results associated to the marginal regression on explicative covariates (defined by colSums(Z)==0)
• pred
  Results associated to the plug-in regression model.
• compl$A
  Vector of the regression coefficients (the first is the intercept).(also have expl$A and pred$A)
• compl$BIC
  BIC criterion associated to the model (also have expl$A and pred$A)
• compl$AIC
  AIC criterion associated to the model (also have expl$A)
• compl$CVMSE
  Cross-validated MSE associated to the model (also have expl$A)

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)

   #Regression coefficients estimation
    select="lar"#variable selection with lasso (using lar algorithm)
   resY=correg(X=X_appr,Y=Y_appr,Z=TrueZ,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")