correg: Linear regression using CorReg's method, with variable...
In CorReg: Linear Regression Based on Linear Structure Between Variables

Description Usage Arguments Value Examples

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).

correg(
  X = NULL,
  Y = NULL,
  Z = NULL,
  B = NULL,
  compl = TRUE,
  expl = FALSE,
  pred = FALSE,
  select = c("lar", "lasso", "forward.stagewise", "stepwise", "elasticnet", "NULL",
    "ridge", "adalasso", "clere", "spikeslab"),
  criterion = c("MSE", "BIC"),
  X_test = NULL,
  Y_test = NULL,
  intercept = TRUE,
  K = 10,
  groupe = NULL,
  Amax = NULL,
  lambda = 1,
  alpha = NULL,
  g = 5
)

`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 or ridge (quadratic penalty) if select="elasticnet" or "ridge".
`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"

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)

# 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

barplot(as.matrix(MSE), main = "MSE on validation dataset", sub = paste("select =", select))
abline(h = MSE_complete, col = "red")