CorReg (version 1.2.17)

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 http://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 {
set.seed(1)
# 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 = 8, 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_true = BicZ(X = X_appr, Z = TrueZ, Bic_null_vect = Bic_null_vect)
sum(bicopt_vect)
sum(bicopt_true)

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

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

# 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 = "Results obtained without selection method (lasso and other are available)")
abline(h = MSE_complete, col = "red")

# }