R/CorReg-package.R

In CorReg: Linear Regression Based on Linear Structure Between Variables

#' @import Rcpp lars glmnet elasticnet Matrix
#' @import glmnet MASS rpart corrplot mvtnorm
# ' @import parcor clere spikeslab rtkpp
#' @rawNamespace import(mclust, except = "dmvnorm")
#' @importFrom grDevices col2rgb gray rgb colors
#' @importFrom utils install.packages
#' @importFrom graphics abline arrows barplot boxplot hist legend matplot par plot points rect text title
#' @importFrom stats AIC BIC aov as.formula chisq.test coef confint.default kruskal.test cor dnorm lm pf predict qnorm qt rbinom rgamma rmultinom rnorm rpois rstudent runif sd var
#' @importFrom methods as
#' 
#' @useDynLib CorReg
#' 
#' 
#' @name CorReg-package
#' @aliases CorReg-package
#' @docType package
#' @title 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 \url{http://www.correg.org} for article and Phd Thesis about CorReg.
#' 
#' @author Clement THERY <clement.thery@@arcelormittal.com>
#'
#' @references Model-based covariable decorrelation in linear regression (CorReg): application to missing data and to steel industry. C Thery - 2015. 
#' See \url{http://www.theses.fr/2015LIL10060} to read the associated PhD Thesis.
#' 
#' @keywords package
#'
#'
#' @examples
#' 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")
#' 
NULL
# la puissance CorReg!!!!!!!!!