R/ebic.lm.bsreg.R

In MXM: Feature Selection (Including Multiple Solutions) and Bayesian Networks

ebic.lm.bsreg <- function(target, dataset, gam = NULL, wei = NULL) {
  
  dm <- dim(dataset)
  n <- dm[1]  ## sample size 
  p <- dm[2]  ## number of variables
  if ( p > n ) {
    res <- paste("The number of variables is higher than the sample size. No backward procedure was attempted")
    
  } else {
    
    tic <- proc.time()
    logn <- log(n)
    if ( is.null(gam) ) {
      con <- 2 - log(p) / logn
    } else con <- 2 * gam
    if ( (con) < 0 )  con <- 0
    tool <- numeric(p + 1)
    
    ini <- lm( target ~.,  data = dataset, weights = wei )
    bic0 <-  BIC(ini)   ## initial bic  
    tool[1] <- bic0
    bic <- numeric(p)
    M <- dim(dataset)[2] - 1
    
    if ( M == 0 ) {
      mod <- lm( target ~ 1, weights = wei)
      bic <- BIC(mod)      
      if (bic0 - bic < 0 ) {
        info <- matrix( 0, nrow = 0, ncol = 2 )
        mat <- matrix( c(1, bic - bic0), ncol = 2 )
      } else {
        info <- matrix( c(1, bic), ncol = 2 )
        mat <- matrix(0, nrow = 0, ncol = 2 )
      }
      runtime <- proc.time() - tic
      colnames(info) <- c("Variables", "eBIC")
      colnames(mat) <- c("Variables", "eBIC")
      res <- list(runtime = runtime, info = info, mat = mat )
      
    } else { 
      ###########   
    for (j in 1:p) {
      mod <- lm( target ~.,  data = dataset[, -j, drop = FALSE], weights = wei)
      bic[j] <- BIC(mod) + con * lchoose(p, M)
    }
    
    mat <- cbind(1:p, bic )
    sel <- which.min( mat[, 2] )
    info <- matrix( c(0, 0), ncol = 2 )
    colnames(info) <- c("Variables", "eBIC")
    colnames(mat) <- c("Variables", "eBIC")
    
    if ( bic0 - mat[sel, 2] < 0  ) {
      runtime <- proc.time() - tic		
      info <- info[ info[, 1] > 0, , drop = FALSE]
      res <- list(runtime = runtime, info = info, mat = mat ) 
      
    } else {
      info[1, ] <- mat[sel, ]
      mat <- mat[-sel, , drop = FALSE] 
      dat <- dataset[, -sel, drop = FALSE] 
      tool[2] <- info[1, 2]
    
    i <- 2  
    
    if ( tool[2] != 0 ) {
      
      while ( tool[i - 1] - tool[i ] > 0  &  NCOL(dat) > 0 )  {   
        
        ini <- lm( target ~., data = dat, weights = wei )
	     	M <- dim(dat)[2]
        bic0 <-  BIC(ini) + con * lchoose(p, M)
        i <- i + 1        

        if ( M == 1 ) {
          mod <- lm(target ~ 1, weights = wei )
          bic <-  BIC(mod) 
          tool[i] <- bic
          if ( bic0 - bic < 0 ) {
            runtime <- proc.time() - tic		
            res <- list(runtime = runtime, info = info, mat = mat )
          } else {
            runtime <- proc.time() - tic		
            info <- rbind(info, c(mat[, 1], bic) )
            mat <- mat[-1, , drop = FALSE]
            res <- list(runtime = runtime, info = info, mat = mat )
            dat <- dataset[, -info[, 1], drop = FALSE ]
          }  
          
        } else { 
          bic <- numeric(M)
		      M <- dim(dat)[2] - 1
          for ( j in 1:(M + 1) ) {
            mod <- lm( target ~.,  data = dat[, -j, drop = FALSE], weights = wei )
            bic[j] <-  BIC(mod) + con * lchoose(p, M)
          }
          mat[, 2] <- bic
          sel <- which.min( mat[, 2] )
          tool[i] <- mat[sel, 2]
          if ( bic0 - mat[sel, 2] < 0 ) {
            runtime <- proc.time() - tic		
            res <- list(runtime = runtime, info = info, mat = mat )
          } else {
            info <- rbind(info, mat[sel, ] )
            mat <- mat[-sel, , drop = FALSE] 
            dat <- dataset[, -info[, 1], drop = FALSE ]
          }  ## end  if ( bic0 - mat[sel, 2] < 0 )
        }  ## end if  (M == 1)
      }  ## end while
    }  ## end if ( tool[2] > 0 )
   }  ## end  if ( bic0 - mat[sel, 2] < 0  )
  }  ## end  if (M == 0)
    runtime <- proc.time() - tic
    res <- list(runtime = runtime, info = info, mat = mat )
  }  ## end if ( p > n )
  
  res
}