R/model2v4pB.R

In JonathanVSV/RSModels: Contains functions that enable the construction of linear models with different parameters, cross validation implementation and the calculation of a random goodness-of-fit ditribution. These models are specially useful for studies that use remote sensing variables as independent variables to describe or predict measured-in-field community attributes.

#' @title Modeling function 2v4pB
#'
#' @description This function constructs every possible linear model with two independent variables, one linear and
#' one exponential term (y = mx + nx^2 + oy + b) for nx number of dependent variables.
#'
#' @param model.data=data.frame  Data.frame that contains both the dependent and independent variables
#'
#' @param ny=number Number of dependent variables to be tested.
#'
#' @param nx=number Number of independent variables to be tested. Do not confuse number of available independent
#' variables with number of independent variables OF THE MODEL.
#'
#' @param CV=boolean T if a cross-validation should be performed, F if not.
#'
#' @param CV_n=number Number of observations to be left out in the cross-validation process. For example
#' CV = T & CV_n = 1 will perform a 1-leave-out-cross-validation, while the same command with CV_n = 2, will
#' performa a 2-leave-out-cross-validation
#'
#' @param r2random=boolean T if an R^2 maximum random distribution should be computed with the data. Calculating
#' this random distribution enables a comparison of the observed R^2 values of the best models with a completely
#' random scenario. This distribution shows if the goodness-of-fit values obtained in the models correspond to a
#' significntly higher value than the expected at random (>= value of percentile 95) or not.
#'
#' @param runs=number Number indicating the number of runs to perform the goodness-of-fit random distribution.
#'
#' @examples model2v4pB(df, ny=9, nx=16)
#'
#' @export model2v4pB
#'

model2v4pB<-function(model.data, ny, nx, CV=F, CV_n=1, r2random=F, runs=1000)
{
  #Set model parameters
  p <- 4
  n <- nrow(model.data)

  #Possible combinations for independent variables
  combs.var <- combn(nx, 2)
  #Possible combinations for cross validation procedure
  combs.data <- combn(n, CV_n)

  timer <- round(proc.time()[3])

  #------------------------------Descriptive models---------------------------------
  results <- array(dim = c(ny, choose(nx, 2), 10))
  results.ord <- array(dim = c(ny, choose(nx,2), 10))
  for(i in 1:ny)
  {
    y <- i + 1
    for(j in 1:choose(nx, 2))
    {
      x1 <- combs.var[1, j] + ny + 1
      x2 <- combs.var[2, j] + ny + 1
      model <- lm(model.data[, y] ~ model.data[, x1] + I(model.data[, x1]^2) + model.data[, x2])
      coef <- model$coef
      r2 <- summary(model)$r.squared
      AICc <- AIC(model) + (2 * p * (p - 1)) / (n - p - 1)
      F.p.value.x1 <- summary(aov(model))[[1]][, 5][1]
      F.p.value.x2 <- summary(aov(model))[[1]][, 5][2]
      F.p.value.x1.x2 <- summary(aov(model))[[1]][, 5][3]
      results[i, j, ] <- c(paste(names(model.data)[y], "vs",names(model.data)[x1], "&",
                              paste0(names(model.data)[x1], "^2"),"&",names(model.data)[x2]), r2, AICc, F.p.value.x1,
                        F.p.value.x2,F.p.value.x1.x2, coef[1], coef[2], coef[3], coef[4])
    }
    results.ord[i, , ] <- results[i, order(as.numeric(results[i, , 2]), decreasing=T), ]
    write.table(as.table(results.ord[i, , ]),paste("Results-var2par4B",names(model.data)[i + 1], "", ".xls", sep = ""),
                sep = "\t",row.names = F,col.names = c("Y vs X1 & X^2 & X2", "r2", "AICc", "F.p.value.x1", "F.p.value.x1^2",
                                                       "F.p.value.x2", "Intercept", "Slope x1 (coef2)", "Slope x1^2 (coef3)",
                                                       "Slope x2 (coef4)"))
  }

  #------------------------------------------Models with highest R2--------------------------------------
  mejores <- matrix(nrow=ny,ncol=12)
  colnames(mejores) <- c("Atributo","Var imagen 1","Var imagen 2","R2","F. p-value 1","F. p-value 1^2",
                       "F. p-value x2","AIC","Intercept","Slope x1","Slope x1^2","Slope x2")
  for (i in 1:ny)#Cada [i,] es el conjunto de modelos posibles para cada atributo de la comunidad
  {
    mejormo <- which(as.numeric(results[, , 2][i, ]) == max(as.numeric(results[, , 2][i, ])))
    mejores[i, 1] <- results[, , 1][i, mejormo]
    mejores[i, 4] <- max(as.numeric(results[, , 2][i, ]))
    mejores[i, 5] <- results[, , 4][i, mejormo]
    mejores[i, 6] <- results[, , 5][i, mejormo]
    mejores[i, 7] <- results[, , 6][i, mejormo]
    mejores[i, 8] <- results[, , 3][i, mejormo]
    mejores[i, 9] <- results[, , 7][i, mejormo]
    mejores[i, 10] <- results[, , 8][i, mejormo]
    mejores[i, 11] <- results[, , 9][i, mejormo]
    mejores[i, 12] <- results[, , 10][i, mejormo]
  }

  for (i in 1:ny)#Cada [i,] es el conjunto de modelos posibles para cada atributo de la comunidad
  {
    colsa<-unlist(strsplit(mejores[i, 1], " vs "))
    mejores[i, 1] <- colsa[1]
    colsa2<-unlist(strsplit(colsa[2], " & "))
    mejores[i, 2] <- colsa2[1]
    mejores[i, 3] <- colsa2[2]
  }
  
  write.table(as.table(mejores),paste("Best mod R2-var2par4B", ".xls",sep = ""), sep = "\t", row.names = F,
              col.names = colnames(mejores))

  ##---------------------------Cross-validation--------------------------------
  if(CV == T)
  {
    combs.data.CV <- combs.data

    pred <- vector(length = CV_n)
    CV.CV <- vector(length = choose(n, CV_n))
    r2.CV <- vector(length = choose(n, CV_n))
    r2.data.vs.pred <- vector(length = choose(n, CV_n))
    time <- vector(length = choose(n, CV_n))
    means <- array(data = 0,dim = c(ny, choose(nx, 2), 8))
    means.ord <- array(data = 0, dim = c(ny,choose(nx, 2), 8))

    coefs <- matrix(nrow = choose(n, CV_n),ncol = p)
    mean.coefs <- vector(length = p)

    for(i in 1:ny)
    {
      y <- i + 1
      mean.y <- mean(model.data[, y])
      mean.sstt <- sum((model.data[, y] - mean.y)^2) / n
      for(j in 1:choose(nx,2))
      {
        x1 <- combs.var[1, j] + ny + 1
        x2 <- combs.var[2, j] + ny + 1
        for(k in 1:choose(n, CV_n))
        {
          time1 <- proc.time()[3]
          print(paste("vary = ",i,", varx1 = ", combs.var[1,j], ", varx2 = ", combs.var[2,j],", comb = ", k, sep = ""))
          validation.data <- model.data[combs.data.CV[, k], ]
          calibration.data <- model.data[ - combs.data.CV[, k], ]
          model <- lm(calibration.data[, y] ~ calibration.data[, x1] + I(calibration.data[, x1]^2) + calibration.data[, x2])
          coef <- model$coef
          for(l in 1:CV_n)
          {
            pred[l] <- coef[1] + coef[2] * validation.data[l, x1] + coef[3] * (validation.data[l, x1]^2) + coef[4] * validation.data[l, x2]
          }
          mean.y.validation <- mean(validation.data[, y])
          msse.validation <- sum((validation.data[, y] - pred)^2) / CV_n
          CV.CV[k] <- sqrt(msse.validation) / mean.y.validation
          r2.CV[k] <- 1-msse.validation / mean.sstt
          r2.data.vs.pred[k] <- (cor(validation.data[, y], pred,method = "pearson"))^2
          coefs[k, ] <- coef
          time2 <- proc.time()[3]
          time[k] <- time2 - time1
        }
        mean.time <- mean(time)
        print(paste("mean time = ",mean.time,sep = ""))
        mean.CV.CV <- mean(CV.CV)
        mean.r2.CV <- mean(r2.CV)
        mean.coefs[1] <- mean(coefs[,1])
        mean.coefs[2] <- mean(coefs[,2])
        mean.coefs[3] <- mean(coefs[,3])
        mean.coefs[4] <- mean(coefs[,4])
        mean.r2.data.vs.pred <- mean(r2.data.vs.pred)
        means[i, j, ] <- c(paste(names(model.data)[y], "vs", names(model.data)[x1], "&", paste0(names(model.data)[x1],
                                                                                                "^2"),"&",
                                 names(model.data)[x2]), mean.r2.CV, mean.r2.data.vs.pred, mean.CV.CV, mean.coefs[1],
                           mean.coefs[2], mean.coefs[3], mean.coefs[4])
      }
      means.ord[i, , ] <- means[i, order(as.numeric(means[i, , 2]),decreasing = T), ]
      write.table(as.table(means.ord[i, , ]), paste("Results-var2par4B-CV", names(model.data)[i + 1],"", ".xls", sep = ""),
                  sep = "\t",row.names = F,col.names = c("Y vs X1 & X1^2 & X2", "mean r2.CV", "mean r2 data vs pred",
                                                         "mean CV.CV", "mean Interc", "mean Slope", "mean Slope 2",
                                                         "mean Slope 3"))
    }
  }else{
    print("No Cross Validation performed")
  }


  #-------------------------------------Random highest R2 distribution--------------------------------

  if(r2random==T)
  {
    model.data.permut = model.data
    r2.max.permut = matrix(nrow = ny,ncol = runs)
    r2.model.pvalue = matrix(nrow = ny,ncol = choose(nx,2))
    r2 = array(dim = c(ny,choose(nx,2),runs))
    for(k in 1:runs)
    {
      print(paste("run = ",k,sep = ""))
      for(i in 2:(nx+ny+1))
        model.data.permut[,i] = gtools::permute(model.data[,i])
      for(i in 1:ny)
      {
        for(j in 1:choose(nx,2))
        {
          y = i+1
          x1 = combs.var[1,j]+ny+1
          x2 = combs.var[2,j]+ny+1
          model = lm(model.data.permut[,y]~model.data.permut[,x1]+I(model.data.permut[,x1]^2)+model.data.permut[,x2])
          r2[i,j,k] = summary(model)$r.squared
        }
        r2.max.permut[i,k] = max(r2[i,,k])
      }
    }
    for(i in 1:ny)
      r2.max.permut[i,] = sort(r2.max.permut[i,],decreasing = T)
    
    colnames = vector(length = (choose(nx,2)))
    for(i in 1:choose(nx,2))
    {
      x1 = combs.var[1,i]+ny+1
      x2 = combs.var[2,i]+ny+1
      colnames[i] = paste(names(model.data)[x1],"&",paste0(names(model.data)[x1],"^2"),names(model.data)[x2])
    }

    #Pa escribir chido las tablas, arreglar el desface de columnas
    rownames(r2.max.permut)<-names(model.data)[2:(ny+1)]
    colnames(r2.max.permut)<-seq(1:runs)
    write.table(as.table(t(r2.max.permut)),paste("Results-var2par4B-r2maxpermut",".xls",sep = ""),sep = "\t",
                col.names = NA,row.names = T)
    rownames(r2.model.pvalue)<-names(model.data)[2:(ny+1)]
    colnames(r2.model.pvalue)<-colnames
    write.table(as.table(r2.model.pvalue),paste("Results-var2par4B-r2modelpvalue",".xls",sep = ""),sep = "\t",
                col.names = NA,row.names = T)

  }else{
    print("No R2 distribution at random performed")
  }
  print(paste0("Process finished. Files can be found in the following directory: ",getwd()))
}#end function