linearTrend.R

#' Linear Trend in Remote Sensing
#'
#' Linear trend is useful for mapping forest degradation, land degradation, etc.
#' This algorithm is capable of obtaining the slope of an ordinary least-squares
#' linear regression and its reliability (p-value).
#'
#' @details
#' Linear regression is widely used to analyze forest degradation or land degradation.
#' Specifically, the slope and its reliability are used as main parameters and they
#' can be obtained with this function. On the other hand, logistic regression allows
#' obtaining a degradation risk map, in other words, it is a probability map. Please see
#' the references or see [Tarazona and Maria-Miyasiro (2020)](https://doi.org/10.1016/j.rsase.2020.100337).
#'
#' @references
#' Tarazona, Y., Maria, Miyasiro-Lopez. (2020). Monitoring tropical forest degradation using
#' remote sensing. Challenges and opportunities in the Madre de Dios region, Peru. Remote
#' Sensing Applications: Society and Environment, 19, 100337.
#'
#' Wilkinson, G.N., Rogers, C.E., 1973. Symbolic descriptions of factorial models for
#' analysis of variance. Appl. Stat. 22, 392-399.
#'
#' Chambers, J.M., 1992. Statistical Models in S. CRS Press.
#'
#' @importFrom dplyr bind_rows
#'
#' @param x RasterStack, RasterBrick or Matrix (row*col, n_images)
#' @param type There are two options: "lm" for a linear regression and "glm" for Generalized Linear Models
#' @param ... For "lm" and "glm": arguments to be used to form the default control argument
#' if it is not supplied directly. See \link[stats]{lm} and \link[stats]{glm}.
#'
#' @export
#'
#' @examples
#' library(ForesToolboxRS)
#' library(raster)
#'
#' data(serie_pv)
#'
#' e <- extent(350420.9, 352028.8, -1417869, -1416288)
#' imgs <- crop(serie_pv, e)
#'
#' trend <- linearTrend(x = imgs)
#' plot(trend[[1]]) # raster of slope
#' plot(trend[[2]]) # raster of p-value
#'
linearTrend <- function(x, type = "lm", ...) {
  if (type == "lm") {
    if (inherits(x, "RasterStack") | inherits(x, "RasterBrick")) {
      mat <- raster::as.matrix(x)
    } else if (inherits(x, "matrix")) {
      mat <- x
    } else {
      stop(class(x), " class is not supported", call. = TRUE)
    }

    x_axis <- 1:dim(mat)[2]
    my_lms <- lapply(1:dim(mat)[1], function(i) reg <- stats::lm(mat[i, ] ~ x_axis, ...))
    summy <- suppressWarnings(
      lapply(my_lms, function(x) summary(x)$coefficients[2, 1:4])
    )

    summy <- as.data.frame(bind_rows(summy))

    if (inherits(x, "RasterStack") | inherits(x, "RasterBrick")) {
      slope <- raster(x[[1]])
      p_value <- raster(x[[2]])

      slope[] <- summy[, 1]
      p_value[] <- summy[, 4]
      result <- raster::stack(slope, p_value)
      names(result) <- c("slope", "p_value")

      return(result)
    } else if (inherits(x, "matrix")) {
      result <- array(c(summy[, 1], summy[, 4]), c(dim(x)[1], dim(x)[2], 2))

      return(result)
    }
  } else if (type == "glm") {
    if (inherits(x, "RasterStack") | inherits(x, "RasterBrick")) {
      names(x[[1]]) <- c("FD")
      df <- raster::as.matrix(x)

      mod <- stats::glm(FD ~ ., data = df, ...)

      prob <- predict(mod, type = "response")

      result <- raster(x[[1]])
      result[] <- prob
      names(result) <- c("MapProbability")

      return(result)
    } else if (inherits(x, "list")) {
      if (class(try(raster::stack(x), silent = TRUE)) == "try-error") {
        master <- raster(x[1])
        meta <- raster(extent(master), nrows = master@nrows, ncols = master@ncols)

        varib_rast <- c()
        for (k in 1:length(x)) {
          ras_ini <- raster(x[[k]])
          ras_post <- raster::resample(ras_ini, meta, method = "ngb")
          ras_post[is.na(ras_post)] <- 0
          varib_rast <- c(varib_rast, ras_post)
        }

        x <- varib_rast
        names(x[[1]]) <- c("FD")
      } else {
        x <- raster::stack(x)
        names(x[[1]]) <- c("FD")
      }

      df <- raster::as.matrix(x)

      mod <- stats::glm(FD ~ ., data = df, ...)
      prob <- predict(mod, type = "response")

      result <- master
      result[] <- prob

      names(result) <- c("MapProbability")

      return(result)
    } else {
      stop(class(x), " class is not supported", call. = TRUE)
    }
  } else {
    stop(" Method is not supported", call. = TRUE)
  }
}