R/glskrigeidwpred.R

In spm2: Spatial Predictive Modeling

#' @title Generate spatial predictions using the hybrid methods of
#' generalised least squares ('gls'), 'kriging' and inverse distance weighted ('IDW')
#'
#' @description This function is for generating spatial predictions using the
#' hybrid methods of 'gls', 'kriging' and 'IDW', including all methods implemented
#' in 'glskrigeidwcv'.
#'
#' @param model a formula defining the response variable and predictive variables.
#' @param longlat	a dataframe contains longitude and latitude of point samples.
#' @param trainxy a dataframe contains longitude (long), latitude (lat),
#' predictive variables and the response variable of point samples. That is,
#' the location information must be names as 'long' and 'lat'.
#' @param predx	a dataframe or matrix contains columns of predictive variables
#' for the grids to be predicted.
#' @param y a vector of the response variable in the formula, that is, the left
#' part of the formula.
#' @param longlatpredx	a dataframe contains longitude and latitude of point locations
#' (i.e., the centers of grids) to be predicted. The location information must be
#' named as 'long' and 'lat'.
#' @param weights describing the within-group heteroscedasticity structure. Defaults
#'  to "NULL", corresponding to homoscedastic errors. See '?gls' in 'nlme'
#' for details.
#' @param transformation transform the residuals of 'gls' to normalise the data for 'krige';
#' can be "sqrt" for square root, "arcsine" for arcsine, "log" or "none"
#' for non transformation. By default, "none" is used.
#' @param delta numeric; to avoid log(0) in the log transformation. The default is 1.
#' @param formula.krige formula defining the response vector and (possible) regressor.
#' an object (i.e., 'variogram.formula') for 'variogram' or a formula for
#' 'krige'. see 'variogram' and 'krige' in 'gstat' for details.
#' @param vgm.args arguments for 'vgm', e.g. variogram model of response
#' variable and anisotropy parameters. see 'vgm' in 'gstat' for details.
#' By default, "Sph" is used.
#' @param anis anisotropy parameters: see notes 'vgm' in 'gstat' for details.
#' @param alpha direction in plane (x,y). see variogram in 'gstat' for details.
#' @param block block size. see 'krige' in 'gstat' for details.
#' @param beta for simple kriging. see 'krige' in 'gstat' for details.
#' @param nmaxkrige for a local predicting: the number of nearest observations that
#'  should be used for a prediction or simulation, where nearest is defined in
#'  terms of the space of the spatial locations. By default, 12 observations
#'  are used.
#' @param idp	 a numeric number specifying the inverse distance weighting power.
#' @param nmaxidw for a local predicting: the number of nearest observations that
#'  should be used for a prediction or simulation, where nearest is defined in
#'  terms of the space of the spatial locations. By default, 12 observations
#'  are used.
#' @param hybrid.parameter the default is 2 that is for 'glskrigeglsidw';
#' for 'glsglskrigeglsidw', it needs to be 3.
#' @param lambda, ranging from 0 to 2; the default is 1 for 'glskrigeglsidw'
#' and 'glsglskrigeglsidw'; and if it is < 1, more weight is placed on 'krige',
#' otherwise more weight is placed on 'idw'; and if it is 0, 'idw' is not
#' considered and the resultant methods is 'glskrige' when the default
#' 'hybrid.parameter' is used; and if it is 2, then the resultant method is
#' 'glsidw' when the default 'hybrid.parameter' is used.
#' @param corr.args arguments for 'correlation' in 'gls'. See '?corClasses' in 'nlme'
#' for details. By default, "NULL" is used. When "NULL" is used,
#' then 'gls' is actually performing 'lm'.
#' @param ... other arguments passed on to 'gls', 'krige' and 'gstat'.
#'
#' @return A dataframe of longitude, latitude, and predictions.
#'
#' @references Pinheiro, J. C. and D. M. Bates (2000). Mixed-Effects Models
#' in S and S-PLUS. New York, Springer.
#'
#' Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package.
#' Computers & Geosciences, 30: 683-691.
#'
#' @author Jin Li
#' @examples
#' \donttest{
#' library(spm)
#' library(nlme)
#'
#' data(petrel)
#' data(petrel.grid)
#'
#' gravel <- petrel[, c(1, 2, 6:9, 5)]
#' longlat <- petrel[, c(1, 2)]
#' range1 <- 0.8
#' nugget1 <- 0.5
#' model <- log(gravel + 1) ~  long + lat +  bathy + dist + I(long^2) + I(lat^2) +
#' I(lat^3) + I(bathy^2) + I(bathy^3) + I(dist^2) + I(dist^3) + I(relief^2) + I(relief^3)
#' y <- log(gravel[, 7] +1)
#'
#' glskrigeidwpred1 <- glskrigeidwpred(model = model, longlat = longlat, trainxy = gravel,
#' predx = petrel.grid, y = y, longlatpredx = petrel.grid[, c(1:2)],
#' transformation = "none", formula.krige = res1 ~ 1, vgm.args = "Sph", nmaxkrige = 12,
#' idp = 2, nmaxidw = 12,  corr.args = corSpher(c(range1, nugget1),
#' form = ~ lat + long, nugget = TRUE))
#'
#' names(glskrigeidwpred1)
#'
#' # Back transform 'glskrigeidwpred$predictions' to generate the final predictions
#' glskrigeidw.predictions <- exp(glskrigeidwpred1$predictions) - 1
#' range(glskrigeidw.predictions)
#'}
#'
#' @export
glskrigeidwpred <- function (model = var1 ~ 1, longlat, trainxy, predx, y, longlatpredx, corr.args = NULL, weights = NULL, transformation = "none", delta = 1, formula.krige = res1 ~ 1, vgm.args = c("Sph"), anis = c(0, 1), alpha = 0, block = 0, beta, nmaxkrige = 12, idp = 2, nmaxidw = 12, hybrid.parameter = 2, lambda = 1, ...) {
      # gls modeling
      gls1 <- nlme::gls(model, trainxy, correlation = corr.args, weights = weights)

      # gls predictions
      pred.gls1 <- stats::predict(gls1, predx, type = "response")

      # the residuals of gls for idw
      data.dev1 <- longlat
      data.pred1 <- longlatpredx
      dev.gls1 <- stats::predict(gls1, trainxy, type="response")

      res1 <- y - dev.gls1
      data.dev1$res1 <- res1

      # idw of the residuals
      gstat1 <- gstat::gstat(id = "res1", formula = res1 ~ 1, locations = ~ long + lat, data = data.dev1, set = list(idp = idp), nmax = nmaxidw)

      # idw predictions
      pred.idw1 <- stats::predict(gstat1, data.pred1)

      # for krige
      if (transformation == "none") {data.dev1$res1 = res1} else (
        if (transformation == "sqrt") {data.dev1$res1 = sqrt(res1 + abs(min(res1)))} else (
          if (transformation == "arcsine") {data.dev1$res1 = asin(sqrt((res1 + abs(min(res1))) / 100))} else (
            if (transformation == "log") {data.dev1$res1 = log(res1 + abs(min(res1)) + delta)} else (
              stop ("This transfromation is not supported in this version!")))))
      # The '+ abs(min(res1))' above is to set possible negative values to 0.

      # vgm of the residuals
      sp::coordinates(data.dev1) = ~ long + lat
      vgm1 <- gstat::variogram(object = formula.krige, data.dev1, alpha = alpha)
      model.1 <- gstat::fit.variogram(vgm1, gstat::vgm(mean(vgm1$gamma), vgm.args, mean(vgm1$dist), min(vgm1$gamma)/10, anis = anis))
      if (model.1$range[2] <= 0) (cat("A zero or negative range was fitted to variogram", "\n"))
      if (model.1$range[2] <= 0) (model.1$range[2] <- min(vgm1$dist))  # set negative range to be positive

      # krige predictions
      sp::coordinates(data.pred1) = ~long + lat
      pred.krige1 <- gstat::krige(formula = formula.krige, data.dev1, data.pred1, model = model.1, nmax=nmaxkrige, block = block, beta = beta)$var1.pred

      if (transformation == "none") {pred.krige = pred.krige1}
      if (transformation == "sqrt") {pred.krige = pred.krige1 ^ 2 - abs(min(res1))}
      if (transformation == "arcsine") {pred.krige = (sin(pred.krige1)) ^ 2 * 100 -  abs(min(res1))}
      if (transformation == "log") {pred.krige = exp(pred.krige1) - abs(min(res1)) - delta}

      predictions <- (pred.krige * (2 - lambda) + pred.idw1$res1.pred * lambda + pred.gls1 * hybrid.parameter) / hybrid.parameter
      glskrigeidw.pred <- cbind(longlatpredx, predictions)
      glskrigeidw.pred
}