inst/misc/2d_lgcp_residuals_functions.R

In inlabru: Bayesian Latent Gaussian Modelling using INLA and Extensions

# Niharika Reddy Peddinenikalva
# Vacation Scholarship project

suppressPackageStartupMessages(library("INLA"))
suppressPackageStartupMessages(library("inlabru"))
suppressPackageStartupMessages(library("RColorBrewer"))
suppressPackageStartupMessages(library("ggplot2"))
suppressPackageStartupMessages(library("dplyr"))
suppressPackageStartupMessages(library("lwgeom"))
suppressPackageStartupMessages(library("patchwork"))
suppressPackageStartupMessages(library("terra"))
suppressPackageStartupMessages(library("data.table"))
theme_set(theme_bw())



#' ----------------------------------
#' prepare_residual_calculations
#' ----------------------------------
#'
#' Computes the A_sum, A_integrate matrices and the data frame used for
#' calculating the residuals for the given set of polygons B

#' Input:
#' @param samplers A SpatialPolygonDataFrame containing partitions for which
#' residuals are to be calculated
#' @param domain A mesh object
#' @param observations A SpatialPointsDataFrame containing observed data
#'
#' Output:
#' @return A_sum - matrix used to compute the summation term of the residuals
#' @return A_integrate - matrix used to compute the integral term
#' @return df - SpatialPointsDataFrame containing all the locations 'u' for
#' calculating residuals
#'
prepare_residual_calculations <- function(samplers, domain, observations) {
  # Calculate the integration weights for A_integrate
  ips <- fm_int(domain = domain, samplers = samplers)

  # Set-up the A_integrate matrix
  # A_integrate has as many rows as polygons in the samplers,
  # as many columns as mesh points
  A_integrate <- inla.spde.make.A(
    mesh = domain, ips, weights = ips$weight,
    block = ips$.block, block.rescale = "none"
  )


  # Set-up the A_sum matrix
  # A_sum has as many rows as polygons in the samplers,
  # as many columns as observed points
  # each row has 1s for the points in the corresponding polygon
  idx <- sf::st_within(sf::st_as_sf(observations), sf::st_as_sf(samplers), sparse = TRUE)
  A_sum <- sparseMatrix(
    i = unlist(idx),
    j = rep(
      seq_len(nrow(observations)),
      vapply(idx, length, 1L)
    ),
    x = rep(1, length(unlist(idx))),
    dims = c(nrow(samplers), nrow(observations))
  )


  # Setting up the data frame for calculating residuals
  observations$obs <- TRUE
  df <- SpatialPointsDataFrame(
    coords = rbind(domain$loc[, 1:2], coordinates(observations)),
    data = bind_rows(data.frame(obs = rep(FALSE, domain$n)), observations@data),
    proj4string = fm_CRS(domain)
  )

  # Return A-sum, A_integrate and the data frame for predicting the residuals
  list(A_sum = A_sum, A_integrate = A_integrate, df = df)
}



#' ------------
#' residual_df
#' ------------
#'
#' Computes the three types if residuals and returns a data frame containing
#' information about all 3 residuals for each partition of 'B'
#'
#' Inputs:
#' @param model fitted model for which residuals need to be calculated
#' @param df SpatialPointsDataFrame object containing all the locations 'u'
#' for calculating residuals
#' @param expr an expression object containing the formula of the model
#' @param A_sum matrix used to compute the summation term of the residuals
#' @param A_integrate matrix that computes the integral term of the residuals
#'
#' Outputs:
#' @return Data frame containing residual information for each of the
#' partitions of the subset 'B'
#'

residual_df <- function(model, df, expr, A_sum, A_integrate) {
  # Compute residuals
  res <- predict(
    object = model,
    newdata = df,
    ~ {
      lambda <- eval(expr)
      h1 <- lambda * 0 + 1
      h2 <- 1 / lambda
      h3 <- 1 / sqrt(lambda)
      data.frame(
        Scaling_Residuals =
          as.vector(A_sum %*% h1[obs]) -
            as.vector(A_integrate %*% (h1 * lambda)[!obs]),
        Inverse_Residuals =
          as.vector(A_sum %*% h2[obs]) -
            as.vector(A_integrate %*% (h2 * lambda)[!obs]),
        Pearson_Residuals =
          as.vector(A_sum %*% h3[obs]) -
            as.vector(A_integrate %*% (h3 * lambda)[!obs])
      )
    },
    used = bru_used(expr)
  )

  # Label the three types of residuals
  res$Scaling_Residuals$Type <- "Scaling Residuals"
  res$Inverse_Residuals$Type <- "Inverse Residuals"
  res$Pearson_Residuals$Type <- "Pearson Residuals"
  do.call(rbind, res)
}





#' --------------
#' set_csc
#' --------------
#'
#' Sets the colour scale for the three types of residuals
#'
#' Inputs:
#' @param residuals frame containing residual information for each of the
#' partitions of the subset 'B'
#' @param col_theme vector of themes for each type of residual
#'
#' Outputs:
#' @return a list of 3 colour scales for each type of residual
#'

set_csc <- function(residuals, col_theme) {
  # Store data for the colour scale of the plots for each type of residual
  cscrange <- data.frame(
    residuals %>%
      group_by(Type) %>%
      summarise(maxabs = max(abs(mean)))
  )

  # Set the colour scale for all three types of residuals
  scaling_csc <-
    scale_fill_gradientn(
      colours = brewer.pal(9, col_theme[1]),
      name = "Scaling Residual",
      limits =
        cscrange[cscrange$Type == "Scaling Residuals", 2] *
          c(-1, 1)
    )

  inverse_csc <-
    scale_fill_gradientn(
      colours = brewer.pal(9, col_theme[2]),
      name = "Inverse Residual",
      limits =
        cscrange[cscrange$Type == "Inverse Residuals", 2] *
          c(-1, 1)
    )

  pearson_csc <-
    scale_fill_gradientn(
      colours = brewer.pal(9, col_theme[3]),
      name = "Pearson Residual",
      limits =
        cscrange[cscrange$Type == "Pearson Residuals", 2] *
          c(-1, 1)
    )

  list("Scaling" = scaling_csc, "Inverse" = inverse_csc, "Pearson" = pearson_csc)
}



#' ---------------
#' residual_plot
#' ---------------
#'
#' plots the three types of residuals for each polygon
#'
#' Input:
#' @param samplers A SpatialPolygonsDataFrame containing partitions for which
#' residuals are to be calculated
#' @param residuals frame containing residual information for each of the
#' partitions of the subset 'B'
#' @param csc list of three colour scales for the three types of residuals
#' @param model_name string containing the name of the model being assessed
#'
#' Output:
#' @return a list of three subplots scaling, inverse and Pearson residuals
#' for the different partitions of samplers


residual_plot <- function(samplers, residuals, csc, model_name) {
  # Initialise the scaling residuals plot
  samplers$Residual <- residuals %>%
    filter(Type == "Scaling Residuals") %>%
    pull(mean)
  scaling <- ggplot() +
    gg(samplers, aes(fill = Residual), alpha = 1, colour = NA) +
    csc["Scaling"] +
    theme(legend.position = "bottom") +
    labs(subtitle = paste(model_name, "Scaling"))

  # Initialise the inverse residuals plot
  samplers$Residual <- residuals %>%
    filter(Type == "Inverse Residuals") %>%
    pull(mean)
  inverse <- ggplot() +
    gg(samplers, aes(fill = Residual), alpha = 1, colour = NA) +
    csc["Inverse"] +
    theme(legend.position = "bottom") +
    labs(subtitle = paste(model_name, "Inverse"))

  # Initialise the Pearson residuals plot
  samplers$Residual <- residuals %>%
    filter(Type == "Pearson Residuals") %>%
    pull(mean)
  pearson <- ggplot() +
    gg(samplers, aes(fill = Residual), alpha = 1, colour = NA) +
    csc["Pearson"] +
    theme(legend.position = "bottom") +
    labs(subtitle = paste(model_name, "Pearson"))

  # Return the three plots in a list
  list(
    Scaling = scaling, Inverse = inverse,
    Pearson = pearson
  )
}




#' ------------------
#' partition
#' ------------------
#'
#' Partitions the region based on the given criteria for calculating residuals
#' in each partition. Parts of this function are taken from concepts in
#' https://rpubs.com/huanfaChen/grid_from_polygon
#'
#' Input:
#' @param samplers A SpatialPolygonsDataFrame containing region for which
#' partitions need to be created
#' @param resolution resolution of the grids that are required
#' @param nrows number of rows of grids that are required
#' @param ncols number of columns of grids that are required
#'
#' Output:
#' @return a partitioned SpatialPolygonsDataFrame as required
#'
#'
partition <- function(samplers, resolution = NULL, nrows = NULL, ncols = NULL) {
  # Create a grid for the given boundary
  if (is.null(resolution)) {
    grid <- rast(terra::ext(samplers),
      crs = proj4string(samplers),
      nrows = nrows, ncols = ncols
    )
  }

  if (is.null(c(nrows, ncols))) {
    grid <- rast(terra::ext(samplers),
      crs = proj4string(samplers),
      resolution = resolution
    )
  }

  gridPolygon <- terra::as.polygons(grid)

  # Extract the boundary with subpolygons only
  sf::as_Spatial(sf::st_as_sf(terra::intersect(gridPolygon, terra::vect(samplers))))
}


#' ------------------
#' edit_df
#' ------------------
#'
#' Edits the residual data frames to remove columns that need not be displayed
#'
#' Input:
#' @param df the data frame which needs to be edited
#' @param columns a vector of columns that need to be deleted from df
#'
#' Output:
#' @return the edited data frame with only the desired columns
#'
#'
edit_df <- function(df, columns) {
  # Remove the columns that are not required
  df[, !(colnames(df) %in% columns)]
}