Variance and correlations measures for prediction components

Calculates local and integrated variance and correlation measures as introduced by Yuan et al. (2017).

Usage

devel.cvmeasure(joint, prediction1, prediction2, samplers = NULL, mesh = NULL)

Arguments

joint

A joint prediction of two latent model components.

prediction1

A prediction of the first component.

prediction2

A prediction of the second component.

samplers

A SpatialPolygon object describing the area for which to compute the cumulative variance measure.

mesh

The inla.mesh for which the prediction was performed (required for cumulative Vmeasure).

Value

Variance and correlations measures.

References

Y. Yuan, F. E. Bachl, F. Lindgren, D. L. Brochers, J. B. Illian, S. T. Buckland, H. Rue, T. Gerrodette. 2017. Point process models for spatio-temporal distance sampling data from a large-scale survey of blue whales. https://arxiv.org/abs/1604.06013

Examples

# \donttest{
if (bru_safe_inla() &&
    require(ggplot2, quietly = TRUE) &&
    bru_safe_sp() &&
    require("sp")) {

  # Load Gorilla data

  data("gorillas", package = "inlabru")

  # Use RColorBrewer

  library(RColorBrewer)

  # Fit a model with two components:
  # 1) A spatial smooth SPDE
  # 2) A spatial covariate effect (vegetation)

  pcmatern <- INLA::inla.spde2.pcmatern(gorillas$mesh,
    prior.sigma = c(0.1, 0.01),
    prior.range = c(0.01, 0.01)
  )

  cmp <- coordinates ~ vegetation(gorillas$gcov$vegetation, model = "factor_contrast") +
    spde(coordinates, model = pcmatern) -
    Intercept(1)

  fit <- lgcp(cmp, gorillas$nests,
    samplers = gorillas$boundary,
    domain = list(coordinates = gorillas$mesh),
    options = list(control.inla = list(int.strategy = "eb"))
  )

  # Predict SPDE and vegetation at the mesh vertex locations

  vrt <- fm_vertices(gorillas$mesh, format = "sp")
  pred <- predict(
    fit,
    vrt,
    ~ list(
      joint = spde + vegetation,
      field = spde,
      veg = vegetation
    )
  )

  # Plot component mean

  multiplot(ggplot() +
    gg(gorillas$mesh, color = pred$joint$mean) +
    coord_equal() +
    theme(legend.position = "bottom"),
  ggplot() +
    gg(gorillas$mesh, color = pred$field$mean) +
    coord_equal() +
    theme(legend.position = "bottom"),
  ggplot() +
    gg(gorillas$mesh, color = pred$veg$mean) +
    coord_equal() +
    theme(legend.position = "bottom"),
  cols = 3
  )

  # Plot component variance

  multiplot(ggplot() +
    gg(gorillas$mesh, color = pred$joint$var) +
    coord_equal() +
    theme(legend.position = "bottom"),
  ggplot() +
    gg(gorillas$mesh, color = pred$field$var) +
    coord_equal() +
    theme(legend.position = "bottom"),
  ggplot() +
    gg(gorillas$mesh, color = pred$veg$var) +
    coord_equal() +
    theme(legend.position = "bottom"),
  cols = 3
  )

  # Calculate variance and correlation measure

  vm <- devel.cvmeasure(pred$joint, pred$field, pred$veg)
  lprange <- range(vm$var.joint, vm$var1, vm$var2)

  # Variance contribution of the components

  csc <- scale_fill_gradientn(colours = brewer.pal(9, "YlOrRd"), limits = lprange)
  boundary <- gorillas$boundary

  plot.1 <- ggplot() +
    gg(gorillas$mesh, color = vm$var.joint, mask = boundary) +
    csc +
    coord_equal() +
    ggtitle("joint") +
    theme(legend.position = "bottom")
  plot.2 <- ggplot() +
    gg(gorillas$mesh, color = vm$var1, mask = boundary) +
    csc +
    coord_equal() +
    ggtitle("SPDE") +
    theme(legend.position = "bottom")
  plot.3 <- ggplot() +
    gg(gorillas$mesh, color = vm$var2, mask = boundary) +
    csc +
    coord_equal() +
    ggtitle("vegetation") +
    theme(legend.position = "bottom")

  multiplot(plot.1, plot.2, plot.3, cols = 3)

  # Covariance of SPDE field and vegetation

  ggplot() +
    gg(gorillas$mesh, color = vm$cov)

  # Correlation between field and vegetation

  ggplot() +
    gg(gorillas$mesh, color = vm$cor)

  # Variance and correlation integrated over space

  vm.int <- devel.cvmeasure(pred$joint, pred$field, pred$veg,
    samplers = fm_int(gorillas$mesh, gorillas$boundary),
    mesh = gorillas$mesh
  )
  vm.int
}



#>    var.joint        var1       var2          cor
#> 1 0.02464766 0.004192524 0.02053771 -0.004449308
# }