Calibrate a bayesian model to fit log(AGBD) ~ log(raster metric)

After applying the subplot_summary() function, this function fits a log-log bayesian regression model with spatially varying coefficient process, on AGBD and raster metric simulated values (see Details).

Usage

calibrate_model(
  long_AGB_simu,
  nb_rep = 30,
  useCache = FALSE,
  plot_model = TRUE,
  intercept = FALSE,
  spatial = TRUE,
  chains = 3,
  thin = 20,
  iter = 3000,
  warmup = 1000,
  cores = 3,
  ...
)

Arguments

long_AGB_simu: The '$long_AGB_simu' output of the subplot_summary() function (see Details).
nb_rep: Number of simulation to provide in the brms fit (defaults to 30; nb_rep > 50 will not improved significantly the model and will be much longer to fit).
useCache: A logical that determines wether to use the cache when building a Bayesian model (see Details).
plot_model: A logical indicating whether the model should be plotted (defaults to TRUE).
intercept: A logical indicating whether the regression model should include an intercept (defaults to FALSE).
spatial: A logical indicating whether explicit spatial correlation should be modeled (defaults to TRUE).
chains: Number of Markov chains (defaults to 3), see brms::brm()
thin: Thinning rate (defaults to 20), see brms::brm()
iter: Number of total iterations per chain (including warmup; defaults to 3000), see brms::brm()
warmup: Number of warmup (aka burnin) iterations (defaults to 1000), see brms::brm()
cores: Number of cores to use when executing the chains in parallel (defaults to 3), see brms::brm()
...: Further arguments passed to brm(), e.g: prior, cores, etc. See brms::brm()

Value

The function return a brmsfit object.

Details

The 'long_AGB_simu' argument must be a data frame or data frame extension containing the following variables:

'N_simu': a numeric indicating the simulation number.
'x_center' and 'y_center': the coordinates of the plots/subplots in the projected coordinate system.
'AGBD': the AGBD value of the simulation.
'raster_metric': the raster metric value of the simulation.

The model describing the relationship between plot-level AGBD and LiDAR metrics is a log-log regression, with a Gaussian error model. To capture the spatial structure that may exists in the data, we use a Spatially Varying Coefficient (SVC) regression with Gaussian random fields (Gelfand et al. 2003, Spatial modeling with spatially varying coefficient processes).

The general equation can be written as follow, for a subplot $s_i$:

$Y_i \sim \mathrm{N}(\mu_i, \sigma)$

$\mu_i = \beta_0 + (\beta_1 + \eta_i) \times X_i$

$\eta_i \sim \mathrm{MVNormal}(0, \Sigma)$

$X_i$ stands for the logarithm of plot-level AGBD, $Y_i$ is the logarithm of a LiDAR metric measurement for the corresponding plot.

$\Sigma$, the covariance matrix, is defined by the $\frac{3}{2}$ Matern kernel between two locations $s_i$ and $s_j$: $k(\mathbf{s}_i, \mathbf{s}_j) = \psi^2 \left( 1 + \frac{\sqrt{3}d_{i,j}}{l} \right) \exp \left( -\frac{\sqrt{3}d_{i,j}}{l} \right)$ $d_{i,j}$ is the distance between locations $s_i$ and $s_j$, parameter $\psi$ controls the magnitude and parameter $l$ the range of the kernel.

Note that the spatial structure integration can be turned off by setting argument spatial to FALSE, leading to a classic log-log regression.

If useCache = TRUE and this is the first time the model is being built, the model will be saved as a .rds file in the defined cache path (see createCache()). If useCache = TRUE and the model has already been built using the user cache, the model will be loaded and updated to avoid wasting time re-compiling it. If useCache = NULL, the cache is first cleared before building the model.

Author

Arthur BAILLY, Dominique LAMONICA