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

Source: R/calibrate_model.R
calibrate_model.Rd

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,
  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).

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.

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