optimization_function: Compute optimization scores for spatial predictor selection

In spatialRF: Easy Spatial Modeling with Random Forest

Compute optimization scores for spatial predictor selection

Description

Computes optimization scores for candidate spatial predictor sets using either the "moran.i" or "p.value" method. Higher scores indicate better trade-offs between spatial autocorrelation reduction, model performance, and parsimony.

Usage

optimization_function(
  x = NULL,
  weight.r.squared = NULL,
  weight.penalization.n.predictors = NULL,
  optimization.method = "moran.i"
)

Arguments

x	Data frame containing optimization metrics for candidate spatial predictor sets. Generated internally by select_spatial_predictors_sequential() or select_spatial_predictors_recursive(). Must include columns: moran.i, r.squared, penalization.per.variable, and p.value.binary (for "p.value" method).
weight.r.squared	Numeric value between 0 and 1 specifying the weight for R-squared in the optimization score. Higher values prioritize model performance.
weight.penalization.n.predictors	Numeric value between 0 and 1 specifying the weight for penalizing the number of spatial predictors. Higher values favor more parsimonious models.
optimization.method	Character string specifying the optimization method: "moran.i" (default) or "p.value". Default: "moran.i".

Details

This function balances three objectives when selecting spatial predictors:

1. Reduce spatial autocorrelation: Maximize ⁠1 - Moran's I⁠ to minimize residual spatial autocorrelation

2. Maintain model performance: Account for model R-squared

3. Favor parsimony: Penalize models with many spatial predictors

Optimization methods:

The "moran.i" method computes:

⁠score = (1 - Moran's I) + w1 × R² - w2 × penalization⁠

where all components are rescaled to the range 0 to 1, w1 = weight.r.squared, and w2 = weight.penalization.n.predictors.

The "p.value" method computes:

⁠score = max(1 - Moran's I, binary p-value) + w1 × R² - w2 × penalization⁠

where the binary p-value is 1 if p equal or lower than 0.05 (no significant spatial autocorrelation), and 0 otherwise.

Practical differences:

• The "moran.i" method uses continuous Moran's I values and typically selects more spatial predictors to achieve lower spatial autocorrelation

• The "p.value" method uses binary significance thresholds and typically selects fewer predictors, stopping once spatial autocorrelation becomes non-significant

The optimal model is the one with the highest optimization score.

Value

Numeric vector of optimization scores, one per row in x. Higher scores indicate better solutions. All values are rescaled between 0 and 1 for comparability.

See Also

select_spatial_predictors_recursive(), select_spatial_predictors_sequential(), moran()

Other utilities: .vif_to_df(), auc(), beowulf_cluster(), objects_size(), prepare_importance_spatial(), rescale_vector(), root_mean_squared_error(), setup_parallel_execution(), standard_error(), statistical_mode(), thinning(), thinning_til_n()

Examples

## Not run: 
# This function is typically called internally during spatial predictor selection
# Example showing the structure of input data:

# Simulated optimization data frame
opt_data <- data.frame(
  moran.i = c(0.5, 0.3, 0.2, 0.15),
  r.squared = c(0.6, 0.65, 0.68, 0.69),
  penalization.per.variable = c(0.1, 0.2, 0.3, 0.4),
  p.value.binary = c(0, 0, 1, 1)
)

# Compute optimization scores
scores_moran <- optimization_function(
  x = opt_data,
  weight.r.squared = 0.5,
  weight.penalization.n.predictors = 0.5,
  optimization.method = "moran.i"
)

# Compare methods
scores_pvalue <- optimization_function(
  x = opt_data,
  weight.r.squared = 0.5,
  weight.penalization.n.predictors = 0.5,
  optimization.method = "p.value"
)

# Higher score indicates better solution
which.max(scores_moran)
which.max(scores_pvalue)

## End(Not run)

spatialRF documentation built on Dec. 20, 2025, 1:07 a.m.