Compute optimization scores for spatial predictor selection

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".

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.

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.

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

if (FALSE) { # \dontrun{
# 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)
} # }