Estimates, for each observation, the minimum and maximum feasible values of the
directional distance parameter \(\beta\) used in projection-based efficiency
analysis. This function is an internal step of PEAXAI_targets,
providing the initial search bounds for the iterative determination of efficiency targets.
find_beta_maxmin(
data,
x,
y,
final_model,
efficiency_thresholds,
n_expand,
vector_gx,
vector_gy,
max_y,
min_x
)A data.frame with two numeric columns:
minMinimum feasible value of \(\beta\) for each observation.
maxMaximum feasible value of \(\beta\) for each observation.
A data.frame or matrix containing input and output variables.
A numeric vector with the column indexes of input variables in data.
A numeric vector with the column indexes of output variables in data.
A fitted caret model of class "train" that supports
predict(type = "prob") and returns a probability column for the efficient class.
A numeric vector of probability levels in (0,1). Its minimum and maximum values delimit the target interval used to bracket \(\beta\).
Integer. Increment step size applied to \(\beta\) at each iteration.
A numeric vector or data.frame with directional changes for inputs
(typically negative direction), usually built inside PEAXAI_targets.
A numeric vector or data.frame with directional changes for outputs
(positive direction).
Numeric. Upper-limit multiplier for output expansion relative to observed maxima.
Numeric. Lower-limit multiplier for input contraction relative to observed minima.
For each DMU, the function expands outputs and contracts inputs along the specified
direction until the predicted probability of efficiency (from final_model)
reaches the maximum in efficiency_thresholds or feasible domain limits.
The resulting interval \([\beta_{\min}, \beta_{\max}]\) is then used by
PEAXAI_targets to refine projections via grid search.
PEAXAI_targets (efficiency projections based on \(\beta\));
train (model training with class probabilities).