find_optimal_lambda {utilityFunctionTools}

Finds an optimal penalty weight lambda given the parameters

Description

Finds an optimal penalty weight lambda given the parameters

Usage

find_optimal_lambda(
  xi,
  yi,
  lambda_max = 10000,
  n_penalty_dimensions = 1,
  penalty_order = 4,
  ndx = 20,
  deg = 6,
  cross_validation_mode = 0,
  grid_dim = 5
)

Arguments

xi

a vector containing the certainty equivalents (x-values of utility points) for a given participant in each use case.

yi

can be a vector or a matrix representing the corresponding utility values (y-values of utility points).

lambda_max

maximum lambda used for computing the optimal lambda. The default value is 10000.

n_penalty_dimensions

number of dimensions (i.e., derivatives) to penalize. Possible values are 1 or 2. The default value is 1.

penalty_order

highest dimension (i.e., derivative) to penalize. Must be lower than deg.

ndx

number of intervals to partition the distance between the lowest and highest x-values of the utility points.

deg

degree of the B-spline basis. Determines the degree of the function to be estimated. If deg = 2, the estimated utility function will consist of quadratic functions.

cross_validation_mode

determines which cross validation mode should be used. If 0, then the cross validation method is leave-one-third-out. If 1, then the cross validation method is a theoretical leave-one-out, i.e., based on a formula. The default value is 1.

grid_dim

dimension of the search grid for the initial grid search before the actual optimization. Default value is 5.

Value

the optimal lambda for the given set of utility points and (possibly default) settings according to the specified cross validation method.

Examples

x <- c(0.0000000, 0.2819824, 0.3007812, 0.4375000, 0.5231934, 0.7784882, 0.8945312, 1.0000000)
y <- c(0.0000, 0.1250, 0.2500, 0.5000, 0.6250, 0.6875, 0.7500, 1.0000)
find_optimal_lambda(x, y)