Lorenz.GA {LorenzRegression}

Estimates the parameter vector in Lorenz regression using a genetic algorithm

Description

Lorenz.GA estimates the vector of parameters in Lorenz regression using the unit-norm normalization It also returns the Lorenz-R^2 of the regression as well as the estimated explained Gini coefficient.

Usage

Lorenz.GA(
  YX_mat,
  standardize = TRUE,
  popSize = 50,
  maxiter = 1500,
  run = 150,
  ties.method = c("random", "mean"),
  ties.Gini = c("random", "mean"),
  seed.random = NULL,
  weights = NULL,
  parallel = FALSE
)

Arguments

YX_mat

A matrix with the first column corresponding to the response vector, the remaining ones being the explanatory variables.

standardize

Should the variables be standardized before the estimation process? Default value is TRUE.

popSize

Size of the population of candidates in the genetic algorithm. Default value is 50.

maxiter

Maximum number ot iterations in the genetic algorithm. Default value is 1500.

run

Number of iterations without improvement in the best fitness necessary for the algorithm to stop. Default value is 150.

ties.method

What method should be used to break the ties in optimization program. Possible values are "random" (default value) or "mean". If "random" is selected, the ties are broken by further ranking in terms of a uniformly distributed random variable. If "mean" is selected, the average rank method is used.

ties.Gini

what method should be used to break the ties in the computation of the Gini coefficient at the end of the algorithm. Possible values and default choice are the same as above.

seed.random

seed.random imposed for the generation of the vector of uniform random variables used to break the ties. Default is NULL, in which case no seed.random is imposed.

weights

vector of sample weights. By default, each observation is given the same weight.

parallel

Whether parallel computing should be used to distribute the computations in the genetic algorithm. Either a logical value determining whether parallel computing is used (TRUE) or not (FALSE, the default value). Or a numerical value determining the number of cores to use.

Details

The genetic algorithm is solved using function ga from the GA package. The fitness function is coded in Rcpp to speed up computation time. When discrete covariates are introduced and ties occur in the index, the default option randomly breaks them, as advised in Section 3 of Heuchenne and Jacquemain (2020)

Value

A list with several components:

theta

the estimated vector of parameters.

LR2

the Lorenz-R^2 of the regression.

Gi.expl

the estimated explained Gini coefficient.

niter

number of iterations attained by the genetic algorithm.

fit

value attained by the fitness function at the optimum.

References

Heuchenne, C. and A. Jacquemain (2022). Inference for monotone single-index conditional means: A Lorenz regression approach. Computational Statistics & Data Analysis 167(C).

See Also

Lorenz.Reg, ga

Examples

data(Data.Incomes)
YX_mat <- cbind(Data.Incomes$Income, Data.Incomes$Age, Data.Incomes$Work.Hours)
Lorenz.GA(YX_mat, popSize = 40)