ga.lts: Function for estimating the LTS (Least Trimmed Squares)...

In galts: Genetic Algorithms and C-Steps Based LTS (Least Trimmed Squares) Estimation

Function for estimating the LTS (Least Trimmed Squares) regression parameters using genetic algorithms.

Description

This function estimates the LTS (Least Trimmed Squares) regression parameters using genetic algorithms. LTS is a robust regression estimator with high breakdown property. LTS is a resistant estimator even the number of outliers is up to half of the data. However, calculating LTS estimator is computaionally expensive. ga.lts() uses evolutionary algorithms (genetic algorithms by default, optionally differential evolution) to construct a basic subset and iterates C-steps as defined in Rousseeuw and van-Driessen (2006). Despite lower time efficiency of the ga.lts(), estimations have lower mean square errors, as a result of lower biases and lower variances.

Usage

ga.lts(formula, h = NULL, iters = 2, popsize = 50, lower, upper, 
		csteps = 2, method = "ga", verbose = FALSE)

Arguments

formula	Dependent ~ Independents style formula as same in lm() and glm().
h	User defined variable to define the majority of the data. Default is floor(n/2)+floor((p+1)/2) where n is the number of observations and p is the number of parameters to estimate
iters	Number of generations of the evolutionary algorithm. This variable can be kept larger if the precision is more important than the computation time. Default is 2.
popsize	Number of candidates (chromosomes) in the population of evolutionary algorithm. Default is 50.
lower	Lower bound for the initial estimates of the parameters.
upper	Upper bound for the initial estimates of the parameters.
csteps	Number of C-steps to be performed for each candidate solution. Default is 2.
method	A string variable for the evolutionary algorithm. 'ga' for the genetic algorithms and 'de' for the differential evolution. Default is 'ga'
verbose	A boolean variable for printing the current status of algorithms to screen. Default is FALSE.

Value

coefficients	A vector of estimated parameters
crit	LTS criterion value for the reported coefficients
method	Name of the method used in the optimization process

Author(s)

Mehmet Hakan Satman

References

Rousseeuw, P. J., van Driessen, K. (2006). Computing LTS Regression for Large Data Sets ,Data Mining and Knowledge Discovery, 12, 29-45.

Satman, M.,H. (2012). A Genetic Algorithm Based Modification on the LTS Algorithm for Large Data Sets, Communications in Statistics - Simulation and Computation, Vol 41, Issue 5, pp. 644-652.

Examples

# Data generating process
x1 <- rnorm(100)
x2 <- rnorm(100)
e <- rnorm(100)

# Setting betas to 5
y <- 5 + 5 * x1 + 5 * x2 + e

# Contaminate the data on the dimension of X's randomly
# This is the maximum contamination rate that the LTS can cope with.
outlyings <- sample(1:100, 48)
x1[outlyings] <- 10
x2[outlyings] <- 10

# Estimating LTS with ga (Default optimization method)
lts <- ga.lts(y ~ x1 + x2, popsize = 40, iters = 2, lower = -20, upper = 20)
print(lts)


# Estimating LTS with differential evolution
lts <- ga.lts(y ~ x1 + x2, popsize = 40, iters = 2, lower = -20, upper = 20, method = "de")
print(lts)

galts documentation built on Aug. 20, 2023, 9:08 a.m.