Package 'eive' reference manual

Title:	An Algorithm for Reducing Errors-in-Variable Bias in Simple and Multiple Linear Regressions
Description:	Performs a compact genetic algorithm search to reduce errors-in-variables bias in linear regression. The algorithm estimates the regression parameters with lower biases and higher variances but mean-square errors (MSEs) are reduced.
Authors:	Mehmet Hakan Satman (Ph.D.), Erkin Diyarbakirlioglu (Ph.D.)
Maintainer:	Mehmet Hakan Satman <[email protected]>
License:	GPL
Version:	3.1.3
Built:	2024-11-09 04:37:48 UTC
Source:	https://github.com/jbytecode/eive

EIVE - Errors-in-Variable estimation

Description

This package includes functions for compact genetic algorithms and errors-in-variable estimation. The function 'eive' performs a genetic search to reduce the errors-in-variable bias in ordinary least squares estimator.

Change log:

# In version 3.1.2

- Add eive.cga.formula for lm() compatible regression settings.

- Implement roxygen type documentation system

# In version 3.1.1,

- Enhance document for multivariate eive (eivem)

# In version 3.1,

- Errors-in-variables with multiple response variables.

- eive.cga() now returns 2 new items: $cleanx and $measurementerror which are also accessable using the keys $proxy$fitted.values and $proxy$residuals, respectively.

- eivem() added for multiple y values

- new tests added and can be triggered using devtools:::test()

- updated docs

# In version 2.1, more speed improvements by using lm.fit instead lm in critical code.

# In version 2.0, some routines are rewritten in C++ and wrapped using Rcpp so a substantial speed improvement achieved.

Author(s)

Mehmet Hakan Satman <[email protected]> Erkin Diyarbakirlioglu <[email protected]>

Maintainer: Mehmet Hakan Satman <[email protected]>

Compact Genetic Algorithm

Description

Performs a Compact Genetic Algorithm (CGA) search for a given chromosome size, population size (mutation rate), and an objective function.

Usage

cga(chsize, popsize, evalFunc)
cga(chsize, popsize, evalFunc)

Arguments

`chsize`	Number of bits.
`popsize`	Size of population. The value is used for mutating the probability vector by 1/popsize.
`evalFunc`	Objective function.

Value

Binary vector of size chsize.

Generate Chromosome

Description

Generate a binary vector using a probability vector This function is not directly called by user. CGAs (Compact genetic algorithms) sample chromosomes using this probability vector. A probability vector contains[P1, P2, ..., PN] and the function generates and returns a chromosome[B1, B2, ..., BN]. The probability of BK having the value of 1 is PK. So, it has more chance to have [1, 1, 1, 0, 0] rather than [0, 0, 0, 1, 1] when the probability vector is [0.9, 0.9, 0.9, 0.1, 0.1].

Usage

cga_generate_chromosome(prob_vec, vect)
cga_generate_chromosome(prob_vec, vect)

Arguments

`prob_vec`	Vector of probabilities
`vect`	Vector of bits.

Value

Mutates the vect. Returns null.

Performs CGA based errors-in-variables correction for a given set of variables. A single independent variable is supposed to be measured subject to error.

Description

Performs CGA based errors-in-variables correction for a given set of variables. A single independent variable is supposed to be measured subject to error.

Usage

eive.cga(dirtyx, otherx = NULL, y, numdummies = 10, popsize = 20)
eive.cga(dirtyx, otherx = NULL, y, numdummies = 10, popsize = 20)

Arguments

`dirtyx`	Vector of independent variable that is measured with error.
`otherx`	Matrix of other independent variables. If the model has a single independent variable, it is NULL by default.
`y`	Vector of response variable
`numdummies`	Number of dummy variables used in auxiliary regression.
`popsize`	Population size parameter for compact genetic algorithm. 1/popsize is the mutation rate.

Value

A list() of regression equations.

Slots

ols: lm object calculated using original values
eive: lm object calculated using the predicted variable by eive
proxy: lm object of proxy regression obtained by genetic search.
cleanedx: Error-free estimate of the x variable (dirtyx) that is measured with error.
measurementerror: Estimate of the measurement error.

Examples

# Creating an artificial data
# Loading required package
require("eive")

# Setting random number generator seed to 12345
# so each time the script runs, same numbers will
# be generated
set.seed(12345)

# Number of observations is set to 30
n <- 30

# Unobserved X values are drawn from a Normal distribution
# with mean 10 and variance 7
clean.x <- rnorm(n, mean = 10, sd = sqrt(7))

# Measurement error values are dranw from a Normal distribution
# with mean 0 and variance 3
delta.x <- rnorm(n, mean = 0, sd = sqrt(3))

# Error term of regression. Normally distributed with mean 0 and
# variance 5
e <- rnorm(n, mean = 0, sd = sqrt(5))

# Generating Y values using the linear model
# In this model, intercept is 20 and slope is 10.
y <- 20 + 10 * clean.x + e

# Generating observed X values by adding measurement errors
# to unobserved X
dirty.x <- clean.x + delta.x

# Performs a genetic search to find dummy variables that
# used in two stage least squares.
# Please un-comment the line below
# result <- eive.cga (dirtyx=dirty.x, y=y, numdummies=10)

# Print the result
# Please un-comment the line below
# print(result)

########################################### OUTPUT #############################################
# $ols
#
# Call:
# lm(formula = y ~ dirtyx)
#
# Coefficients:
# (Intercept)       dirtyx
#     63.590        5.533
#
#
# $eive
#
# Call:
# lm(formula = y ~ ols.proxy$fitted.values)
#
# Coefficients:
#            (Intercept)  ols.proxy$fitted.values
#                 23.863                    9.229
#
#
# $proxy
#
# Call:
# lm(formula = dirtyx ~ matrix(best, nrow = n))
#
# Coefficients:
#              (Intercept)   matrix(best, nrow = n)1   matrix(best, nrow = n)2
#                 12.9321                   -0.6252                   -1.9923
# matrix(best, nrow = n)3   matrix(best, nrow = n)4   matrix(best, nrow = n)5
#                  0.7537                   -0.7076                   -0.5247
# matrix(best, nrow = n)6   matrix(best, nrow = n)7   matrix(best, nrow = n)8
#                 -0.9196                   -2.0802                   -0.9246
# matrix(best, nrow = n)9  matrix(best, nrow = n)10
#                 -0.6164                    1.9694
######################################### END OF OUTPUT ##########################################
# Creating an artificial data
# Loading required package
require("eive")

# Setting random number generator seed to 12345
# so each time the script runs, same numbers will
# be generated
set.seed(12345)

# Number of observations is set to 30
n <- 30

# Unobserved X values are drawn from a Normal distribution
# with mean 10 and variance 7
clean.x <- rnorm(n, mean = 10, sd = sqrt(7))

# Measurement error values are dranw from a Normal distribution
# with mean 0 and variance 3
delta.x <- rnorm(n, mean = 0, sd = sqrt(3))

# Error term of regression. Normally distributed with mean 0 and
# variance 5
e <- rnorm(n, mean = 0, sd = sqrt(5))

# Generating Y values using the linear model
# In this model, intercept is 20 and slope is 10.
y <- 20 + 10 * clean.x + e

# Generating observed X values by adding measurement errors
# to unobserved X
dirty.x <- clean.x + delta.x

# Performs a genetic search to find dummy variables that
# used in two stage least squares.
# Please un-comment the line below
# result <- eive.cga (dirtyx=dirty.x, y=y, numdummies=10)

# Print the result
# Please un-comment the line below
# print(result)

########################################### OUTPUT #############################################
# $ols
#
# Call:
# lm(formula = y ~ dirtyx)
#
# Coefficients:
# (Intercept)       dirtyx
#     63.590        5.533
#
#
# $eive
#
# Call:
# lm(formula = y ~ ols.proxy$fitted.values)
#
# Coefficients:
#            (Intercept)  ols.proxy$fitted.values
#                 23.863                    9.229
#
#
# $proxy
#
# Call:
# lm(formula = dirtyx ~ matrix(best, nrow = n))
#
# Coefficients:
#              (Intercept)   matrix(best, nrow = n)1   matrix(best, nrow = n)2
#                 12.9321                   -0.6252                   -1.9923
# matrix(best, nrow = n)3   matrix(best, nrow = n)4   matrix(best, nrow = n)5
#                  0.7537                   -0.7076                   -0.5247
# matrix(best, nrow = n)6   matrix(best, nrow = n)7   matrix(best, nrow = n)8
#                 -0.9196                   -2.0802                   -0.9246
# matrix(best, nrow = n)9  matrix(best, nrow = n)10
#                 -0.6164                    1.9694
######################################### END OF OUTPUT ##########################################

Performs CGA based errors-in-variables correction for given formula and data. A single independent variable is supposed to be measured subject to error.

Description

Performs CGA based errors-in-variables correction for given formula and data. A single independent variable is supposed to be measured subject to error.

Usage

eive.cga.formula(formula, data, dirtyx.varname, numdummies = 10, popsize = 20)
eive.cga.formula(formula, data, dirtyx.varname, numdummies = 10, popsize = 20)

Arguments

`formula`	Formula object.
`data`	data.frame that holds the regression data.
`dirtyx.varname`	String key value of the erroneous independent variable.
`numdummies`	Number of dummy variables used in auxiliary regression.
`popsize`	Population size parameter for compact genetic algorithm. 1/popsize is the mutation rate.

Value

A list() of regression equations.

Slots

ols: lm object calculated using original values
eive: lm object calculated using the predicted variable by eive
proxy: lm object of proxy regression obtained by genetic search.
cleanedx: Error-free estimate of the x variable (dirtyx) that is measured with error.
measurementerror: Estimate of the measurement error.

Examples

set.seed(12345)
n <- 30
clean_x <- rnorm(n, mean = 10, sd = sqrt(7))
delta_x <- rnorm(n, mean = 0, sd = sqrt(3))

e <- rnorm(n, mean = 0, sd = sqrt(5))
y <- 20 + 10 * clean_x + e

dirty_x <- clean_x + delta_x

mydata <- data.frame(y = y, dirtyx = dirty_x)

result <- eive.cga.formula(
     formula = y ~ dirtyx,
     dirtyx.varname = "dirtyx",
     data = mydata,
     numdummies = 10
)
set.seed(12345)
n <- 30
clean_x <- rnorm(n, mean = 10, sd = sqrt(7))
delta_x <- rnorm(n, mean = 0, sd = sqrt(3))

e <- rnorm(n, mean = 0, sd = sqrt(5))
y <- 20 + 10 * clean_x + e

dirty_x <- clean_x + delta_x

mydata <- data.frame(y = y, dirtyx = dirty_x)

result <- eive.cga.formula(
     formula = y ~ dirtyx,
     dirtyx.varname = "dirtyx",
     data = mydata,
     numdummies = 10
)

Performs CGA based errors-in-variables correction for a given set of variables in case of multiple Y variables are provided.

Description

A single independent variable is supposed to be measured subject to error. This functions is the multivariate version of the classical algorithm. Additional response variables are used to get better estimates.

Usage

eivem(dirtyx, otherx = NULL, y, numdummies = 10, popsize = 20)
eivem(dirtyx, otherx = NULL, y, numdummies = 10, popsize = 20)

Arguments

`dirtyx`	Vector of independent variable that is measured with error.
`otherx`	Matrix of other independent variables. If the model has a single independent variable, it is NULL by default.
`y`	Matrix of response variables. Y_i is placed in the ith row of the matrix.
`numdummies`	Number of dummy variables used in auxiliary regression. Default is 10.
`popsize`	Population size parameter for compact genetic algorithm. Default is 20. 1/popsize is the mutation rate.

Value

A list() of regression equations.

Slots

ols: List of lm objects calculated using original values
eive: List of lm objects calculated using the predicted variable by eive
proxy: lm object of proxy regression obtained by genetic search.
cleanedx: Error-free estimate of the x variable (dirtyx) that is measured with error.
measurementerror: Estimate of the measurement error.

Examples

# Creating an artificial data

# Loading required package
require("eive")

# Setting random number generator seed to 12345
# so each time the script runs, same numbers will
# be generated
set.seed(12345)

# Number of observations is set to 30
n <- 30

# Unobserved X values are drawn from a Normal distribution
# with mean 10 and variance 7
clean_x1 <- rnorm(n, mean = 10, sd = sqrt(7))
clean_x2 <- rnorm(n, mean = 10, sd = sqrt(7))

# Measurement error values are dranw from a Normal distribution
# with mean 0 and variance 3
delta_x1 <- rnorm(n, mean = 0, sd = sqrt(3))

# Error term of regression. Normally distributed with mean 0 and
# variance 5
e1 <- rnorm(n, mean = 0, sd = sqrt(5))
e2 <- rnorm(n, mean = 0, sd = sqrt(5))

# Generating Y values using the linear model
# In this model, intercept is 20 and slope is 10.
y1 <- 20 + 10 * clean_x1 + 10 * clean_x2 + e1
y2 <- 10 + 5 * clean_x1 + 5 * clean_x2 + e2

# Generating observed X values by adding measurement errors
# to unobserved X
dirty_x1 <- clean_x1 + delta_x1

# Performs a genetic search to find dummy variables that
# used in two stage least squares.
# Please un-comment the line below
result <- eivem(dirtyx = dirty_x1, otherx = clean_x2, y = cbind(y1, y2), numdummies = 10)

# Print the result
# Please un-comment the line below
# print(result)

########################################### OUTPUT #############################################
#> result
# $ols
# $ols[[1]]
#
# Call:
# lm(formula = y[, reg.index] ~ dirtyx + otherx)
#
# Coefficients:
# (Intercept)       dirtyx       otherx
#      54.141        6.067       10.137
#
#
# $ols[[2]]
#
# Call:
# lm(formula = y[, reg.index] ~ dirtyx + otherx)
#
# Coefficients:
# (Intercept)       dirtyx       otherx
#      24.814        3.205        5.089
#
#
#
# $eive
# $eive[[1]]
#
# Call:
# lm(formula = y[, reg.index] ~ ols_proxy$fitted.values + otherx)
#
# Coefficients:
#             (Intercept)  ols_proxy$fitted.values                   otherx
#                  24.737                    9.727                    9.147
#
#
# $eive[[2]]
#
# Call:
# lm(formula = y[, reg.index] ~ ols_proxy$fitted.values + otherx)
#
# Coefficients:
#             (Intercept)  ols_proxy$fitted.values                   otherx
#                   8.313                    5.240                    4.552
#
#

# $proxy
#
# Call:
# lm(formula = dirtyx ~ matrix(best, nrow = n))
#
# Coefficients:
#              (Intercept)   matrix(best, nrow = n)1   matrix(best, nrow = n)2
#                 6.314397                 -0.211580                  1.729143
#  matrix(best, nrow = n)3   matrix(best, nrow = n)4   matrix(best, nrow = n)5
#                 1.994915                  0.947531                 -0.363107
#  matrix(best, nrow = n)6   matrix(best, nrow = n)7   matrix(best, nrow = n)8
#                 0.001768                  1.742553                 -0.023750
#  matrix(best, nrow = n)9  matrix(best, nrow = n)10
#                 0.134750                  2.324853
#
#
# $cleanedx
#         1         2         3         4         5         6         7         8
# 12.730307 12.130102 11.065586  9.795474 12.697138  6.450915 12.673388 10.516553
#         9        10        11        12        13        14        15        16
# 11.095771  7.981887 11.694464 14.841812 11.098755 12.290371  8.988344 12.704789
#        17        18        19        20        21        22        23        24
#  7.671861  9.477178 13.458999 10.964004 11.465852 14.591473  9.771724  6.239335
#        25        26        27        28        29        30
#  6.425397 15.031410  8.992839 12.808138 13.435249  9.799758
#
# $measurementerror
#          1          2          3          4          5          6          7
# -0.9220426 -2.5783644 -0.3964263  1.7585818 -2.1106159 -4.4345451  0.5319987
#          8          9         10         11         12         13         14
#  1.5127360 -0.9523682 -2.6583539 -1.9074299 -1.3927085 -1.9356982  3.1225578
#         15         16         17         18         19         20         21
#  1.4554922  1.0891572  1.4141792 -1.7600789  0.3310142  1.5952156  1.7146703
#         22         23         24         25         26         27         28
#  1.0669497 -2.0036393  3.9419318  1.0296643  2.9783401  0.8968531 -1.7001587
#         29         30
# -0.8864360  1.1995241
#
######################################### END OF OUTPUT ##########################################
# Creating an artificial data

# Loading required package
require("eive")

# Setting random number generator seed to 12345
# so each time the script runs, same numbers will
# be generated
set.seed(12345)

# Number of observations is set to 30
n <- 30

# Unobserved X values are drawn from a Normal distribution
# with mean 10 and variance 7
clean_x1 <- rnorm(n, mean = 10, sd = sqrt(7))
clean_x2 <- rnorm(n, mean = 10, sd = sqrt(7))

# Measurement error values are dranw from a Normal distribution
# with mean 0 and variance 3
delta_x1 <- rnorm(n, mean = 0, sd = sqrt(3))

# Error term of regression. Normally distributed with mean 0 and
# variance 5
e1 <- rnorm(n, mean = 0, sd = sqrt(5))
e2 <- rnorm(n, mean = 0, sd = sqrt(5))

# Generating Y values using the linear model
# In this model, intercept is 20 and slope is 10.
y1 <- 20 + 10 * clean_x1 + 10 * clean_x2 + e1
y2 <- 10 + 5 * clean_x1 + 5 * clean_x2 + e2

# Generating observed X values by adding measurement errors
# to unobserved X
dirty_x1 <- clean_x1 + delta_x1

# Performs a genetic search to find dummy variables that
# used in two stage least squares.
# Please un-comment the line below
result <- eivem(dirtyx = dirty_x1, otherx = clean_x2, y = cbind(y1, y2), numdummies = 10)

# Print the result
# Please un-comment the line below
# print(result)

########################################### OUTPUT #############################################
#> result
# $ols
# $ols[[1]]
#
# Call:
# lm(formula = y[, reg.index] ~ dirtyx + otherx)
#
# Coefficients:
# (Intercept)       dirtyx       otherx
#      54.141        6.067       10.137
#
#
# $ols[[2]]
#
# Call:
# lm(formula = y[, reg.index] ~ dirtyx + otherx)
#
# Coefficients:
# (Intercept)       dirtyx       otherx
#      24.814        3.205        5.089
#
#
#
# $eive
# $eive[[1]]
#
# Call:
# lm(formula = y[, reg.index] ~ ols_proxy$fitted.values + otherx)
#
# Coefficients:
#             (Intercept)  ols_proxy$fitted.values                   otherx
#                  24.737                    9.727                    9.147
#
#
# $eive[[2]]
#
# Call:
# lm(formula = y[, reg.index] ~ ols_proxy$fitted.values + otherx)
#
# Coefficients:
#             (Intercept)  ols_proxy$fitted.values                   otherx
#                   8.313                    5.240                    4.552
#
#

# $proxy
#
# Call:
# lm(formula = dirtyx ~ matrix(best, nrow = n))
#
# Coefficients:
#              (Intercept)   matrix(best, nrow = n)1   matrix(best, nrow = n)2
#                 6.314397                 -0.211580                  1.729143
#  matrix(best, nrow = n)3   matrix(best, nrow = n)4   matrix(best, nrow = n)5
#                 1.994915                  0.947531                 -0.363107
#  matrix(best, nrow = n)6   matrix(best, nrow = n)7   matrix(best, nrow = n)8
#                 0.001768                  1.742553                 -0.023750
#  matrix(best, nrow = n)9  matrix(best, nrow = n)10
#                 0.134750                  2.324853
#
#
# $cleanedx
#         1         2         3         4         5         6         7         8
# 12.730307 12.130102 11.065586  9.795474 12.697138  6.450915 12.673388 10.516553
#         9        10        11        12        13        14        15        16
# 11.095771  7.981887 11.694464 14.841812 11.098755 12.290371  8.988344 12.704789
#        17        18        19        20        21        22        23        24
#  7.671861  9.477178 13.458999 10.964004 11.465852 14.591473  9.771724  6.239335
#        25        26        27        28        29        30
#  6.425397 15.031410  8.992839 12.808138 13.435249  9.799758
#
# $measurementerror
#          1          2          3          4          5          6          7
# -0.9220426 -2.5783644 -0.3964263  1.7585818 -2.1106159 -4.4345451  0.5319987
#          8          9         10         11         12         13         14
#  1.5127360 -0.9523682 -2.6583539 -1.9074299 -1.3927085 -1.9356982  3.1225578
#         15         16         17         18         19         20         21
#  1.4554922  1.0891572  1.4141792 -1.7600789  0.3310142  1.5952156  1.7146703
#         22         23         24         25         26         27         28
#  1.0669497 -2.0036393  3.9419318  1.0296643  2.9783401  0.8968531 -1.7001587
#         29         30
# -0.8864360  1.1995241
#
######################################### END OF OUTPUT ##########################################

Generates simulated errors-in-variables regression data

Description

Generates simulated errors-in-variables regression data

Usage

generate.eive.data(n, e.sd, delta.sd, seed = 12345, useotherx = FALSE)
generate.eive.data(n, e.sd, delta.sd, seed = 12345, useotherx = FALSE)

Arguments

`n`	Number of observations
`e.sd`	Standard deviation of error term of regression
`delta.sd`	Standard deviation of error in exploratory variable
`seed`	Seed for random number generator. 12345 by default
`useotherx`	Logical. If TRUE, an additional independent variable is added.

Value

A matrix of variables.

Slots

xdelta: Errorenous X variable
otherx: Other X variable
y: Response variable

Package 'eive'

Help Index

EIVE - Errors-in-Variable estimation

Description

Author(s)

Compact Genetic Algorithm

Description

Usage

Arguments

Value

Generate Chromosome

Description

Usage

Arguments

Value

Performs CGA based errors-in-variables correction for a given set of variables. A single independent variable is supposed to be measured subject to error.

Description

Usage

Arguments

Value

Slots

Examples

Performs CGA based errors-in-variables correction for given formula and data. A single independent variable is supposed to be measured subject to error.

Description

Usage

Arguments

Value

Slots

See Also

Examples

Performs CGA based errors-in-variables correction for a given set of variables in case of multiple Y variables are provided.

Description

Usage

Arguments

Value

Slots

Examples

Generates simulated errors-in-variables regression data

Description

Usage

Arguments

Value

Slots