eivem {eive}

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)

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 ##########################################