| Title: | Iterated Ordinary Least Squares Regression |
|---|---|
| Description: | Addresses the 'log of zero' by developing a new family of estimators called iterated Ordinary Least Squares. This family nests standard approaches such as log-linear and Poisson regressions, offers several computational advantages, and corresponds to the correct way to perform the popular log(Y + 1) transformation. For more details about how to use it, see the notebook at: <https://www.davidbenatia.com/>. |
| Authors: | Nassim Zbalah [cre], David Benatia [aut] |
| Maintainer: | Nassim Zbalah <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.4 |
| Built: | 2024-10-29 04:17:52 UTC |
| Source: | https://github.com/cran/IOLS |
A simple data_frame obtained by a Data Generating Process that is for testing and running of examples
outcome variable
two bivariate normal variables x1 and x2
DATASETDATASET
An object of class data.frame with 1000 rows and 3 columns.
iOLS regression is used to fit
log-linear model/log-log model, adressing the "log of zero" problem,
based on the theoretical results developed
in the following paper :
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3444996.
iOLS(y, X, VX, tX, d, epsi = 10^-5, b_init, error_type = "HC0")iOLS(y, X, VX, tX, d, epsi = 10^-5, b_init, error_type = "HC0")
y |
the dependent variable, a vector. |
X |
the regressors matrix x with a column of ones added. |
VX |
a matrix that MUST be equal to (X'X)^-1. |
tX |
a matrix that MUST be equal to X^t (the transpose of X). |
d |
the value of the hyper-parameter delta, numeric. |
epsi |
since the estimated parameters are obtained by converging, we need a convergence criterion epsi (supposed to be small, usually around 10^-5), to make the program stop once the estimations are near their limits. A numeric. |
b_init |
the point from which the solution starts its converging trajectory. A vector that has the same number of elements as there are parameters estimated in the model. |
error_type |
a character string specifying the estimation type of the covariance matrix. Argument of the vcovHC function, then click this link for details. "HC0" is the default value, this the White's estimator. |
an iOLS fitted model object.
data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) tX = t(X) library(matlib) ; VX = inv(tX %*% X) f = iOLS(y, X, VX, tX, 20, b_init = lm_coef)data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) tX = t(X) library(matlib) ; VX = inv(tX %*% X) f = iOLS(y, X, VX, tX, 20, b_init = lm_coef)
iOLS regression repeated for several values
of the hyper-parameter delta.
iOLS_path( y, X, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, b_init, error_type = "HC0" )iOLS_path( y, X, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, b_init, error_type = "HC0" )
y |
the dependent variable, a vector. |
X |
the regressors matrix x with a column of ones added. |
deltainf |
numeric, the lowest hyper-parameter delta we want to apply iOLS with. The default value is 10^-5. |
deltasup |
numeric, the highest hyper-parameter delta we want to apply iOLS with. The default value is 10000. |
nbre_delta |
integer, the number of hyper-parameters delta we want between deltainf and deltasup. |
epsi |
since the estimated parameters are obtained by converging, we need a convergence criterion epsi (supposed to be small, usually around 10^-5), to make the program stop once the estimations are near their limits. A numeric. |
b_init |
the point from which the solution starts its converging trajectory. A vector that has the same number of elements as there are parameters estimated in the model. |
error_type |
a character string specifying the estimation type of the covariance matrix. Argument of the vcovHC function, then click this link for details. "HC0" is the default value, this the White's estimator. |
an iOLS_path fitted model object.
data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) k = iOLS_path(y, X, b_init = lm_coef, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, error_type = "HC0")data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) k = iOLS_path(y, X, b_init = lm_coef, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, error_type = "HC0")
Function that plots an iOLS_path fitted model object.
iOLS_path_plot(m, delta_rank = NULL, plot_beta = "", ...)iOLS_path_plot(m, delta_rank = NULL, plot_beta = "", ...)
m |
An |
delta_rank |
Among all the hyper-parameters delta, we can choose to plot the "iOLS_path" fitted model object corresponding to the chosen delta_rank. If a value is not precised, the default value is NULL and the function will only display the estimated parameter(s) in function of log(delta). |
plot_beta |
If you want to see the trajectory of one estimated parameter beta only, just precise plot_beta = k (k=0 if you want to see the intercept's trajectory for example). Otherwise, write plot_beta = "" (the default value), and you will see all parameters' trajectory. In this case, the colors of each curve is assigned randomly, but by precising which parameters' trajectory you want to see, it will be drawn in black. |
... |
other parameters. |
a plot of an iOLS_path fitted model object.
data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) k = iOLS_path(y, X, b_init = lm_coef, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, error_type = "HC0") #All the parameters, as a function of log(delta) (ie. each triplet from an iOLS regression) : iOLS_path_plot(k) #All the parameters from the 6th iOLS regression : iOLS_path_plot(k, delta_rank = 6) #Intercept from the 6th iOLS regression : iOLS_path_plot(k, delta_rank = 6, plot_beta = 0)data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) k = iOLS_path(y, X, b_init = lm_coef, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, error_type = "HC0") #All the parameters, as a function of log(delta) (ie. each triplet from an iOLS regression) : iOLS_path_plot(k) #All the parameters from the 6th iOLS regression : iOLS_path_plot(k, delta_rank = 6) #Intercept from the 6th iOLS regression : iOLS_path_plot(k, delta_rank = 6, plot_beta = 0)
Function that plots an iOLS fitted model object.
iOLS_plot(m, ..., plot_beta = "")iOLS_plot(m, ..., plot_beta = "")
m |
An |
... |
other parameters. |
plot_beta |
If you want to see the trajectory of one estimated parameter beta only, just precise plot_beta = k (k=0 if you want to see the intercept's trajectory for example). Otherwise, write plot_beta = "" (the default value), and you will see all parameters' trajectory. In this case, the colors of each curve is assigned randomly, but by precising which parameters' trajectory you want to see, it will be drawn in black. |
a plot of an iOLS fitted model object.
data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) tX = t(X) library(matlib) ; VX = inv(tX %*% X) f = iOLS(y, X, VX, tX, 20, b_init = lm_coef) iOLS_plot(f) #Only one of the estimated parameters, for example k=0 (the intercept): iOLS_plot(f, plot_beta = 0)data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) tX = t(X) library(matlib) ; VX = inv(tX %*% X) f = iOLS(y, X, VX, tX, 20, b_init = lm_coef) iOLS_plot(f) #Only one of the estimated parameters, for example k=0 (the intercept): iOLS_plot(f, plot_beta = 0)
Printing and plotting of the lambda-test.
lambda_test(f, nB)lambda_test(f, nB)
f |
An |
nB |
The number of iteration that you want to be done in the bootstrap process used in the function. |
a lambda_test object.
data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) k = iOLS_path(y, X, b_init = lm_coef, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, error_type = "HC0") L = lambda_test(k, nB = 5)data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) k = iOLS_path(y, X, b_init = lm_coef, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, error_type = "HC0") L = lambda_test(k, nB = 5)
Function that prints an iOLS fitted model object.
print(m, ...)print(m, ...)
m |
An |
... |
other parameters. |
a display of an iOLS fitted model object.
data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) tX = t(X) library(matlib) ; VX = inv(tX %*% X) f = iOLS(y, X, VX, tX, 20, b_init = lm_coef) print(f)data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) tX = t(X) library(matlib) ; VX = inv(tX %*% X) f = iOLS(y, X, VX, tX, 20, b_init = lm_coef) print(f)
Function that prints an iOLS_path
fitted model object.
## S3 method for class 'iOLS_path' print(m, delta_rank = NULL, ...)## S3 method for class 'iOLS_path' print(m, delta_rank = NULL, ...)
m |
An |
delta_rank |
Among all the hyper-parameters delta, we can choose to plot the "iOLS_path" fitted model object corresponding to the chosen delta_rank. If a value is not precised, the default value is NULL and the function will only display the estimated parameter(s) in function of log(delta). |
... |
other parameters. |
a display of a iOLS_path fitted model object.
data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) k = iOLS_path(y, X, b_init = lm_coef, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, error_type = "HC0") #Printing of all the iOLS regression: print(k) #Printing of the 6th iOLS regression : print(k, delta_rank = 6)data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) k = iOLS_path(y, X, b_init = lm_coef, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, error_type = "HC0") #Printing of all the iOLS regression: print(k) #Printing of the 6th iOLS regression : print(k, delta_rank = 6)
Function that prints a lambda_test object.
## S3 method for class 'lambda_test' print(m, ...)## S3 method for class 'lambda_test' print(m, ...)
m |
A |
... |
other parameters. |
a display and a plot of a lambda_test object.
data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) k = iOLS_path(y, X, b_init = lm_coef, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, error_type = "HC0") L = lambda_test(k, nB = 5) print(L)data(DATASET) y = DATASET$y x = as.matrix(DATASET[,c("X1","X2")]) lm = lm(log(y+1) ~ x) lm_coef = c(coef(lm)) X = cbind(rep(1, nrow(x)), x) k = iOLS_path(y, X, b_init = lm_coef, deltainf = 10^-5, deltasup = 10^4, nbre_delta = 20, epsi = 10^-3, error_type = "HC0") L = lambda_test(k, nB = 5) print(L)