iOLS {IOLS}

iOLS

Description

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.

Usage

iOLS(y, X, VX, tX, d, epsi = 10^-5, b_init, error_type = "HC0")

Arguments

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.

Value

an iOLS fitted model object.

Examples

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)