qcreg {qcauchyreg} | R Documentation |
Quasi-Cauchy quantile regression
Description
Returns an object of class rq()
that represents a Quasi-Cauchy quantile regression fit. Quasi-Cauchy quantile regression is useful when you want to perform quantile regression analysis on data limited to the unit range.
Usage
qcreg(formula, data, tau=0.5, npi=100, criterion="bic", tau_i=0.05, tau_f=0.95)
Arguments
formula |
a formula object, with the response on the left of a ~ operator, and the terms, separated by + operators, on the right. |
data |
a |
tau |
the quantile to be estimated, this is a number strictly between 0 and 1. The default value is 0.5. |
npi |
(optional) the number of Pi's that will be considered for choosing the Pi that best fits the model. The default value is 100. |
criterion |
(optional) criterion to decide the Pi that fits the model. Choose "aic" for AIC, "bic" for BIC and "R2" for pseudo-R2. Or, indicate a numerical value between 0<Pi<pi to use a particular Pi. The default is the automatic choice of Pi following the BIC criterion. |
tau_i |
(optional) if you want to estimate several quantiles simultaneously, enter the lower limit of the range of coatis you want to estimate here. The default value is 0.05. |
tau_f |
(optional) if you want to estimate several quantiles simultaneously, enter the upper limit of the range of coatis you want to estimate here. The default value is 0.95. |
Details
The Quasi-Cauchy quantile regression model is based on the traditional quantile model, proposed by Koenker (2005) (doi:10.1017/CBO9780511754098), to which the Quasi-Cauchy link function is added, allowing the estimation of quantile regression when modeling a variable of nature limited to the ranges [0,1], (0,1], [0,1) or (0,1). For more details on Quasi-Cauchy quantile regression, see de Oliveira, Ospina, Leiva, Figueroa-Zuniga and Castro (2023) (doi:10.3390/fractalfract7090667).
Value
qcreg()
returns an object of class rq()
, hence all outputs of an rq()
object are accessible.
index
returns the Pi value used in estimating the model and 4 goodness-of-fit criteria, namely: AIC, BIC, pseudo-R2, adjusted pseudo-R2.
effects
returns the marginal effect on the average.
quantregplot
returns argument for graphical visualization of estimates (and confidence intervals) considering a range of values for tau instead of a single value.
pis
returns the values of Pi considered in the procedure for choosing the ideal Pi, as well as the corresponding goodness-of-fit criterion values. Available only when Pi is chosen via goodness-of-fit criteria.
Author(s)
Jose Sergio Case de Oliveira
References
[1] Koenker, R. W. (2005). Quantile Regression, Cambridge U. Press. doi:10.1017/CBO9780511754098
[2] de Oliveira, J.S.C.; Ospina, R.; Leiva, V.; Figueroa-Zuniga, J.; Castro, C. (2023). Quasi-Cauchy Regression Modeling for Fractiles Based on Data Supported in the Unit Interval. Fractal Fract. 7, 667. doi:10.3390/fractalfract7090667
Examples
data("Democratization", package = "qcauchyreg")
fit <- qcreg(democratization ~ schooling + press_freedom, data = Democratization, criterion=1)
summary(fit)
fit$effects
fit$index
data("Poverty", package = "qcauchyreg")
fit2 <- qcreg(poverty ~ population + illiteracy + pc_income,
data = Poverty, npi=50, criterion="bic")
summary(fit2)
fit2$effects
fit2$index
plot(fit2$pis, type="l")
plot(fit2$quantregplot)