qcreg {qcauchyreg}

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 data.frame() composed of the variables that will be used in the model.

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)