Package 'qcauchyreg'

Estimation of Democratization Index

Description

Democratization index from "The Quality of Government Basic Dataset” of the University of Gothenburg.

Usage

data("Democratization")

Format

A data frame containing 138 observations on 4 variables.

democratization

democratization index of 138 countries, which can take values in [0, 1].

gdp

real gross domestic product per capita in thousands of dollars.

schooling

average schooling (in years) of people aged 25 years or more.

press_freedom

press freedom index of 138 countries. A lower value indicating greater press freedom, while a higher value indicates limited press freedom.

Details

The data set was collected by "The Quality of Government Basic Dataset” of the University of Gothenburg. The data refers to 138 countries observed in 2010. The dependent variable is the democratization index (democratization), which takes values between 0 and 1 . The closer to 1, the greater the democratization. The explanatory variables are real gross domestic product per capita in thousands of dollars (gdp), average schooling (in years) of people aged 25 years or more (schooling) and press freedom index (press_freedom), a lower value indicating greater press freedom, while a higher value indicates limited press freedom.

Source

https://www.gu.se/en/quality-government/qog-data/data-downloads/basic-dataset

References

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")

## de Oliveira, J.S.C.; Ospina, R.; Leiva, V.; Figueroa-Zuniga, J.; Castro, C. (2023)
fit <- qcreg(democratization ~ schooling + press_freedom, data = Democratization, npi=50)
summary(fit)

fit$effects

plot(fit$pis, type="l")

plot(fit$quantregplot)

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Percentage of extremely poor.

Description

Percentage of extremely poor, by Brazilian municipality for the year 2010. Data made available by http://www.atlasbrasil.org.br/.

Usage

data("Poverty")

Format

A data frame containing 5501 observations on 4 variables.

poverty

Percentage of extremely poor, by Brazilian municipality for the year 2010.

population

Total municipal population in 2010, in thousands.

illiteracy

Municipal illiteracy rate of people aged 15 or over, in 2010.

pc_income

Municipal per capita income (in Brazilian reais), in 2010.

Details

The dataset is available at http://www.atlasbrasil.org.br/. The data refer to 5501 Brazilian municipalities observed in 2010. The dependent variable is the percentage of people in extreme poverty (poverty). Naturally, it is a limited variable that takes values in the unit range. The explanatory variables are total population in thousands of people (population), illiteracy rate of people aged 15 or over (illiteracy) and per capita income in Brazilian reais (pc_income). Municipalities with missing information on any of the variables were excluded from the sample.

Source

http://www.atlasbrasil.org.br/

Examples

data("Poverty", package = "qcauchyreg")

reg <- qcreg(poverty ~ population + illiteracy + pc_income, data = Poverty, npi=50)
summary(reg)
reg$effects

plot(reg$pis, type="l")

plot(reg$quantregplot)

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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)

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