The L-Logistic Bayesian Regression

Description

Bayesian L-Logistic regression package, <URL:https://www.imstat.org/wp-content/uploads/2018/05/BJPS397.pdf>.

Details

Package to estimate an L-Logistic regression model with median and precision regression structures, diagnostics and HPD.

Author(s)

Sara Alexandre Fonsêca saralexandre@alu.ufc.br, Rosineide Fernando da Paz rfpaz2@gmail.com, Jorge Luís Bazán

Source

The L-Losgistic distribution was introduced by Tadikamalla and Johnson (1982), which refer to this distribution as Logit-Logistic distribution. Here, we have a new parameterization of the Logit-Logistic with the median as a parameter.

References

Paz, R.F., Balakrishnan, N and Bazán, J.L. (2018). L-Logistic Distribution: Properties, Inference and an Application to Study Poverty and Inequality in Brazil.

Education Development Index

Description

EDI data set is the Education Development Index (EDI), Elementary School and High School of the municipalities of Sergipe state of Brazil.

Usage

data("EDI")

Format

A data frame containing 75 observations on 2 variables.

EDIES

The format is: num [1:75] 3.6 3.6 3.8 3.1 3.5 3.7 3.8 3 3.2 0 ...

EDIHS

The format is: num [1:75] 3.8 2.9 3 2.8 2.8 1.9 3 2.2 2.6 3.6 ...

Details

The quality of education is attributed by a statistical value to educational indicators. This value is assigned by the context economic and social development to which the schools are inserted, not only by the students' performances. The systems educational use mainly of them for the monitoring of educational quality.

References

Fundação Lemann e Meritt (2012): portal QEdu.org.br, acessado em 10/01/2019.

Examples

data(EDI)
## maybe str(EDI) ; plot(EDI) ...

Municipal Human Development Index

Description

MHDI data set is the Municipal Human Development Index (MHDI) of the municipalities of Sergipe state of Brazil.

Usage

data("MHDI")

Format

The format is: num [1:75] 0.611 0.578 0.77 0.595 0.579 0.649 0.604 0.54 0.621 0.569 ...

Details

The MHDI is a summary measure of long-term progress in three basic dimensions of human development that takes into account education, income and longevity indexes in municipalities. The MHDI data is the geometric mean of normalized indexes for each of the three dimensions of human development.

Source

PNUD, IPEA \& FJP. (2013).

References

PNUD, IPEA & FJP. (2013). Atlas do Desenvolvimento Humano no Brasil. PNUD, Brasilia, Brazil. Disponible in: http://www.atlasbrasil.org.br/2013/pt/.

Examples

data(MHDI)
## maybe str(MHDI) ; plot(MHDI) ...

Data of the votes in the presidential elections of the municipalities of Sergipe in the years 1994, 1998, 2002 and 2006

Description

Proportion of votes for a political party (Partido dos Trabalhadores) in presidential elections in Brazil by the different municipalities of Sergipe state.

Usage

data("Votes")

Format

A data frame containing 75 observations on 4 variables.

Votes1994

The format is: num [1:75] 0.228 0.172 0.431 0.105 0.165 ...

Votes1998

The format is: num [1:75] 0.293 0.193 0.427 0.111 0.155 ...

Votes2002

The format is: num [1:75] 0.307 0.278 0.517 0.268 0.223 ...

Votes2006

The format is: num [1:75] 0.492 0.365 0.375 0.426 0.368 ...

Details

Proportion of votes for a political party (Partido dos Trabalhadores) in presidential elections in Brazil by the different municipalities of Sergipe state in the years 1994, 1998, 2002 and 2006.

References

Tribunal Superior Eleitoral. Reposit?rio de Dados Eleitorais: TSE website www.tse.jus.br, accessed 10/01/2018.

Examples

data(Votes)
## maybe str(Votes) ; plot(Votes) ...

Highest Posterior Density for the L-Logistic Bayesian Regression

Description

Compute the highest posterior density for the L-Logistic Bayesian Regression intervals of betas and deltas.

Usage

llHPD(fitll, prob = 0.95, chain = 1)

Arguments

Details

This function compute the highest posterior density intervals for a Bayesian posterior distribution.

Value

Object of class matrix with:

Author(s)

Sara Alexandre Fonsêca saralexandre@alu.ufc.br, Rosineide Fernando da Paz rfpaz2@gmail.com, Jorge Luís Bazán

Source

The L-Losgistic distribution was introduced by Tadikamalla and Johnson (1982), which refer to this distribution as Logit-Logistic distribution. Here, we have a new parameterization of the Logit-Logistic with the median as a parameter.

References

Paz, R.F., Balakrishnan, N and Bazán, J.L. (2018). L-Logistic Distribution: Properties, Inference and an Application to Study Poverty and Inequality in Brazil.

Examples

# Modelation the coeficient with generated data

library(llbayesireg)
library(llogistic)

# Number of elements to be generated

n=50

# Generated response

bin=2005
set.seed(bin)
y=rllogistic(n,0.5, 2)

fitll = llbayesireg(y, niter=100, jump=10)

llHPD(fitll)

 
# Modelation the coeficient with real data
library(llbayesireg)

data("Votes","MHDI")

y = Votes[,4]
X = MHDI

fitll = llbayesireg(y,X)

llHPD(fitll)
 

The L-Logistic Bayesian Regression

Description

Function to estimate a L-Logistic regression model with median and precision regression structures.

Usage

llbayesireg(y,X,W,niter=1000,chains=1,burn=floor(niter/2),jump=1)

Arguments

Details

See https://cran.r-project.org/web/packages/llogistic/llogistic.pdf.

Value

Object of the class matrix, if the user does not provide arguments X and W, with:

Object of the class matrix, if the user provide arguments X and W, with:

Author(s)

Sara Alexandre Fonsêca saralexandre@alu.ufc.br, Rosineide Fernando da Paz rfpaz2@gmail.com, Jorge Luís Bazán

Source

The L-Losgistic distribution was introduced by Tadikamalla and Johnson (1982), which refer to this distribution as Logit-Logistic distribution. Here, we have a new parameterization of the Logit-Logistic with the median as a parameter.

References

Paz, R.F., Balakrishnan, N and Bazán, J.L. (2018). L-Logistic Distribution: Properties, Inference and an Application to Study Poverty and Inequality in Brazil.

Examples

# Modelation the coeficient with generated data

library(llbayesireg)
library(llogistic)

# Number of elements to be generated

n=50

# Generated response

bin=2005
set.seed(bin)
y=rllogistic(n,0.5, 2)

fitll = llbayesireg(y, niter=100, jump=10)

m.hat=mean(fitll$sample.m); m.hat
phi.hat=mean(fitll$sample.phi); phi.hat

 
# Modelation the coeficient with real data
library(llbayesireg)

data("Votes","MHDI")

y = Votes[,4]
X = MHDI

fitll = llbayesireg(y,X)

summary(fitll$object, pars = c("beta","delta"), probs = c(0.025,0.975))

plot(fitll$betas[,1,1], type = "l")
 

Diagnostics from a fitll object

Description

Prints diagnostics or extract those diagnostics from a fitll object.

Usage

lldiagnostics(object)

Arguments

Details

The function calls the check_* functions and the get_* functions are for access to the diagnostics. If the matrix X and W are missing, the coda package is used by test the convergence of the chains by Cramer-von-Mises statistic and an image of the correlation is show for both of generated chains.

Value

lldiagnostics(object) prints diagnostics or extract those diagnostics from a fitll object.

Author(s)

Sara Alexandre Fonsêca saralexandre@alu.ufc.br, Rosineide Fernando da Paz rfpaz2@gmail.com, Jorge Luís Bazán

Source

The L-Losgistic distribution was introduced by Tadikamalla and Johnson (1982), which refer to this distribution as Logit-Logistic distribution. Here, we have a new parameterization of the Logit-Logistic with the median as a parameter.

References

Paz, R.F., Balakrishnan, N and Bazán, J.L. (2018). L-Logistic Distribution: Properties, Inference and an Application to Study Poverty and Inequality in Brazil. The Stan Development Team Stan Modeling Language User's Guide and Reference Manual. http://mc-stan.org/. Plummer, M., Best, N., Cowles, K., and Vines, K. (2006). Coda: Convergence diagnosis and output analysis for mcmc. R News, 6(1):7-11.

Examples

# Modelation the coeficient with generated data

library(llbayesireg)
library(llogistic)

# Number of elements to be generated

n=50

# Generated response

bin=2005
set.seed(bin)
y=rllogistic(n,0.5, 2)

fitll = llbayesireg(y, niter=100, jump=10)

lldiagnostics(fitll$object)
 
# Modelation the coeficient with real data
library(llbayesireg)

data("Votes","MHDI")

y = Votes[,4]
X = MHDI

fitll = llbayesireg(y,X)

lldiagnostics(fitll$object)