Global Beta Regression Model

Description

Fits a global regression model using the beta distribution, recommended for rates and proportions, via maximum likelihood using a parametrization with mean (transformed by the link function) and precision parameter (called phi). For more details see Ferrari and Cribari-Neto (2004).

Usage

betareg_gwbr(
  yvar,
  xvar,
  data,
  link = c("logit", "probit", "loglog", "cloglog"),
  maxint = 100
)

Arguments

Value

A list that contains:

• parameter_estimates - Parameter estimates.

• phi - Precision parameter estimate.

• residuals - Table with observed values (y), estimated values in classical regression (yhatcl), pure residual in classical regression (ecl), estimated values (yhat), the link function applied in the estimated values (eta), pure residual (res), standardized residual (resstd), standardized weighted residual 2 (resstd2), residual deviance (resdeviance), Cooks distance (cookD) and generalized leverage (glbp).

• log_likelihood - Log-likelihood of the fitted model.

• aicc - Corrected Akaike information criterion.

• r2 - Pseudo R2 and adjusted pseudo R2 statistics.

• bp_test - Breusch-Pagan test for heteroscedasticity.

• link_function - The link function used in modeling.

• n_iter - Number of iterations used in convergence.

Examples

data(saopaulo)
output_list=betareg_gwbr("prop_landline",c("prop_urb","prop_poor"),saopaulo)

## Parameters
output_list$parameter_estimates

## R2 and AICc
output_list$r2
output_list$aicc

Golden Section Search Algorithm

Description

The Golden Section Search (GSS) algorithm is used in searching for the best bandwidth for geographically weighted regression. For more details see Da Silva and Mendes (2018).

Usage

gss_gwbr(
  yvar,
  xvar,
  lat,
  long,
  data,
  method = c("fixed_g", "fixed_bsq", "adaptive_bsq"),
  link = c("logit", "probit", "loglog", "cloglog"),
  type = c("cv", "aic"),
  globalmin = TRUE,
  distancekm = TRUE,
  maxint = 100
)

Arguments

Value

A list that contains:

• global_min - Global minimum of the function, giving the best bandwidth (h).

• local_mins - Local minimums of the function.

• type - Function used to estimate the bandwidth.

Examples

data(saopaulo)
output_list=gss_gwbr("prop_landline",c("prop_urb","prop_poor"),"y","x",saopaulo,"fixed_g")

## Best bandwidth
output_list$global_min

Geographically Weighted Beta Regression

Description

Fits a local regression model for each location using the beta distribution, recommended for rates and proportions, using a parametrization with mean (transformed by the link function) and precision parameter (called phi). For more details see Da Silva and Lima (2017).

Usage

gwbr(
  yvar,
  xvar,
  lat,
  long,
  h,
  data,
  xglobal = NA_character_,
  grid = data.frame(),
  method = c("fixed_g", "fixed_bsq", "adaptative_bsq"),
  link = c("logit", "probit", "loglog", "cloglog"),
  distancekm = TRUE,
  global = FALSE,
  maxint = 100
)

Arguments

Value

A list that contains:

• parameter_estimates_qtls - Parameter estimates quartiles and interquartile range.

• parameter_estimates_desc - Parameter estimates mean, minimum and maximum.

• std_qtls - Standard deviation quartiles and interquartile range.

• std_desc - Standard deviation mean, minimum and maximum.

• est_n_parameters - Number of parameters.

• est_gwr_parameters - Effective number of parameters in the local model.

• phi - Vector of precision parameter estimates.

• global_parameter - Global parameter estimates, when existing.

• global_phi - Global scale parameter estimate, when existing.

• global_parameter_tab - Global parameter estimates table, when existing.

• residuals - Table with observed values (y), estimated values (yhat), the link function applied in the estimated values (eta), pure residual (res), standardized residual (resstd), standardized weighted residual 2 (resstd2), residual deviance (resdeviance), Cooks distance (cookD), generalized leverage (glbp) and number of iterations (iteration).

• log_likelihood - Log-likelihood of the fitted model.

• aicc - Corrected Akaike information criterion.

• r2 - Pseudo R2 and adjusted pseudo R2 statistics.

• bp_test - Breusch-Pagan test for heteroscedasticity.

• w - Matrix of weights.

• parameters - Table with parameter estimates of each model.

• significance - Significance level of each model.

• bandwidth - Bandwidth used.

• link_function - The link function used in modeling.

Examples

data(saopaulo)
output_list=gwbr("prop_landline",c("prop_urb", "prop_poor"),"y","x",116.3647,saopaulo)

## Descriptive statistics of the parameter estimates
output_list$parameter_estimates_desc

## Table with all parameter estimates and your respective statistics
output_list$parameters

Sao Paulo dataset

Description

Data from 2010 of the municipalities of Sao Paulo state, Brazil.

Usage

data(saopaulo)

Format

A data frame with 644 observations and 14 variables:

municipality

Municipality name.

state

State.

geocode

Municipality geocode according to IBGE.

households

Number of households.

landline

Number of households with landline.

pop

Total population.

pop_rural

Rural population.

pop_urb

Urban population.

hdim

Municipal Human Development Index.

prop_urb

Proportion of urban population.

prop_poor

Proportion of poor population (Considering per capita household income equal or less than R$140.00 per month).

prop_landline

Proportion of households with landline.

x

Longitude of the centroid of the city.

y

Latitude of the centroid of the city.