Package 'cbq'

cbq: An R Package for Estimating Conditional Binary Quantile Models

Description

Bayesian estimation of conditional binary quantile models.

References

Lu, Xiao. (2020). Discrete Choice Data with Unobserved Heterogeneity: A Conditional Binary Quantile Model. Political Analysis, 28(2), 147-167. https://doi.org/10.1017/pan.2019.29

Stan Development Team (2019). RStan: the R interface to Stan. R package version 2.19.2. https://mc-stan.org

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Fitting conditional binary quantile models

Description

The main function for running the conditional binary quantile model. The function returns a cbq cbq object that can be further investigated using standard functions such as plot, print, coef, and predict.

Usage

cbq(
  formula,
  data,
  q = NULL,
  vi = FALSE,
  nsim = 1000,
  grad_samples = 1,
  elbo_samples = 100,
  tol_rel_obj = 0.01,
  output_samples = 2000,
  burnin = NULL,
  thin = 1,
  CIsize = 0.95,
  nchain = 1,
  seeds = 12345,
  inverse_distr = FALSE,
  offset = 1e-20,
  mc_core = TRUE
)

Arguments

formula	An object of class "Formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
data	A data frame containing the variables in the model.
q	The quantile value.
vi	Indicating whether variantional inference should be used instead of MCMC sampling procedure.
nsim	The number of iterations.
grad_samples	Passed to vb (positive integer), the number of samples for Monte Carlo estimate of gradients, defaulting to 1.
elbo_samples	Passed to vb (positive integer), the number of samples for Monte Carlo estimate of ELBO (objective function), defaulting to 100. (ELBO stands for "the evidence lower bound".)
tol_rel_obj	Passed to vb (positive double), the convergence tolerance on the relative norm of the objective, defaulting to 0.01.
output_samples	Passed to vb (positive integer), number of posterior samples to draw and save, defaults to 1000.
burnin	The number of burnin iterations.
thin	Thinning parameter.
CIsize	The size of confidence interval.
nchain	The number of parallel chains.
seeds	Random seeds to replicate the results.
inverse_distr	If FALSE, the ALD will not be reversed. The default is FALSE.
offset	Offset values to enhance sampling stability. The default value is 1e-20.
mc_core	Indicating whether the estimation will be run in multiple parallel chains. The default is TRUE.

Details

The model can be passed either as a combination of a formula and a data frame data, as in lm().

Convergence diagnotics can be performed using either print(object, "mcmc") or plot(object, "mcmc").

Value

A cbq object, which can be further analyzed with its associated plot.cbq, coef.cbq and print.cbq functions.

An object of class cbq contains the following elements

Call

The matched call.

formula

Symbolic representation of the model.

q

The quantile value.

nsim

The number of MCMC iterations.

burnin

The number of burnin periods.

thin

Thinning.

seeds

Random seeds.

CIsize

The size of confidence interval.

data

Data used.

x

Covaraites used.

y

The dependent variable.

xnames

Names of the covariates.

stanfit

Outputs from stan.

sampledf

A matrix of posterior samples.

summaryout

A summary based on posterior samples.

npars

Number of covariates.

ulbs

Lower and upper confidence bounds.

means

Estimates at the mean.

vi

Indicating whether variational inference has been performed.

output_samples

Sample outputs.

fixed_var

Variables estimated using fixed effects.

random_var

Variables estimated using random effects.

xq

Variables indicating the choice sets.

Author(s)

Xiao Lu

References

Lu, Xiao. (2020). Discrete Choice Data with Unobserved Heterogeneity: A Conditional Binary Quantile Model. Political Analysis, 28(2), 147-167. https://doi.org/10.1017/pan.2019.29

Examples

# Simulate the data
x <- rnorm(50)
y <- ifelse(x > 0, 1, 0)
dat <- as.data.frame(cbind(y, x))

# Estimate the CBQ model
model <- cbq(y ~ x, dat, 0.5, nchain = 1, mc_core = FALSE)

# Show the results
print(model)
coef(model)
plot(model)

---

Extract CBQ Coefficients

Description

Create a table of coefficient results from a cbq object.

Usage

## S3 method for class 'cbq'
coef(object, ...)

Arguments

object	A cbq object.
...	Further arguments passed to or from other methods.

Value

A table of coefficients with their corresponding lower and upper bounds.

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Probability density function of asymmetric Laplace distributions

Description

dald calculates probability densities of asymmetric Laplace distributions.

Usage

dald(x, mu, p, sigma)

Arguments

x	Random variable.
mu	Position parameter.
p	Quantile.
sigma	Scale parameter.

Value

probability density of x.

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Inverse function

Description

inverse generates inverse function of any given function.

Usage

inverse(f, mu, p, sigma, lower = -10000, upper = 10000)

Arguments

f	pald function
mu	Position parameter.
p	Quantile.
sigma	Scale parameter.
lower	Lower bound.
upper	Upper bound.

Value

inversed pald

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Check if a predictor is dichotomous, adopted from package circGLM

Description

Check if a predictor is dichotomous, adopted from package circGLM

Usage

is.dichotomous(x)

Arguments

x	A character or numerical vector to be tested.

Value

A logical, TRUE if the x has dummy coding (0, 1), FALSE otherwise.

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Cumulative density function of asymmetric Laplace distributions

Description

pald calculates cumulative densities of asymmetric Laplace distributions.

Usage

pald(x, mu, p, sigma)

Arguments

x	Random variable.
mu	Position parameter.
p	Quantile.
sigma	Scale parameter.

Value

cumulative probability density of x.

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Make coefficient plots for cbq

Description

Plot traceplots from a cbq object.

Usage

plot_coef.cbq(object, ...)

Arguments

object	A cbq object.
...	Additional parameters to be passed to the plot function.

Value

None.

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Make traceplots for cbq

Description

Plot traceplots from a cbq object.

Usage

plot_trace.cbq(object, ...)

Arguments

object	A cbq object.
...	Additional parameters to be passed to the traceplot function.

Value

None.

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Plot cbq object

Description

General plot function for cbq objects, which dispatches the chosen type of plotting to the corresponding function.

Usage

## S3 method for class 'cbq'
plot(x, type = "trace", ...)

Arguments

x	A cbq object to be plotted.
type	Character string giving the type of plotting. The options are "trace" for trace plots, "coef" for coefficient plots. The default is the traceplot.
...	Additional arguments to be passed to subsequent plot functions.

Value

None.

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Predictions based on the fitted parameter values

Description

Create a vector of predictions from a cbq object.

Usage

## S3 method for class 'cbq'
predict(object, data, ci = 0.95, ...)

Arguments

object	A cbq object.
data	Data used for prediction.
ci	Confidence interval. The default is 0.95.
...	Further arguments passed to or from other methods.

Value

A vector of predictions.

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Print cbq coefficients

Description

Print cbq coefficients

Usage

print_coef.cbq(object, digits = 3)

Arguments

object	A cbq object.
digits	Number of digits to display.

Value

None.

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Print the mcmc results from a cbq object

Description

This prints a number of diagnostics about the results of a cbq objects

Usage

print_mcmc.cbq(object, ...)

Arguments

object	A cbq object.
...	Additional arguments to be passed to the print function.

Value

None.

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Print the main results from a cbq object.

Description

Print the main results from a cbq object.

Usage

print_text.cbq(object, digits = 3)

Arguments

object	A cbq object.
digits	Number of digits to display.

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Print cbq object

Description

General print function for cbq objects, which dispatches the chosen type of printing to the corresponding function.

Usage

## S3 method for class 'cbq'
print(x, type = "text", ...)

Arguments

x	A cbq object to be printed.
type	Character string giving the type of printing, such as "text", "mcmc", "coef".
...	Additional arguments to be passed to print functions.

Value

None.

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Quantile function of asymmetric Laplace distributions

Description

qald calculates quantiles values of asymmetric Laplace distributions.

Usage

qald(y, mu, p, sigma)

Arguments

y	quantile value.
mu	Position parameter.
p	Quantile.
sigma	Scale parameter.

Value

quantile value.

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Random number generator of asymmetric Laplace distributions

Description

rald generates random numbers from asymmetric Laplace distributions.

Usage

rald(n, mu, p, sigma)

Arguments

n	Number of random numbers to be generated.
mu	Position parameter.
p	Quantile.
sigma	Scale parameter.

Value

random numbers.

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