unitquantreg {unitquantreg}

Parametric unit quantile regression models

Description

Fit a collection of parametric unit quantile regression model by maximum likelihood using the log-likelihood function, the score vector and the hessian matrix implemented in C++.

Usage

unitquantreg(
  formula,
  data,
  subset,
  na.action,
  tau,
  family,
  link = c("logit", "probit", "cloglog", "cauchit"),
  link.theta = c("identity", "log", "sqrt"),
  start = NULL,
  control = unitquantreg.control(),
  model = TRUE,
  x = FALSE,
  y = TRUE
)

unitquantreg.fit(
  y,
  X,
  Z = NULL,
  tau,
  family,
  link,
  link.theta,
  start = NULL,
  control = unitquantreg.control()
)

Arguments

formula

symbolic description of the quantile model like y ~ x or y ~ x | z. See below for details.

data

data.frame contain the variables in the model.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

na.action

a function which indicates what should happen when the data contain NAs.

tau

numeric vector. The quantile(s) to be estimated, i.e., number between 0 and 1. If just one quantile is specified an object of class unitquantreg is returned. If a numeric vector of values between 0 and 1 is specified an object of class unitquantregs is returned. See below for details.

family

character. Specify the distribution family.

link

character. Specify the link function in the quantile model. Currently supported are logit, probit, cloglog and cauchit. Default is logit.

link.theta

character. Specify the link function in the shape model. Currently supported are identity, log and sqrt. Default is log.

start

numeric vector. An optional vector with starting values for all parameters.

control

list. Control arguments specified via unitquantreg.control.

model

logical. Indicates whether model frame should be included as a component of the returned value.

x, y

logical. If TRUE the corresponding components of the fit (model frame, response, model matrix) are returned. For unitquantreg.fit y should be the numeric response vector with values in (0,1).

X, Z

numeric matrix. Regressor matrix for the quantile and shape model, respectively. Default is constant shape model, i.e., Z is matrix with column of ones.

Details

The parameter estimation and inference are performed under the frequentist paradigm. The optimx R package is use, since allows different optimization technique to maximize the log-likelihood function. The analytical score function are use in the maximization and the standard errors are computed using the analytical hessian matrix, both are implemented in efficient away using C++.

Value

unitquantreg can return an object of class unitquantreg if tau is a scalar, i.e., a list with the following components.

family

the distribution family name.

coefficients

a list with elements "quantile" and "shape" containing the coefficients from the respective models.

fitted.values

a list with elements "quantile" and "shape" containing the fitted parameters from the respective models.

linear.predictors

a list with elements "quantile" and "shape" containing the fitted linear predictors from the respective models.

link

a list with elements "quantile" and "shape" containing the link objects from the respective models.

tau

the quantile specify.

loglik

log-likelihood of the fitted model.

gradient

gradient evaluate at maximum likelihood estimates.

vcov

covariance matrix of all parameters in the model.

nobs

number of observations.

npar

number of parameters.

df.residual

residual degrees of freedom in the fitted model.

theta_const

logical indicating if the \theta parameter was treated as nuisance parameter.

control

the control parameters used to fit the model.

iterations

number of iterations of optimization method.

converged

logical, if TRUE indicates successful convergence.

kkt

a list of logical kkt1 and kkt2 provide check on Kuhn-Karush-Tucker conditions, first-order KKT test (kkt1) checks whether the gradient at the final parameters estimates is "small" and the second-order KKT test (kkte) checks whether the Hessian at the final parameters estimates is positive definite.

elapsed_time

time elapsed to fit the model.

call

the original function call.

formula

the original model formula.

terms

a list with elements "quantile", "shape" and "full" containing the terms objects for the respective models.

model

the full model frame, if model = TRUE.

y

the response vector, if y = TRUE.

x

a list with elements "quantile" and "shape" containing the model matrices from the respective models, if x = TRUE.

While unitquantreg.fit returns an unclassed list with components up to elapsed_time.

If tau is a numeric vector with length greater than one an object of class unitquantregs is returned, which consist of list of objects of class unitquantreg for each specified quantiles.

Author(s)

André F. B. Menezes