Parametric unit quantile regression models — unitquantreg • unitquantreg

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.

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.

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++.

Author

André F. B. Menezes