1\name{rq.object}
2\alias{rq.object}
3\alias{formula.rq}
4\alias{logLik.rq}
5\alias{logLik.rqs}
6\alias{AIC.rq}
7\alias{AIC.rqs}
8\alias{extractAIC.rq}
9\title{
10Linear Quantile Regression Object
11}
12\description{
13  These are objects of class \code{"rq"}.
14  They represent the fit of a linear conditional quantile function model.
15}
16\section{Generation}{
17  This class of objects is returned from the \code{rq} function
18  to represent a fitted linear quantile regression model.
19}
20\section{Methods}{
21  The \code{"rq"} class of objects has methods for the following generic
22functions:
23\code{coef}, \code{effects}
24, \code{formula}
25, \code{labels}
26, \code{model.frame}
27, \code{model.matrix}
28, \code{plot}
29, \code{logLik}
30, \code{AIC}
31, \code{extractAIC}
32, \code{predict}
33, \code{print}
34, \code{print.summary}
35, \code{residuals}
36, \code{summary}
37}
38\section{Structure}{
39  The following components must be included in a legitimate \code{rq} object.
40  \describe{
41    \item{\code{coefficients}}{
42      the coefficients of the quantile regression fit.
43      The names of the coefficients are the names of the
44      single-degree-of-freedom effects (the columns of the
45      model matrix).
46      If the model was fitted by method \code{"br"} with \code{ci=TRUE}, then
47      the coefficient component consists of a matrix whose
48      first column consists of the vector of estimated coefficients
49      and the second and third columns are the lower and upper
50      limits of a confidence interval for the respective coefficients.
51    }
52    \item{\code{residuals}}{
53      the residuals from the fit.
54    }
55    \item{\code{dual}}{
56      the vector dual variables from the fit.
57    }
58    \item{\code{rho}}{
59      The value(s) of objective function at the solution.
60    }
61    \item{\code{contrasts}}{
62      a list containing sufficient information to construct the contrasts
63      used to fit any factors occurring in the model.
64      The list contains entries that are either matrices or character vectors.
65      When a factor is coded by contrasts, the corresponding contrast matrix
66      is stored in this list.
67      Factors that appear only as dummy variables and variables in the model
68      that are matrices correspond to character vectors in the list.
69      The character vector has the level names for a factor or the column
70      labels for a matrix.
71    }
72    \item{\code{model}}{
73      optionally the model frame, if \code{model=TRUE}.
74    }
75    \item{\code{x}}{
76      optionally the model matrix, if \code{x=TRUE}.
77    }
78    \item{\code{y}}{
79      optionally the response, if \code{y=TRUE}.
80    }
81  }
82}
83\details{
84  The coefficients, residuals, and effects may be extracted
85  by the generic functions of the same name, rather than
86  by the \code{$} operator.   For pure \code{rq} objects this is less critical
87  than for some of the inheritor classes.  In particular, for fitted rq objects
88  using "lasso" and "scad" penalties, \code{logLik} and \code{AIC} functions
89  compute degrees of freedom of the fitted model as the number of estimated
90  parameters whose absolute value exceeds a threshold \code{edfThresh}.  By
91  default this threshold is 0.0001, but this can be passed via the \code{AIC}
92  function if this value is deemed unsatisfactory.  The function \code{AIC}
93  is a generic function in R, with parameter \code{k} that controls the form
94  of the penalty:  the default value of \code{k} is 2 which yields the classical
95  Akaike form of the penalty, while \code{k <= 0} yields the Schwarz (BIC)
96  form of the penalty.
97  Note that the extractor function \code{coef} returns a vector with missing values
98  omitted.
99}
100\seealso{
101  \code{\link{rq}},  \code{\link{coefficients}}.
102}
103\keyword{regression}
104