elf.Rd

% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/elf.R
\name{elf}
\alias{elf}
\title{Extended log-F model with fixed scale}
\usage{
elf(theta = NULL, link = "identity", qu, co)
}
\arguments{
\item{theta}{a scalar representing the log-scale log(sigma).}

\item{link}{the link function between the linear predictor and the quantile location.}

\item{qu}{parameter in (0, 1) representing the chosen quantile. For instance, to fit the median choose \code{qu=0.5}.}

\item{co}{positive constant used to determine parameter lambda of the ELF density (lambda = co / sigma).
Can be vector valued.}
}
\value{
An object inheriting from mgcv's class \code{extended.family}.
}
\description{
The \code{elf} family implements the Extended log-F density of Fasiolo et al. (2017) and it is supposed
             to work in conjuction with the extended GAM methods of Wood et al. (2017), implemented by
             \code{mgcv}. It differs from the \code{elflss} family, because here the scale of the density (sigma, aka the learning rate) is a single scalar, 
             while in \code{elflss} it can depend on the covariates. At the moment the family is mainly intended for internal use, 
             use the \code{qgam} function to fit quantile GAMs based on ELF.
}
\details{
This function is meant for internal use only.
}
\examples{
library(qgam)
set.seed(2)
dat <- gamSim(1,n=400,dist="normal",scale=2)

# Fit median using elf directly: FAST BUT NOT RECOMMENDED
fit <- gam(y~s(x0)+s(x1)+s(x2)+s(x3), 
           family = elf(co = 0.1, qu = 0.5), data = dat)
plot(fit, scale = FALSE, pages = 1)     

# Using qgam: RECOMMENDED
fit <- qgam(y~s(x0)+s(x1)+s(x2)+s(x3), data=dat, qu = 0.8)
plot(fit, scale = FALSE, pages = 1)      


}
\references{
Fasiolo, M., Wood, S.N., Zaffran, M., Nedellec, R. and Goude, Y., 2020. 
            Fast calibrated additive quantile regression. 
            Journal of the American Statistical Association (to appear).
            \url{https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1725521}.
            
            Wood, Simon N., Pya, N. and Safken, B. (2017). Smoothing parameter and model selection for 
            general smooth models. Journal of the American Statistical Association.
}
\author{
Matteo Fasiolo <matteo.fasiolo@gmail.com> and Simon N. Wood.
}