R: Extended log-F model with fixed scale

elf {qgam} | R Documentation

## Extended log-F model with fixed scale

### Description

The `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 `mgcv`. It differs from the `elflss` family, because here the scale of the density (sigma, aka the learning rate) is a single scalar, while in `elflss` it can depend on the covariates. At the moment the family is mainly intended for internal use, use the `qgam` function to fit quantile GAMs based on ELF.

### Usage

    elf(theta = NULL, link = "identity", qu, co)

### Arguments

`theta` | a scalar representing the log-scale log(sigma).
`link` | the link function between the linear predictor and the quantile location.
`qu` | parameter in (0, 1) representing the chosen quantile. For instance, to fit the median choose `qu=0.5`.
`co` | positive constant used to determine parameter lambda of the ELF density (lambda = co / sigma). Can be vector valued.

### Details

This function is meant for internal use only.

### Value

An object inheriting from mgcv's class `extended.family`.

### Author(s)

Matteo Fasiolo <matteo.fasiolo@gmail.com> and Simon N. Wood.

### References

Fasiolo, M., Goude, Y., Nedellec, R. and Wood, S. N. (2017). Fast calibrated additive quantile regression. Available at https://arxiv.org/abs/1707.03307.

Wood, Simon N., Pya, N. and Safken, B. (2017). Smoothing parameter and model selection for general smooth models. Journal of the American Statistical Association.

### 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)

[Package qgam version 1.3.2 Index]