qgam: Fit a smooth additive quantile regression model
In qgam: Smooth Additive Quantile Regression Models

Description Usage Arguments Value Author(s) References Examples

This function fits a smooth additive regression model for a single quantile.

qgam(
  form,
  data,
  qu,
  lsig = NULL,
  err = NULL,
  multicore = !is.null(cluster),
  cluster = NULL,
  ncores = detectCores() - 1,
  paropts = list(),
  control = list(),
  argGam = NULL
)

`form`	A GAM formula, or a list of formulae. See ?mgcv::gam details.
`data`	A data frame or list containing the model response variable and covariates required by the formula. By default the variables are taken from environment(formula): typically the environment from which gam is called.
`qu`	The quantile of interest. Should be in (0, 1).
`lsig`	The value of the log learning rate used to create the Gibbs posterior. By defauls `lsig=NULL` and this parameter is estimated by posterior calibration described in Fasiolo et al. (2017). Obviously, the function is much faster if the user provides a value.
`err`	An upper bound on the error of the estimated quantile curve. Should be in (0, 1). Since qgam v1.3 it is selected automatically, using the methods of Fasiolo et al. (2017). The old default was `err=0.05`.
`multicore`	If TRUE the calibration will happen in parallel.
`cluster`	An object of class `c("SOCKcluster", "cluster")`. This allowes the user to pass her own cluster, which will be used if `multicore == TRUE`. The user has to remember to stop the cluster.
`ncores`	Number of cores used. Relevant if `multicore == TRUE`.
`paropts`	a list of additional options passed into the foreach function when parallel computation is enabled. This is important if (for example) your code relies on external data or packages: use the .export and .packages arguments to supply them so that all cluster nodes have the correct environment set up for computing.
`control`	A list of control parameters. The only one relevant here is `link`, which is the link function used (see `?elf` and `?elflss` for defaults). All other control parameters are used by `tuneLearnFast`. See `?tuneLearnFast` for details.
`argGam`	A list of parameters to be passed to `mgcv::gam`. This list can potentially include all the arguments listed in `?gam`, with the exception of `formula`, `family` and `data`.

A gamObject. See ?gamObject.

Matteo Fasiolo <matteo.fasiolo@gmail.com>.

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). https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1725521.

Fasiolo, M., Wood, S.N., Zaffran, M., Nedellec, R. and Goude, Y., 2021. qgam: Bayesian Nonparametric Quantile Regression Modeling in R. Journal of Statistical Software, 100(9), 1-31, doi: 10.18637/jss.v100.i09.

#####
# Univariate "car" example
####
library(qgam); library(MASS)

# Fit for quantile 0.5 using the best sigma
set.seed(6436)
fit <- qgam(accel~s(times, k=20, bs="ad"), data = mcycle, qu = 0.5)

# Plot the fit
xSeq <- data.frame(cbind("accel" = rep(0, 1e3), "times" = seq(2, 58, length.out = 1e3)))
pred <- predict(fit, newdata = xSeq, se=TRUE)
plot(mcycle$times, mcycle$accel, xlab = "Times", ylab = "Acceleration", ylim = c(-150, 80))
lines(xSeq$times, pred$fit, lwd = 1)
lines(xSeq$times, pred$fit + 2*pred$se.fit, lwd = 1, col = 2)
lines(xSeq$times, pred$fit - 2*pred$se.fit, lwd = 1, col = 2)   

## Not run: 
# You can get a better fit by letting the learning rate change with "accel"
# For instance
fit <- qgam(list(accel ~ s(times, k=20, bs="ad"), ~ s(times)),
           data = mcycle, qu = 0.8)

pred <- predict(fit, newdata = xSeq, se=TRUE)
plot(mcycle$times, mcycle$accel, xlab = "Times", ylab = "Acceleration", ylim = c(-150, 80))
lines(xSeq$times, pred$fit, lwd = 1)
lines(xSeq$times, pred$fit + 2*pred$se.fit, lwd = 1, col = 2)
lines(xSeq$times, pred$fit - 2*pred$se.fit, lwd = 1, col = 2)  

## End(Not run)

#####
# Multivariate Gaussian example
####
library(qgam)
set.seed(2)
dat <- gamSim(1,n=400,dist="normal",scale=2)

fit <- qgam(y~s(x0)+s(x1)+s(x2)+s(x3), data=dat, qu = 0.5)
plot(fit, scale = FALSE, pages = 1)      

######
# Heteroscedastic example
######
## Not run: 
set.seed(651)
n <- 2000
x <- seq(-4, 3, length.out = n)
X <- cbind(1, x, x^2)
beta <- c(0, 1, 1)
sigma =  1.2 + sin(2*x)
f <- drop(X %*% beta)
dat <- f + rnorm(n, 0, sigma)
dataf <- data.frame(cbind(dat, x))
names(dataf) <- c("y", "x")

fit <- qgam(list(y~s(x, k = 30, bs = "cr"), ~ s(x, k = 30, bs = "cr")), 
            data = dataf, qu = 0.95)

plot(x, dat, col = "grey", ylab = "y")
tmp <- predict(fit, se = TRUE)
lines(x, tmp$fit)
lines(x, tmp$fit + 2 * tmp$se.fit, col = 2)
lines(x, tmp$fit - 2 * tmp$se.fit, col = 2)

## End(Not run)