mqgam: Fit multiple smooth additive quantile regression models
In qgam: Smooth Additive Quantile Regression Models

Description Usage Arguments Value Author(s) References Examples

This function fits a smooth additive regression model to several quantiles.

mqgam(
  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`	A vectors of quantiles of interest. Each entry 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). If it is a vector, it should be of the same length of `qu`. 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 list with entries:

fit = a gamObject, one for each entry of qu. Notice that the slots model and smooth of each object has been removed to save memory. See ?gamObject.
model = the model slot of the gamObjects in the fit slot. This is the same for every fit, hence only one copy is stored.
smooth = the smooth slot of the gamObjects in the fit slot. This is the same for every fit, hence only one copy is stored.
calibr = a list which is the output of an internal call to tuneLearnFast, which is used for calibrating the learning rate. See ?tuneLearnFast for details.

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.

#####
# Multivariate Gaussian example
####
library(qgam)
set.seed(2)
dat <- gamSim(1, n=300, dist="normal", scale=2)

fit <- mqgam(y~s(x0)+s(x1)+s(x2)+s(x3), data=dat, qu = c(0.2, 0.8))

invisible( qdo(fit, 0.2, plot, pages = 1) )

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

# Fit for quantile 0.8 using the best sigma
quSeq <- c(0.2, 0.4, 0.6, 0.8)
set.seed(6436)
fit <- mqgam(accel~s(times, k=20, bs="ad"), data = mcycle, qu = quSeq)

# Plot the fit
xSeq <- data.frame(cbind("accel" = rep(0, 1e3), "times" = seq(2, 58, length.out = 1e3)))
plot(mcycle$times, mcycle$accel, xlab = "Times", ylab = "Acceleration", ylim = c(-150, 80))
for(iq in quSeq){
  pred <- qdo(fit, iq, predict, newdata = xSeq)
  lines(xSeq$times, pred, col = 2)
}