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README.Rmd
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---
output: github_document
---
```{r, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "man/figures/README-",
out.width = "100%"
)
```
# gamvinereg: D-Vine GAM Copula based Quantile Regression
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[](https://CRAN.R-project.org/package=gamvinereg)
[](https://github.com/jobstdavid/gamvinereg/actions)
[](https://github.com/jobstdavid/gamvinereg)
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An R package for D-vine copula based quantile regression using bivariate conditional copulas as described in the references.
It depends on the R-packages:
- [VineCopula](https://cran.r-project.org/web/packages/VineCopula/index.html), [gamCopula](https://cran.r-project.org/web/packages/gamCopula/index.html): Including bivariate conditional copulas, where Kendall's $\tau$ or the copula parameter is linked to a partially linear model using GAM and/or spline smoothing. The bivariate conditional copula family set for modeling the dependencies consists of the Gaussian, Student-t, double Clayton type I-IV and double Gumbel type I-IV copula as implemented in the R-package [gamCopula](https://cran.r-project.org/web/packages/gamCopula/index.html). The double Clayton and Gumbel copula type consist of additional rotated versions of the Clayton and Gumbel copula, respectively to cover negative dependence as well.
- [gamlss](https://cran.r-project.org/web/packages/gamlss/index.html): Margins can be selected from a large set of parametric distribution families using generalized additive models for location, scale and shape (GAMLSS).
- [gamlss.tr](https://cran.r-project.org/web/packages/gamlss.tr/index.html): GAMLSS extension to allow for truncated distribution families.
- [gamlss.cens](https://cran.r-project.org/web/packages/gamlss.cens/index.html): GAMLSS extension to allow for censored distribution families.
- [gamlss.dist](https://cran.r-project.org/web/packages/gamlss.dist/index.html): GAMLSS extension to allow for distribution families with transformed response.
## Installation
You can install the development version from GitHub with:
``` r
# install.packages("remotes")
remotes::install_github("jobstdavid/gamvinereg")
```
## Package overview
Below is an overview of the most important functions:
- ``gamvinereg``: selects most relevant predictor variables from the given data to make predictions based on a D-vine GAM copula. It returns an object of class ``gamvinereg``. The class has the following methods:
- ``print``: a brief overview of the model statistics.
- ``summary``: a more detailed overview of the selected response margin distribution and bivariate conditional copulas.
- ``predict``: make predictions at a given quantile level.
- ``cpit``: calculate the conditional probabililty integral transformed (PIT) values for the response given the predictor variables.
- ``cpdf``: calculate the conditional density values for the response given the predictor variables.
- ``gam_control``: configuration of the bivariate conditional copula.
## Example
### Load R-package and data
```{r example1}
# load package
library(gamvinereg)
# load data for station Hannover
data(station)
```
### Specify margins
```{r example2}
## generate margin distributions
# generate left-truncated at 0 normal distribution
gen.trun(par = 0, family = "NO", type = "left")
# generate left-censored normal distribution
gen.cens(family = "NO", type = "left")
# generate log-normal distribution
gen.Family(family = "NO", type = "log")
## margin specifications to select from
margins <- list(
# margin for variable obs (normal distribution)
list(list(family = NO(),
mu.formula = obs ~ sin1 + cos1,
sigma.formula = ~ sin1 + cos1)),
# margin for variable t2m_mean (normal distribution)
list(list(family = NO(),
mu.formula = t2m_mean ~ sin1 + cos1,
sigma.formula = ~ sin1 + cos1)),
# margins for variable t2m_sd (log-normal, left-truncated/censored at 0 normal distribution)
list(list(family = logNO(),
mu.formula = t2m_sd ~ sin1 + cos1,
sigma.formula = ~ sin1 + cos1),
list(family = NOtr(),
mu.formula = t2m_sd ~ sin1 + cos1,
sigma.formula = ~ sin1 + cos1),
list(family = NOlc(),
mu.formula = Surv(t2m_sd, t2m_sd > 0, type = "left") ~ sin1 + cos1,
sigma.formula = ~ sin1 + cos1))
)
```
### Fit gamvinereg
```{r example3}
# fit gamvinereg with time-dependent linear correlation model
(object <- gamvinereg(formula = obs ~ t2m_mean + t2m_sd,
data = station,
control = gam_control(formula = ~ sin1 + cos1),
margins = margins))
```
### Make quantile predictions
```{r example4}
# predict median
med <- predict(object, newdata = station, alpha = 0.5)
# predict deciles
dec <- predict(object, newdata = station, alpha = 1:9/10)
```
### Calculate conditional PIT values
```{r example5, fig.align = "center", out.width = "75%"}
# calculate conditional PIT values
u <- cpit(object, newdata = station)
# should be approximately uniform
hist(u, probability = TRUE)
```
### Calculate conditional density values
```{r example6, fig.align = "center", out.width = "75%"}
# calculate conditional density values
d <- cpdf(object)
# calculate log-likelihood
sum(log(d))
```
## Contact
Feel free to contact [[email protected]](mailto:[email protected]) if you have any questions or suggestions.
## References
Jobst, D., Möller, A., and Groß, J. (2023). D-Vine GAM Copula based Quantile Regression with Application to Ensemble Postprocessing. doi: [10.48550/arXiv.2309.05603](https://arxiv.org/abs/2309.05603).