---
title: "Get started"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Get started}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

The goal of `unitquantreg` is to provide tools for estimation and inference on
parametric quantile regression models for bounded data.

The package was written following the same interface as `stats::glm` function,
containing several S3 methods for inference, residual analysis, prediction,
plotting, and model comparison.

For more computation efficient the [`dpqr`]'s, likelihood, score and
hessian functions are vectorized and written in `C++`.

The parameter estimation and inference are performed under the frequentist
paradigm, and the
[**optimx**](https://CRAN.R-project.org/package=optimx)
package is used to perform the numerical optimization.
Besides that, the analytical score function are provided in the optimization
process and the standard errors are computed from the analytical hessian matrix,
both function are implemented in efficient away using `C++`.


The distribution families available are:

```{r distr-families}
lt_families <- list("unit-Weibull" = "uweibull",
                    "Kumaraswamy" = "kum",
                    "unit-Logistic" = "ulogistic",
                    "unit-Birnbaum-Saunders" = "ubs",
                    "log-extended Exponential-Geometric" = "leeg",
                    "unit-Chen" = "uchen",
                    "unit-Generalized Half-Normal-E" = "ughne",
                    "unit-Generalized Half-Normal-X" = "ughnx",
                    "unit-Gompertz" = "ugompertz",
                    "Johnson-SB" = "johnsonsb",
                    "unit-Burr-XII" = "uburrxii",
                    "arc-secant hyperbolic Weibull" = "ashw",
                    "unit-Gumbel" = "ugumbel")
```


The workhorse function is `unitquantreg`, which follows the same interface as
`stats::glm`.

```{r example}
library(unitquantreg)
data(water)
lt_fits <- lapply(lt_families, function(fam) {
  unitquantreg(
    formula = phpws ~ mhdi + incpc + region + log(pop), data = water, tau = 0.5,
    family = fam, link = "logit", link.theta = "log")
})
t(sapply(lt_fits, coef))
```

You can use the `likelihood_stats` to get likelihood-base statistics:

```{r likelihood-stats}
likelihood_stats(lt = lt_fits)
```

It is also possible to perform pairwise
[Vuong test](https://en.wikipedia.org/wiki/Vuong%27s_closeness_test) to model
selection of nonnested models.

```{r pairwise-vuong}
# Select just a few model to not mess the output
lt_chosen <- lt_fits[c("unit-Logistic", "Johnson-SB", "unit-Burr-XII", "unit-Weibull")]
pairwise.vuong.test(lt = lt_chosen)
```

The currently methods implemented for `unitquantreg` objects are:
```{r methods}
methods(class = "unitquantreg")
```

Another feature of unitquantreg package is to fit different models for several
quantiles values.

```{r various-quantiles}
fits <- unitquantreg(formula = phpws ~ mhdi + incpc + region + log(pop),
                     data = water, tau = 1:49/50, family = "uweibull",
                     link = "logit", link.theta = "log")
class(fits)
```

Then, the user can visualize the results using the `plot` method:

```{r plot-unitquantregs, out.width="80%"}
plot(fits, which = "coef")
```


The currently methods implemented for `unitquantregs` objects are:
```{r }
methods(class = "unitquantregs")
```

