---
title: "Paper: ammonia application"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Paper: ammonia application}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 6,
  fig.height = 5
)
```

```{r setup}
library(simplexgof)
```

## The ammonia application

This article reproduces the ammonia-oxidation application from the
companion methodological paper (Ospina, Espinheira, Silva and Barros,
2026), using the `ammonia` dataset (Brownlee, 1965; $n = 21$).

The model fitted in the paper has

$$
\mathrm{logit}(\mu_t) = \beta_1 + \beta_2 x_{t2} + \beta_3 x_{t3} +
  \beta_4 x_{t2} x_{t3}
$$

for the mean, and

$$
\log(\sigma^2_t) = \gamma_1 + \gamma_2 x_{t3} + \gamma_3 x_{t2} x_{t3}
$$

for the dispersion, where $x_{t2}$ = `corr_ar` (air flow) and $x_{t3}$ =
`temp_agua` (cooling water inlet temperature).

## One-call reproduction

The function `paper_ammonia()` fits this model, runs the bootstrap GoF
test, and produces the diagnostic plots from the paper in a single call.
We use `B = 50` bootstrap replicates here for speed; the paper uses
`B = 1000`.

```{r, fig.alt = "Diagnostic plots for the ammonia application"}
res <- paper_ammonia(B = 50, seed = 123, plot = TRUE, verbose = FALSE)
```

### Parameter estimates (Table 5 of the paper)

```{r}
print(res$table_params, row.names = FALSE)
```

### Goodness-of-fit results (Table 6 of the paper)

```{r}
print(res$table_gof, row.names = FALSE)
```

## Step by step

The same analysis can be reproduced manually with the lower-level
functions of the package:

```{r}
data(ammonia)

X <- cbind(1, ammonia$corr_ar, ammonia$temp_agua,
           ammonia$corr_ar * ammonia$temp_agua)
Z <- cbind(1, ammonia$temp_agua,
           ammonia$corr_ar * ammonia$temp_agua)

fit <- simplex_fit(ammonia$perda, X, Z)
fit

dg <- simplex_diag(fit)
dg$Tn
dg$Un
```

```{r, fig.alt = "Influence index plot for the ammonia model"}
plot_influence(dg)
```

```{r}
set.seed(123)
gof <- simplex_gof(ammonia$perda, X, Z, B = 50, verbose = FALSE)
gof
```

```{r, fig.alt = "Bootstrap distribution of Un for the ammonia application"}
plot_gof_boot(gof)
```

As reported in the paper, the test does not reject $H_0$ at conventional
significance levels for this model, consistent with an adequate fit.

## References

Brownlee, K. A. (1965). *Statistical Theory and Methodology in Science
and Engineering*. Wiley.

Ospina, R., Espinheira, P. L., Silva, F. C., Barros, M. (2026). A
Bootstrap-Calibrated Local Influence Goodness-of-Fit Procedure for
Simplex Regression Models.