---
title: "Shape AIC for Nominal Variables"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Shape AIC for Nominal Variables}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

```{r setup, include=FALSE}
library(nomiShape)
```

## Shape AIC for Nominal Variables

This vignette demonstrates how to compute the Shape AIC for nominal variables using the `shape_aic` function from the `nomiShape` package. Shape AIC quantifies the goodness-of-fit of different shape models to the distribution of a nominal variable.

### Computing Shape AIC

```{r shape-aic-example-1}
# Example usage of shape_aic
shape_aic(categories, "animal")
```

```{r shape-aic-example-2}
# Example usage of shape_aic
shape_aic(categories2, "animal")
```


```{r shape-aic-example-3}
# Example usage of shape_aic
shape_aic(categories3, "animal")
```

```{r shape-aic-example-4}
# Example usage of shape_aic
shape_aic(starwars, "species")
```

```{r}
# approximate rate from top counts
obs <- sort(table(starwars$species), decreasing = TRUE)
ranks <- seq_along(obs)
rate_est <- -coef(lm(log(obs + 1e-6) ~ ranks))[2]  # linear fit in log-space
rate_est
```

```{r}
shape_aic(starwars, "species")
```

```{r}
shape_aic (starwars,"species") 
```
```{r}
shape_aic (mpg,"manufacturer") 
```