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

```{r setup, include = FALSE}
if (requireNamespace("MASS", quietly = TRUE)) {
  library(tidypredict)
  library(dplyr)
  eval_code <- TRUE
} else {
  eval_code <- FALSE
}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  eval = eval_code
)
```

| Function                                                      |Works|
|---------------------------------------------------------------|-----|
|`tidypredict_fit()`, `tidypredict_sql()`, `parse_model()`      |  ✔  |
|`tidypredict_to_column()`                                      |  ✗  |
|`tidypredict_test()`                                           |  ✗  |
|`tidypredict_interval()`, `tidypredict_sql_interval()`         |  ✗  |
|`parsnip`                                                      |  ✔  |

`MASS::qda()` fits quadratic discriminant analysis models. Unlike `MASS::lda()`,
each class gets its own covariance estimate, so the class scores are quadratic
rather than linear in the predictors: one intercept, one coefficient per
predictor, and one coefficient per pair of predictors. The posterior
probabilities are the softmax of those class scores.

Because these models predict one probability per outcome class,
`tidypredict_fit()` returns a *named list* of expressions, one for each class,
rather than a single expression. Since the output is a list,
`tidypredict_to_column()` and `tidypredict_test()` are not supported.

## `tidypredict_` functions

Note that `MASS` is used with `::` below rather than attached, because attaching
it would mask `dplyr::select()`.

```{r}
model <- MASS::qda(Species ~ ., data = iris)
```

- Create the R formulas, one per class
    ```{r}
fit <- tidypredict_fit(model)
names(fit)
fit[["setosa"]]
    ```

- Add the predictions to the original table
    ```{r}
library(dplyr)

iris %>%
  mutate(!!!tidypredict_fit(model)) %>%
  glimpse()
    ```

- Confirm that the results match the model's `predict()` results
    ```{r}
probs <- sapply(fit, \(f) rlang::eval_tidy(f, iris))
all.equal(unname(probs), unname(predict(model, iris)$posterior))
    ```

## parsnip

`parsnip` fitted models are also supported by `tidypredict`:
```{r}
library(parsnip)
library(discrim)

p_model <- discrim_quad() %>%
  set_engine("MASS") %>%
  fit(Species ~ ., data = iris)
```

```{r}
tidypredict_fit(p_model)[["virginica"]]
```

## Parse model spec

Here is an example of the model spec:
```{r}
pm <- parse_model(model)
str(pm, 2)
```