Formulas.rmd

---
title: Formulas
layout: default
---

## Formulas

<!-- 
methods(class = "formula")
-->

There is one other important tool of non-standard evaluation: the formula. The formula operator, `~`, is used extensively by modelling functions, but also by some graphics functions (e.g. lattice and `plot`) and a few data manipulation functions (e.g. `xtabs()` and `aggregate()`).

## Formula as a quoting function

There are two advantages for using `~` over `quote()`:

* It is shorter
* It captures both the expression and the environment in which it was evaluated

The disadvantage of using `~` is that most people are used to its role in models, and may be surprised in the semantics you imply from it are substantially different from standard modelling formulas.   

The formula object is a call that knows in which environment it was evaluated. You can use `length()` to determine if it is one-sided or two-sided, and `[[` to extract the various pieces.

```R
f1 <- ~ a + b
length(f1)
f1[[1]]
f1[[2]]

f2 <- y ~ a + b
length(f2)
f2[[1]]
f2[[2]]
f2[[3]]
```

You can extract the environment of a formula with `environment()`, as demonstrated with this implementation of `subset()`:

```R
subset_f <- function(x, f) {
  stopifnot(inherits(f, "formula"), length(f) == 2)
  r <- eval(f[[2]], x, environment(f))
  x[r, ]
}
subset_f(mtcars, ~ cyl == 4)
```

Note that because the code is evaluated in the environment associated with the formula, the semantics are a little different if you're creating the formula in a function:

```R
f <- function(x) ~ cyl == x
subset_f(mtcars, f(4))
```

### `xtabs()`

Is a pretty horrible example because of it's combination of call mangling and tangles with sparse matrices.

## Formulas for modelling

Keep it brief: focus on main concepts (possibly showing complete lm implmentation using Rcpp), and pointing to documentation where necessary.  Need to discuss specials (e.g. offset/Error) and how splines work?

White book.

Patsy: http://patsy.readthedocs.org/en/latest/R-comparison.html

Formula package (http://cran.r-project.org/web/packages/Formula/vignettes/Formula.pdf)

Models use two steps: first converting the formula into matrices, and then manipulating using matrix algebra.

* RcppEigen:::fastLm.formula

* http://developer.r-project.org/model-fitting-functions.txt
* terms, terms.object, terms.formula
* model.response, model.weights
* model.matrix, model.frame
* lm.fit