This package solves least squares problem with high dimensional fixed effects. For a matrix `D`

of high dimensional fixed effects, it finds `b`

and `ϵ`

such that `y = D'b + ϵ`

with `E[Dϵ] = 0`

.

It is the back end for the package FixedEffectModels.jl, that estimates linear models with high-dimensional fixed effect.

The package defines two functions `solve_coefficients!`

, that returns the coefficients `b`

, and `solve_residuals!`

, that returns the residuals `ϵ`

. See the documentation `?solve_residuals!`

or `?solve_coefficients!`

.

```
using FixedEffects
# define fixed effects:
p1 = FixedEffect(repeat(1:5, inner = 2))
# combine fixed effects
p2 = FixedEffect(repeat(1:2, outer = 5), repeat(1:2, inner = 5))
# define interacted fixed effects
p3 = FixedEffect(repeat(1:5, outer = 2), interaction = rand(10))
# find residuals
x = rand(10)
solve_residuals!(x, [p1, p2])
# find the fixed effect coefficients
solve_coefficients!(x, [p1, p3])
```

## Installation

The package is registered in the `General`

registry and so can be installed at the REPL with `] add FixedEffects`

.