# DiscreteChoiceModels.jl

This is a pure Julia package for estimating discrete choice/random utility models. The models supported so far are:

- Multinomial logit

Support is planned for:

- Nested logit
- Mixed logit

At this point, the package should be considered experimental.

The package allows specifying discrete choice models using an intuitive, expressive syntax. For instance, the following code reproduces Biogeme's multinomial logit model in 28 lines of code, vs. 65 for the Biogeme example:

```
using DiscreteChoiceModels, CSV, DataFrames
# read and filter data, and create binary availability columns
data = CSV.read(replace(pathof(DiscreteChoiceModels), "src/DiscreteChoiceModels.jl" => "") * "/test/data/biogeme_swissmetro.dat", DataFrame, delim='\t')
data = data[in.(data.PURPOSE, [Set([1, 3])]) .& (data.CHOICE .!= 0), :]
data.avtr = (data.TRAIN_AV .== 1) .& (data.SP .!= 0)
data.avsm = data.SM_AV .== 1
data.avcar = (data.CAR_AV .== 1) .& (data.SP .!= 0)
model = multinomial_logit(
@utility(begin
1 ~ αtrain + βtravel_time * TRAIN_TT / 100 + βcost * (TRAIN_CO * (GA == 0)) / 100
2 ~ αswissmetro + βtravel_time * SM_TT / 100 + βcost * SM_CO * (GA == 0) / 100
3 ~ αcar + βtravel_time * CAR_TT / 100 + βcost * CAR_CO / 100
:αswissmetro = 0, fixed # fix swissmetro ASC to zero
end),
:CHOICE,
data,
availability=[
1 => :avtr,
2 => :avsm,
3 => :avcar
]
)
summary(model)
```

## Specifying a model

Models are specified using the `@utility`

macro. Utility functions are specified using `~`

, where the left-hand side is the value in the choice vector passed into the model estimation function (which can be a number, string, etc.). Values on the right-hand side that start with α or β are quantities to estimate (which can be typed into a properly-configured Julia environment as `\alpha`

and `\beta`

), all other values are assumed to be variables in the dataset. For example,
`"car" ~ αcar + βtravel_time * travel_time_car`

specifies that the utility function for the choice "car" is an ASC plus a generic travel time coefficient multiplied by car travel time. By convention, α is used for alternative-specific constants, and β is used for coefficients, but the software treats them as interchangeable.

Starting values for coefficients can be specified using `=`

. For example,
`αcar = 1.3247`

will start estimation for this coefficient at 1.3247. If a coefficient appears in a utility function specification without a starting value being defined, the starting value will be set to zero.

If a coefficient should be fixed (rather than estimated), this can be specified with a `, fixed`

postfix:
`αcar = 0, fixed`

This is most commonly used with 0 to indicate a left-out ASC, but any value can be fixed for a coefficient.

If one choice outcome should not have any values in its utility function (i.e. it is the base outcome), that must be explicitly stated by declaring `"walk" ~ 0`

## Features

- Expressive syntax for model specification
- Many optimization algorithms available using Optim.jl
- Variance-covariance matrices estimated using automatic differentiation

## Performance

It's good. (Benchmarks to come.)