# Is there a better DSL (domain-specific language) for defining a formula in linear models?

**URL:** <https://discourse.julialang.org/t/is-there-a-better-dsl-domain-specific-language-for-defining-a-formula-in-linear-models/22555>\
**Category:** Statistics\
**Created:** [March 31, 2019, 12:05am UTC](https://discourse.julialang.org/t/is-there-a-better-dsl-domain-specific-language-for-defining-a-formula-in-linear-models/22555 "2019-03-31T00:05:29Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![xiaodai](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/xiaodai/32/15937_2.png) [@xiaodai](https://discourse.julialang.org/u/xiaodai)\
**Post date:** [March 31, 2019, 12:05am UTC](https://discourse.julialang.org/t/is-there-a-better-dsl-domain-specific-language-for-defining-a-formula-in-linear-models/22555/1 "2019-03-31T00:05:29Z")

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I have been an R user and I can see where StatsModel’s `@formula` macro came from -  
R! `@formula(x ~ y - 1)` where the `-1` is to fit without an intercept was unintuitive to me, and also `a*b` is the same as `a + b + a&b` i.e. individual and interaction effects. That was also unintuitive, because I actually just wanted `a*b`. I wonder if there’s a better language for a formula somewhere that someone can point me to? Maybe it’s implemented in Julia.

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**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [March 31, 2019, 6:43am UTC](https://discourse.julialang.org/t/is-there-a-better-dsl-domain-specific-language-for-defining-a-formula-in-linear-models/22555/2 "2019-03-31T06:43:56Z")

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There is no need to rely on your intuition, just read the docs.

[https://juliastats.github.io/StatsModels.jl/latest/formula/#Modeling-tabular-data-1](https://juliastats.github.io/StatsModels.jl/latest/formula/#Modeling-tabular-data-1)

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**Author:** ![dave.f.kleinschmidt](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dave.f.kleinschmidt/32/55_2.png) [@dave.f.kleinschmidt](https://discourse.julialang.org/u/dave.f.kleinschmidt)\
**Post date:** [March 31, 2019, 7:47pm UTC](https://discourse.julialang.org/t/is-there-a-better-dsl-domain-specific-language-for-defining-a-formula-in-linear-models/22555/3 "2019-03-31T19:47:28Z")

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If you’re on master (post #71 Terms 2.0) you can wrap things in identity to block the special syntax (so `y ~ identity(a*b - 1)` will regress y against one less than the product of a and b).

As a more general comment, there’s always a tension between supporting the DSL features that people who are super familiar with R expect but that others find really unintuitive. I personally hate the “include intercept by default, use 0 or -1 to block” thing but many people would be surprised if that was removed. In #71 the compromise I came up with is that subtypes of `AbstractStatisticalModel` use the “classical” behavior, but others use the “obvious” behavior (only get what you explicitly ask for at least as far as an intercrpt/constant column goes).

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**Author:** ![dave.f.kleinschmidt](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dave.f.kleinschmidt/32/55_2.png) [@dave.f.kleinschmidt](https://discourse.julialang.org/u/dave.f.kleinschmidt)\
**Post date:** [March 31, 2019, 7:50pm UTC](https://discourse.julialang.org/t/is-there-a-better-dsl-domain-specific-language-for-defining-a-formula-in-linear-models/22555/4 "2019-03-31T19:50:24Z")

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And at an even more general level, one of the primary goals of #71 Terms 2.0 Son of Terms was to make the formula DSL something people could customize and build on top of, instead of a straight clone of the R formula DSL. You could even go as far as writing your own macro that doesn’t do any of the special syntax (is actually just `*` that’s handled at the macro level) but still returns terms and get all the other benefits of the DSL

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**Author:** ![xiaodai](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/xiaodai/32/15937_2.png) [@xiaodai](https://discourse.julialang.org/u/xiaodai)\
**Post date:** [March 31, 2019, 8:40pm UTC](https://discourse.julialang.org/t/is-there-a-better-dsl-domain-specific-language-for-defining-a-formula-in-linear-models/22555/5 "2019-03-31T20:40:17Z")

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@dave.f.kleinschmidt thank you for your understanding and reasonable suggestions. Developing an alternative macro sounds like am interesting option

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**Author:** ![piever](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/piever/32/1815_2.png) [@piever](https://discourse.julialang.org/u/piever)\
**Post date:** [April 1, 2019, 9:22am UTC](https://discourse.julialang.org/t/is-there-a-better-dsl-domain-specific-language-for-defining-a-formula-in-linear-models/22555/6 "2019-04-01T09:22:17Z")

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I’ve come to appreciate when there is a simple way to do things that does not require macros and for that I think a big upgrade to StatsModel has been the possibility to cleanly construct a formula in an explicit, programmatic way: [Modeling tabular data · StatsModels.jl](https://juliastats.github.io/StatsModels.jl/latest/formula/#Constructing-a-formula-programatically-1)

In terms of simplifying the “macro-free” API, maybe it’d be useful to have a vararg `interaction` function to create interaction terms and a `fullinteraction` function for interaction terms with also partial interactions (names could probably be improved). Something like:

```julia
julia> using StatsModels, IterTools

julia> interaction() = ConstantTerm(1) # product of 0 terms
interaction (generic function with 1 method)

julia> interaction(args...) = mapreduce(term, &, args)
interaction (generic function with 2 methods)

julia> function fullinteraction(args...)
           itr = Iterators.filter(!isempty, IterTools.subsets(args))
           mapreduce(v -> interaction(v...), +, itr)
       end
fullinteraction (generic function with 1 method)

julia> interaction(:a, :b, :c)
a(unknown) & b(unknown) & c(unknown)

julia> fullinteraction(:a, :b, :c)
a(unknown)
b(unknown)
a(unknown) & b(unknown)
c(unknown)
a(unknown) & c(unknown)
b(unknown) & c(unknown)
a(unknown) & b(unknown) & c(unknown)

```