Nested blocking vars with vector RT

[palday]

These two formulae should give the same model:

julia> fnested = @formula(Thickness ~ 1 + Source + (1+Source|Lot/Wafer))
FormulaTerm
Response:
  Thickness(unknown)
Predictors:
  1
  Source(unknown)
  (Source,Lot,Wafer)->(1 + Source) | Lot / Wafer

julia> f = @formula(Thickness ~ 1 + Source + (1+Source|Lot) + (1+Source|Lot&Wafer))
FormulaTerm
Response:
  Thickness(unknown)
Predictors:
  1
  Source(unknown)
  (Source,Lot)->(1 + Source) | Lot
  (Source,Lot,Wafer)->(1 + Source) | Lot & Wafer

But fnested fails in construction due to schema problems. I don't think we ever tested the nested RE stuff on a model with a random slope:

julia> fit(MixedModel, fnested, MixedModels.dataset(:oxide))
ERROR: MethodError: no method matching +(::Tuple{InterceptTerm{true},CategoricalTerm{DummyCoding,String,1}}, ::Tuple{RandomEffectsTerm,RandomEffectsTerm})
Closest candidates are:
  +(::Any, ::Any, ::Any, ::Any...) at operators.jl:538
  +(::MutableArithmetics.Zero, ::Any) at /home/XXX/.julia/packages/MutableArithmetics/0tlz5/src/rewrite.jl:52
  +(::Tuple{Vararg{Union{AbstractTerm, Tuple{Vararg{AbstractTerm,N}} where N},N}} where N, ::AbstractTerm) at /home/XXX/.julia/packages/StatsModels/cpRh6/src/terms.jl:404
  ...
Stacktrace:
 [1] +(::InterceptTerm{true}, ::CategoricalTerm{DummyCoding,String,1}, ::Tuple{RandomEffectsTerm,RandomEffectsTerm}) at ./operators.jl:538
 [2] sum(::Tuple{InterceptTerm{true},CategoricalTerm{DummyCoding,String,1},Tuple{RandomEffectsTerm,RandomEffectsTerm}}) at ./tuple.jl:396
 [3] apply_schema(::Tuple{ConstantTerm{Int64},Term,FunctionTerm{typeof(|),var"#107#109",(:Source, :Lot, :Wafer)}}, ::MixedModels.MultiSchema{StatsModels.FullRank}, ::Type{T} where T) at /home/XXX/Work/MixedModels.jl/src/schema.jl:30
 [4] apply_schema(::FormulaTerm{Term,Tuple{ConstantTerm{Int64},Term,FunctionTerm{typeof(|),var"#107#109",(:Source, :Lot, :Wafer)}}}, ::StatsModels.Schema, ::Type{LinearMixedModel}) at /home/XXX/Work/MixedModels.jl/src/schema.jl:53
 [5] LinearMixedModel(::FormulaTerm{Term,Tuple{ConstantTerm{Int64},Term,FunctionTerm{typeof(|),var"#107#109",(:Source, :Lot, :Wafer)}}}, ::NamedTuple{(:Source, :Lot, :Wafer, :Site, :Thickness),Tuple{Arrow.DictEncoded{String,UInt32,SentinelArrays.ChainedVector{String,Arrow.List{String,Int32,Array{UInt8,1}}}},Arrow.DictEncoded{String,UInt32,SentinelArrays.ChainedVector{String,Arrow.List{String,Int32,Array{UInt8,1}}}},Arrow.DictEncoded{String,UInt32,SentinelArrays.ChainedVector{String,Arrow.List{String,Int32,Array{UInt8,1}}}},Arrow.DictEncoded{String,UInt32,SentinelArrays.ChainedVector{String,Arrow.List{String,Int32,Array{UInt8,1}}}},Arrow.Primitive{Float64,Array{Float64,1}}}}; contrasts::Dict{Symbol,Any}, wts::Array{Any,1}) at /home/XXX/Work/MixedModels.jl/src/linearmixedmodel.jl:67

Originally posted by @palday in #447 (comment)

[palday]

@kleinschmidt Assigning this to us in a separate issue so that both of us think about it when we get a free minute. 😄

[kleinschmidt]

I think the underlying issue here is actually the 1 + Source in the FIXED
effects, I think that's a StatsModels bug...

[palday]

Woops.

[kleinschmidt]

Yeah, with these extra methods it's fine:

Base.:+(as::TupleTerm, bs::TupleTerm) = (as..., bs...)
Base.:+(a::AbstractTerm, b::AbstractTerm) = (a, b)

(We already had the ones for the other two combinations but not these for some
reason).

At some point I was working on an alternative implementation that didn't rely on
tuples of terms as the representation of a "multi term" but obviously lost track
of that...

[palday]

Cool. Then I'll give you the joy of closing this issue when the fix is merged upstream. 😄