Interaction

[matthieugomez]

At some point do better path if there is fe + fe * interaction. I think one simple way is to demean interaction variable within each fixed effect, cause one can see that the resuling intercept is of Y on intercept and interaction within each group is simply given by E[Y] + E[YX] / E[X^2] * X

[matthieugomez]

Something like

function demean_interaction!(feM::FixedEffectSolverCPU{T}) where T
	m = feM.m
	fes = m.fes
	weights = feM.weights
	outs = Any[]
	for (i, fe) in enumerate(fes)
		# if fe is interacted fixed effects
		if !isa(fe.interaction, UnitWeights)
			# find if there is the non interacted version somewhere
			for fe2 in fes
				if isa(fe2.interaction, UnitWeights) && (fe.n == fe2.n) && (fe.refs == fe2.refs)
					# if so, we can demean interaction. Will speed up process.
					interaction_demeaned = deepcopy(fe.interaction)
					out = zeros(T, fe.n)
					gather!(out, fe.refs, 1, interaction_demeaned, weights)
					out2 = zeros(T, fe.n)
					gather!(out2, fe.refs, 1, weights, uweights(length(weights)))
					out .= out ./ out2
					scatter!(interaction_demeaned, -1, out, fe.refs, uweights(length(weights)))
					fes[i] = FixedEffect{typeof(fe.refs), typeof(fe.interaction)}(fe.refs, interaction_demeaned, fe.n)
					scale!(m.scales[i], fe.refs, fe.interaction, weights)
					cache!(m.caches[i], fe.refs, fe.interaction, weights, m.scales[i])
					push!(outs, [i, out])
					break
				end
			end
		end
	end
	return outs
end

function remean_interaction!(feM::FixedEffectSolverCPU{T}, outs) where {T}
	m = feM.m
	fes = m.fes
	weights = feM.weights
	for (i, out) in outs
		fe = fes[i]
		interaction_demeaned = deepcopy(fe.interaction)
		scatter!(interaction_demeaned, 1, out, fe.refs, uweights(length(weights)))
		fes[i] = FixedEffect{typeof(fe.refs), typeof(fe.interaction)}(fe.refs, interaction_demeaned, fe.n)
		scale!(m.scales[i], fe.refs, interaction_demeaned, weights)
		cache!(m.caches[i], fe.refs, interaction_demeaned, weights, m.scales[i])
	end
end