unintuitive behavior with multiple terms with same grouping factor

[kleinschmidt]

Currently, if you have a formula like y ~ 1 + (1|G) + (0+A|G) where A is a categorical variable with n levels, then you'll generate 1 variance term for the random intercept, and n terms for A, leading to an overparametrized model. This may not be what you want; listing these as separate terms is a way to indicate that you want to zero out the correlation terms between the random intercept and the random slopes for A, and you end up changing the number of variance terms (relative to the (1+A|G) formula).

This can be fixed by changing the way that the schema is applied. Currently, a fresh StatsModels.FullRank schema is prepared for every random effect term, meaning that the 0+A is treated as independent from the 1. An alternative approach would be to add yet another level of schema wrapping (which I'll prepare a PR for), which stores one FullRank schema for each grouping variable and applies it across multiple terms. But this is a breaking change and may require changing how amalgamate works as well. It's tested here:

MixedModels.jl/test/pls.jl

Lines 277 to 290 in c87e8d1

	# combining [ReMat{T,S1}, ReMat{T,S2}] for S1 ≠ S2
	slpcat = categorical!(deepcopy(slp), [:days])
	fm_cat = LMM(@formula(reaction ~ 1 + days + (1|subj) + (0 + days|subj)), slpcat)
	@test fm_cat isa LMM
	σρ = fit!(fm_cat).σρs
	@test σρ isa NamedTuple
	@test isone(length(σρ))
	@test first(keys(σρ)) == :subj
	@test keys(σρ.subj) == (:σ, :ρ)
	@test length(σρ.subj) == 2
	@test length(first(σρ.subj)) == 11
	@test length(σρ.subj.ρ) == 55
	@test iszero(σρ.subj.ρ[46])
	@test σρ.subj.ρ[46] === -0.0

[palday]

@kleinschmidt Have you had time to implement this?

[kleinschmidt]

not beyond what's in #269, which IIRC needs some love to work with amalgamate but maybe that's changed in the mean time?