Real Covariate Design

[vladdez]

using Distributions

begin
	des = SingleSubjectDesign(;conditions=Dict(:cond => ["car","face"],
										   :cat => ["cat","dog","horse"]
#									:continuous => range(-2,2,8),
#								   :continuousB => range(-2,2,8)
								   ))
cov_des = CovariateDesign(des,120,
						  Dict(:continuousA => Uniform(-1,2),
							   :continuousB => Normal(5,1.2)))
end

	UnfoldSim.@with_kw struct CovariateDesign <: UnfoldSim.AbstractDesign
		design = nothing
		n_trials::Int
		covariates::Dict
	end

begin
	UnfoldSim.size(design::CovariateDesign) = design.n_trials
		
	function UnfoldSim.generate_events(rng::UnfoldSim.AbstractRNG, design::CovariateDesign)
		
		all_evts = []
		for (covariate,dist) in design.covariates
			push!(all_evts,covariate =>rand(rng,dist,design.n_trials))
		end	
		events = UnfoldSim.DataFrame(all_evts)
		if !isnothing(design.design)
			n_rep = design.n_trials ./ size(des)[1]
			try 
				Int(n_rep) 
			catch
				error("design.n_trials need to be divisible by size(design.design)")
			end
			categorical_events = generate_events(deepcopy(rng),RepeatDesign(design.design,n_rep))
			return hcat(categorical_events,events)
		else
		return events#DataFrame(all_evts)
		end
	end
end

generate_events(UnfoldSim.Random.MersenneTwister(), cov_des)
generate_events(des)

[behinger]

to add any context - I programmed this for Benjamins BSc thesis.

What is missing is documentation, tutorials, and the important feature of correlated predictor values.

We should discuss whether including the covariates::Dict into SingleSubjectDesign, or have it as an extra Design as of now

[jschepers]

@behinger Thanks for adding the context. I was going to ask about that. What is the purpose/background for this code?

[behinger]

I can imagine an interface for correlated predictors now (I got nerd sniped)

using Distributions, LinearAlgebra, Random
dists = Dict(:a=>Uniform(1,2), :b=>LogNormal(0.2,1), :c=>Normal(0,1))  # Example distributions
Σ = [1 0.5 0.1; 0.5 1 0.2; 0.1 0.2 1]  # Correlation matrix
n = 1000  # Number of samples
μ = zeros(size(Σ,1))
Z = rand(MvNormal(μ, Σ), n)
# Transform to desired marginal distributions using inverse CDF method
samples = Dict()
for (i, (key, dist)) in enumerate(dists)
    samples[key] = quantile.(dist, cdf.(Normal(), Z[i, :]))
end
samples

this works in return arbitrary correlated marginals - nice! Let's

• add a cehck that \ſigma is positive definite

and we are good - or are we?
While this preserves the rank correlation, it doesnt work perfectly for normal correlations (except with normals ;-)

So I next tried Copula's which is a branch of math I havent touched like ever. Very strange put powerful stuff. turns out (havent really understood much), you can describe any multivarate distribution using their marginals and a copula. Maybe intuitively this even makes a bit of sense, but mh 🤷 anyway - probably an ICA hidden somewhere there ;-) ok, back to topic - I thought this should kind of work

using Copulas

copula = GaussianCopula(Σ)
U = rand(copula, n)
samples = Dict()
for (i, (key, dist)) in enumerate(dists)
    samples[key] = quantile(dist, U[:, i])
end
samples

but it doesnt for some reason that I shouldnt dive in deeper now. Already spending too much time

What's left?

• propose an interface to specify the \sigma correlation matrix
• decide whether we should just use conditions = Dict(...) and always evaluate the distributions accordingly? e.g.

\sigma = [...correlation-matrix...]
conditions = Dict(:condition=>[:face,:car],[:a,:b,:c]=>[Uniform(1,2), LogNormal(0.2,1)], Normal(0,1), \Sigma],:x=>Uniform(-2,2)` , which would be the nicest way, no nested designs etc?