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sims_ml.jl
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######################################################################################################################
# Author: Alex Keil
# Program: sims_ml.R
# Language: Julia (tested on v1.3.0)
# Date: Tuesday, March 31, 2020 at 3:12:51 PM
# Project: Bayesian G-Computation to Estimate Impacts of Interventions on Exposure Mixtures:
# Demonstration with Metals from Coal-fired Power Plants and Birthweight
# Tasks:
# Data in:
# Data out:
# Description:
# Keywords: mixtures, bayes, g-computation, causal inference, coal, environment
# Released under the GNU General Public License: http://www.gnu.org/copyleft/gpl.html
######################################################################################################################
using Distributed
cd("/workingdirectory")
@everywhere include("Gibbs.jl") # most functions not necessary here, but calls in some required packages
@everywhere using Distributions, Random, SharedArrays
# data generating function
@everywhere function dgm(n)
alpha = [2.0, 1.0, 0.0]
Z = permutedims(rand(MvNormal([0.,0.,0.], 1.), n))
X = 15. .+ Z * alpha + rand(Normal(0.0, 1.0), n)
X2 = 15. .+ Z * alpha + rand(Normal(0.0, 1.0), n)
Xint1 = X*0. .+ 1.0
Xint15 = X*0. .+ 15.0
beta = vcat(
[1.0], #x (x2 has no effect)
[1.0, 0.5, 1.5], #z
[-0.1, -0.15, -0.2], #z*z
[-0.3, -0.25, -0.2] #x*z
)
y = hcat(X, Z, Z .* Z, X .* Z) * beta + rand(Normal(0.0, 3.0), n)
y1 = hcat(Xint1, Z, Z .* Z, Xint1 .* Z) * beta# + rand(Normal(0.0, 1.0), n)
y15 = hcat(Xint15, Z, Z .* Z, Xint15 .* Z) * beta# + rand(Normal(0.0, 1.0), n)
y,X,X2,Z,Xint1, Xint15,y1, y15
end
# full model
@everywhere function analyze(n=100)
y,Xi,X2i,Zi,Xinti,Xint15i,y1,y15 = dgm(n);
X = hcat(ones(n), Xi, X2i, Zi, Zi .* Zi, Xi .* Zi, X2i .* Zi);
Xint = [hcat(ones(n), Xinti, Xinti, Zi, Zi .* Zi, Xinti .* Zi, Xinti .* Zi),
hcat(ones(n), Xint15i, Xint15i, Zi, Zi .* Zi, Xint15i .* Zi, Xint15i .* Zi)];
res = fit(GeneralizedLinearModel,X,y, Normal())
m1e, m0e = mean(predict(res, Xint[1])),mean(predict(res, Xint[2]))
m1 = mean(y1)
m0 = mean(y15)
hcat(
m1,m0, m1-m0,
m1e, m0e, m1e-m0e
)
end
# misspecified model
@everywhere function analyze2(n=100)
y,Xi,X2i,Zi,Xinti,Xint15i,y1,y15 = dgm(n);
X = hcat(ones(n), Xi, X2i, Zi);
Xint = [hcat(ones(n), Xinti, Xinti, Zi), hcat(ones(n), Xint15i, Xint15i, Zi)];
res = fit(GeneralizedLinearModel,X,y, Normal())
m1e, m0e = mean(predict(res, Xint[1])),mean(predict(res, Xint[2]))
m1 = mean(y1)
m0 = mean(y15)
hcat(
m1,m0, m1-m0,
m1e, m0e, m1e-m0e
)
end
# trigger JIT compiler
rti = analyze(100)
Niter=2
sampsize=100
res = SharedArray{Float64}(Niter,size(rti)[2], pids=procs(myid()))
@inbounds @sync @distributed for i in 1:Niter
res[i,:] = analyze(sampsize)
#res[i,:] = analyze2(sampsize, chains=1)
#res[i,:] = analyze3(sampsize, chains=1)
println("testing")
end
Niter=2000
println(string(Niter)*" iterations")
sampsize=100
println("Sample size="*string(sampsize))
res = SharedArray{Float64}(Niter,size(rti)[2], pids=procs(myid()));
@inbounds @sync @distributed for i in 1:Niter
res[i,:] = analyze(sampsize)
end
resfin = DataFrame(res);
rename!(resfin, [:m1t, :m0t, :mdt, :m1, :m0, :md]);
CSV.write("n100mle.csv", resfin)
sampsize=1000
println("Sample size="*string(sampsize))
res = SharedArray{Float64}(Niter,size(rti)[2], pids=procs(myid()));
@inbounds @sync @distributed for i in 1:Niter
res[i,:] = analyze(sampsize)
end
resfin = DataFrame(res);
rename!(resfin, [:m1t, :m0t, :mdt, :m1, :m0, :md]);
CSV.write("n1000mle.csv", resfin)
sampsize=10000
println("Sample size="*string(sampsize))
res = SharedArray{Float64}(Niter,size(rti)[2], pids=procs(myid()));
@inbounds @sync @distributed for i in 1:Niter
res[i,:] = analyze(sampsize)
end
resfin = DataFrame(res);
rename!(resfin, [:m1t, :m0t, :mdt, :m1, :m0, :md]);
CSV.write("n10000mle.csv", resfin)
sampsize=5000
println("Sample size="*string(sampsize))
res = SharedArray{Float64}(Niter,size(rti)[2], pids=procs(myid()));
@inbounds @sync @distributed for i in 1:Niter
res[i,:] = analyze(sampsize)
end
resfin = DataFrame(res);
rename!(resfin, [:m1t, :m0t, :mdt, :m1, :m0, :md]);
CSV.write("n5000mle.csv", resfin)
println("Misspecified")
sampsize=10000
println("Sample size="*string(sampsize))
res = SharedArray{Float64}(Niter,size(rti)[2], pids=procs(myid()));
@inbounds @sync @distributed for i in 1:Niter
res[i,:] = analyze2(sampsize)
end
resfin = DataFrame(res);
rename!(resfin, [:m1t, :m0t, :mdt, :m1, :m0, :md]);
CSV.write("n10000mle_misspec.csv", resfin)
sampsize=100
println("Sample size="*string(sampsize))
res = SharedArray{Float64}(Niter,size(rti)[2], pids=procs(myid()));
@inbounds @sync @distributed for i in 1:Niter
res[i,:] = analyze2(sampsize)
end
resfin = DataFrame(res);
rename!(resfin, [:m1t, :m0t, :mdt, :m1, :m0, :md]);
CSV.write("n100mle_misspec.csv", resfin)
sampsize=1000
println("Sample size="*string(sampsize))
res = SharedArray{Float64}(Niter,size(rti)[2], pids=procs(myid()));
@inbounds @sync @distributed for i in 1:Niter
res[i,:] = analyze2(sampsize)
end
resfin = DataFrame(res);
rename!(resfin, [:m1t, :m0t, :mdt, :m1, :m0, :md]);
CSV.write("n1000mle_misspec.csv", resfin)
sampsize=5000
println("Sample size="*string(sampsize))
res = SharedArray{Float64}(Niter,size(rti)[2], pids=procs(myid()));
@inbounds @sync @distributed for i in 1:Niter
res[i,:] = analyze2(sampsize)
end
resfin = DataFrame(res);
rename!(resfin, [:m1t, :m0t, :mdt, :m1, :m0, :md]);
CSV.write("n5000mle_misspec.csv", resfin)