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Store only the covariance matrix in CoxModel, not the information #41

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Store only the covariance matrix in CoxModel, not the information #41

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2d96905
Store Cholesky of the OIM rather than separate matrices
ararslan Jul 10, 2022
2aaa59e
Merge remote-tracking branch 'origin/main' into aa/cholesky-meets-fisher
ararslan Jul 26, 2022
d2f0563
Check for collinearity when fitting a Cox model
ararslan Jul 26, 2022
e2810db
Store the covariance matrix only, not the information
ararslan Jul 26, 2022
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28 changes: 22 additions & 6 deletions src/cox.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -78,13 +78,12 @@ end

# Structure of Cox regression output

struct CoxModel{T<:Real} <: RegressionModel
struct CoxModel{T<:Real,C<:Union{Cholesky{T},CholeskyPivoted{T}}} <: RegressionModel
aux::CoxAux{T}
β::Vector{T}
loglik::T
score::Vector{T}
fischer_info::Matrix{T}
vcov::Matrix{T}
chol::C
end

function StatsAPI.coeftable(obj::CoxModel)
Expand Down Expand Up @@ -119,7 +118,7 @@ StatsAPI.dof(obj::CoxModel) = length(coef(obj))

StatsAPI.dof_residual(obj::CoxModel) = nobs(obj) - dof(obj)

StatsAPI.vcov(obj::CoxModel) = obj.vcov
StatsAPI.vcov(obj::CoxModel) = inv(obj.chol)
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My point is that this one will error in the rank deficient case since

julia> inv(cholesky([0 0; 0 1], Val(true), check=false))
ERROR: SingularException(2)
Stacktrace:
 [1] chknonsingular
   @ /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/lapack.jl:49 [inlined]
 [2] potri!(uplo::Char, A::Matrix{Float64})
   @ LinearAlgebra.LAPACK /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/lapack.jl:3118
 [3] inv(C::CholeskyPivoted{Float64, Matrix{Float64}})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/cholesky.jl:688
 [4] top-level scope
   @ REPL[150]:1

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Ohhh okay yeah, I see. And in that case then there's no point in using a pivoted factorization since we primarily care about the inverse. 👍

Could still be worth checking for collinearity ahead of time though.


StatsAPI.stderror(obj::CoxModel) = sqrt.(diag(vcov(obj)))

Expand Down Expand Up @@ -193,6 +192,19 @@ function _cox_fgh!(β, grad, hes, c::CoxAux{T}) where T
return y
end

function _chol_me_maybe(A)
C = cholesky(A; check=false)
if issuccess(C)
return C
else
@static if VERSION >= v"1.8.0-DEV.1139"
return cholesky(A, RowMaximum())
else
return cholesky(A, Val(true))
end
end
end

_coxph(X::AbstractArray{<:Integer}, s::AbstractVector; tol, l2_cost) = _coxph(float(X), s; tol=tol, l2_cost=l2_cost)

function _coxph(X::AbstractArray{T}, s::AbstractVector; l2_cost, tol) where T
Expand All @@ -201,8 +213,12 @@ function _coxph(X::AbstractArray{T}, s::AbstractVector; l2_cost, tol) where T
β₀ = zeros(R, size(X, 2))
fgh! = TwiceDifferentiable(Optim.only_fgh!((f, G, H, x)->_cox_fgh!(x, G, H, c)), β₀)
res = optimize(fgh!, β₀, NewtonTrustRegion(), Optim.Options(g_tol = tol))
β, neg_ll, grad, hes = Optim.minimizer(res), Optim.minimum(res), Optim.gradient(fgh!), Optim.hessian(fgh!)
return CoxModel{R}(c, β, -neg_ll, -grad, hes, pinv(hes))
β = Optim.minimizer(res)
neg_ll = minimum(res)
grad = Optim.gradient(fgh!)
hes = Symmetric(Optim.hessian(fgh!))
chol = _chol_me_maybe(hes)
return CoxModel{R,typeof(chol)}(c, β, -neg_ll, -grad, chol)
end

StatsModels.drop_intercept(::Type{CoxModel}) = true
Expand Down
7 changes: 4 additions & 3 deletions test/runtests.jl
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Expand Up @@ -201,7 +201,7 @@ end
@test modelmatrix(outcome) == modelmatrix(outcome_without_formula)

@test sprint(show, outcome_without_formula) == """
CoxModel{Float64}
CoxModel{Float64, Cholesky{Float64, Matrix{Float64}}}

Coefficients:
──────────────────────────────────────────────
Expand Down Expand Up @@ -241,8 +241,9 @@ x7 0.0914971 0.0286485 3.19378 0.0014
@test dof(outcome) == 7
@test dof_residual(outcome) == 425
@test loglikelihood(outcome) > nullloglikelihood(outcome)
@test all(x->x > 0, eigen(outcome.model.fischer_info).values)
@test outcome.model.fischer_info * vcov(outcome) ≈ I atol=1e-10
fisher_info = Matrix(outcome.model.chol)
@test all(x->x > 0, eigen(fisher_info).values)
@test fisher_info * vcov(outcome) ≈ I atol=1e-10
@test norm(outcome.model.score) < 1e-5
@test hcat(outcome_coefmat.cols[1:3]...) ≈ expected_coefs[:,1:3] atol=1e-5

Expand Down