Fixed linear model with perfectly collinear rhs variables and weights

[dwinkler1]

This is my probably not very efficient suggestion to fix #420
Suggestions very welcome!!

[dwinkler1]

Please let me know if I should change anything in the PR. :)

[andreasnoack]

Looks right to me. Could you please add a test case as well?

[dwinkler1]

I tried to add a teset but for me the earlier testset "linear model with weights" errors already. I feel like it is related to the PR but I am not sure how we even end up with a CholeskyPivoted in this case.

This would be my testset

@testset "collinearity and weights" begin
    rng = StableRNG(1234321)
    x1 = randn(100)
    x1_2 = 3 * x1
    x2 = 10 * randn(100)
    x2_2 = -2.4 * x2
    y = 1 .+ randn() * x1 + randn() * x2 + 2 * randn(100)
    df = DataFrame(y = y, x1 = x1, x2 = x1_2, x3 = x2, x4 = x2_2, weights = repeat([1, 0.5],50))
    f = @formula(y ~ x1 + x2 + x3 + x4)
    lm_model = lm(f, df, wts = df.weights)#, dropcollinear = true)
    X = [ones(length(y)) x1_2 x2_2]
    W = Diagonal(df.weights)
    coef_naive = (X'W*X)\X'W*y
    @test lm_model.model.pp.chol isa CholeskyPivoted
    @test rank(lm_model.model.pp.chol) == 3
    @test isapprox(filter(!=(0.0), coef(lm_model)), coef_naive)
end

This is what goes wrong earlier

julia>     lm_model = lm(f, df, wts = df.weights)
StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}

FoodExp ~ 1 + Income

Coefficients:
──────────────────────────────────────────────────────────────────────────────
                     Coef.  Std. Error      t  Pr(>|t|)   Lower 95%  Upper 95%
──────────────────────────────────────────────────────────────────────────────
(Intercept)  -2794.53        2.92818e5  -0.01    0.9924  -5.77698e5  5.72109e5
Income           3.63222e6   3.36375e8   0.01    0.9914  -6.56787e8  6.64051e8
──────────────────────────────────────────────────────────────────────────────

[nalimilan]

I tried to add a teset but for me the earlier testset "linear model with weights" errors already. I feel like it is related to the PR but I am not sure how we even end up with a CholeskyPivoted in this case.

We use dropcollinear=true by default, so you get a CholeskyPivoted unless you pass dropcollinear=false explicitly. From a quick check, it appears that the new failure is due to changes this PR makes for the if rnk == length(ch.p) case. Do you really need to change the code in that branch?

[dwinkler1]

@nalimilan you were of course correct. I fixed that and added tests (all test passing now). However, I made a mess with autoformatting in vscode. What would be the best way to get just the stuff I changed in without the unnecessary indentation changes? Should I just fork again?
Sorry my experience with git pull requests is quite limited.

EDIT: I gave it a try let me know if that is ok!

[codecov-commenter]

Codecov Report

Base: 87.08% // Head: 87.27% // Increases project coverage by +0.19% 🎉

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Additional details and impacted files

@@            Coverage Diff             @@
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[nalimilan]

Thanks. There are still some failures which may well be random given that they happen on different versions. Any idea what may be going on? Can you reproduce these locally?

[dwinkler1]

Looks like numeric instability to me. I'll investigate. Maybe I can write a more stable version of the test case. They do not happen on my machine (ubuntu with 1.6)

[nalimilan]

Bump. Maybe try a different set of values?

[alecloudenback]

Bump on this PR. I am encountering the issue in #420 as well.

On my local machine (1.8RC4, Mac M1) the tests pass. I agree with @danielw2904 that this appears to just be a numerical difference which stands out because the failing tests were printing +/- 0.0...

All four failing test cases in the F test for model comparison testset were a change in +/- 0.0, for example:

Screen.Recording.2022-08-13.at.11.53.45.PM.mov

[dwinkler1]

Sorry, I am unable to work on this anymore.

[nalimilan]

Unfortunately it seems to me that something more serious is going on. Locally, tests always fail, even on Julia 1.7. Maybe this has to do with BLAS and the CPU? The following models give completely different coefficients here:

julia> using GLM, StableRNGs

julia> rng = StableRNG(1234321);

julia> x1 = randn(rng, 100);

julia> x1_2 = 3 * x1;

julia> x2 = 10 * randn(rng, 100);

julia> x2_2 = -2.4 * x2;

julia> y = 1 .+ randn(rng) * x1 + randn(rng) * x2 + 2 * randn(rng, 100);

julia> df = DataFrame(y = y, x1 = x1, x2 = x1_2, x3 = x2, x4 = x2_2, weights = repeat([1, 0.5],50));

julia> lm_collinear = lm(@formula(y ~ x1 + x2 + x3 + x4), df, wts=df.weights)
StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}

y ~ 1 + x1 + x2 + x3 + x4

Coefficients:
───────────────────────────────────────────────────────────────────────────
                  Coef.  Std. Error       t  Pr(>|t|)  Lower 95%  Upper 95%
───────────────────────────────────────────────────────────────────────────
(Intercept)  0.00389006    7.74397     0.00    0.9996  -15.4334    15.4412
x1           0.0         NaN         NaN       NaN     NaN        NaN
x2           0.594857      2.78844     0.21    0.8317   -4.96379    6.1535
x3           0.0         NaN         NaN       NaN     NaN        NaN
x4           4.11564       0.351608   11.71    <1e-17    3.41472    4.81656
───────────────────────────────────────────────────────────────────────────

julia> lm_reduced = lm(@formula(y ~ x2 + x4), df, wts=df.weights)
StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}

y ~ 1 + x2 + x4

Coefficients:
────────────────────────────────────────────────────────────────────────
                Coef.  Std. Error      t  Pr(>|t|)  Lower 95%  Upper 95%
────────────────────────────────────────────────────────────────────────
(Intercept)  1.29678    0.265978    4.88    <1e-05  0.766565    1.827
x2           0.215149   0.0973285   2.21    0.0302  0.0211286   0.40917
x4           0.648579   0.0124034  52.29    <1e-58  0.623853    0.673305
────────────────────────────────────────────────────────────────────────

julia> deviance(lm_collinear)
410484.4884591147

julia> deviance(lm_reduced)
355.2246843374244

On current master, both models have the same deviance and the same predictions, so it seems that this PR introduces a regression at least in some cases.

[nalimilan]

Though if #487 (comment) fixes it, then maybe we don't need this PR after all?

[nalimilan]

@alecloudenback If you're interested in making a PR, you could extract the relevant part from #487 so that we can fix this bug without waiting for the more general improvements of weighting.