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Fix handling of zero weights #638

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a0e1815
Fix handling of zero weights
nalimilan Jan 11, 2026
add9660
Review fixes
nalimilan Jan 12, 2026
19e10d4
Merge branch 'master' into nl/zerowts
nalimilan Apr 26, 2026
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11 changes: 6 additions & 5 deletions src/glmfit.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -25,7 +25,7 @@ struct GlmResp{V<:FPVector,D<:UnivariateDistribution,L<:Link,W<:AbstractWeights}
wrkresid::V
end

link(rr::GlmResp) = rr.d
distr(rr::GlmResp) = rr.d

function GlmResp(y::V, d::D, l::L, η::V, μ::V, off::V, wts::W) where {V<:FPVector,D,L,W}
n = length(y)
Expand Down Expand Up @@ -79,7 +79,7 @@ end
function deviance(r::GlmResp)
wts = weights(r)
d = sum(r.devresid)
return wts isa ProbabilityWeights ? d * nobs(r) / sum(wts) : d
return wts isa ProbabilityWeights ? d * sum(!iszero, wts) / sum(wts) : d
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end

weights(r::GlmResp) = r.wts
Expand Down Expand Up @@ -342,7 +342,7 @@ function loglikelihood(m::AbstractGLM)
y = r.y
mu = r.mu
wts = weights(r)
d = link(r)
d = distr(r)
ll = zero(eltype(mu))
N = length(y)
δ = deviance(r)
Expand Down Expand Up @@ -860,7 +860,8 @@ function checky(y, d::Binomial)
end

function nobs(r::GlmResp{V,D,L,W}) where {V,D,L,W<:AbstractWeights}
return oftype(sum(one(eltype(weights(r)))), length(r.y))
n = W<:ProbabilityWeights ? sum(!iszero, weights(r)) : length(r.y)
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return oftype(sum(one(eltype(weights(r)))), n)
end
nobs(r::GlmResp{V,D,L,W}) where {V,D,L,W<:FrequencyWeights} = sum(r.wts)

Expand All @@ -884,7 +885,7 @@ end
function momentmatrix(m::GeneralizedLinearModel)
X = modelmatrix(m; weighted=false)
r = varstruct(m)
if link(m) isa Union{Gamma,InverseGaussian}
if distr(m) isa Union{Gamma,InverseGaussian}
r .*= sum(working_weights(m)) / sum(abs2, r)
end
return Diagonal(r) * X
Expand Down
17 changes: 14 additions & 3 deletions src/linpred.jl
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Expand Up @@ -316,7 +316,7 @@ function vcov(x::LinPredModel)
s = nobs(x) / (nobs(x) - 1)
mm = momentmatrix(x)
A = invloglikhessian(x)
if link(x) isa Union{Gamma,InverseGaussian}
if distr(x) isa Union{Gamma,InverseGaussian}
r = varstruct(x)
A ./= sum(working_weights(x)) / sum(abs2, r)
end
Expand All @@ -326,7 +326,7 @@ function vcov(x::LinPredModel)
end
end

link(x::LinPredModel) = link(x.rr)
distr(x::LinPredModel) = distr(x.rr)

function _vcov(pp::LinPred, Z::AbstractMatrix, A::AbstractMatrix)
if linpred_rank(pp) < size(Z, 2)
Expand Down Expand Up @@ -434,8 +434,19 @@ end
For linear and generalized linear models, return the number of rows when
the model is unweighted or uses analytical or probability weights.
If the model uses frequency weights, return the sum of weights.
Rows with zero weights are not counted.
"""
nobs(obj::LinPredModel) = nobs(obj.rr)
function nobs(m::LinPredModel)
wts = weights(m)
n = if wts isa UnitWeights
length(wts)
elseif wts isa FrequencyWeights
sum(wts)
elseif wts isa Union{ProbabilityWeights,AnalyticWeights}
sum(!iszero, wts)
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end
return oftype(sum(one(eltype(wts))), n)
end

weights(m::LinPredModel) = weights(m.rr)
weights(pp::LinPred) = pp.wts
Expand Down
11 changes: 3 additions & 8 deletions src/lm.jl
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Expand Up @@ -67,23 +67,18 @@ function deviance(r::LmResp)
v += abs2(y[i] - mu[i]) * wts[i]
end
end
return wts isa ProbabilityWeights ? v ./ (sum(wts) / length(y)) : v
return wts isa ProbabilityWeights ? v ./ (sum(wts) / sum(!iszero, wts)) : v
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end

weights(r::LmResp) = r.wts
function isweighted(r::LmResp)
return weights(r) isa Union{AnalyticWeights,FrequencyWeights,ProbabilityWeights}
end

nobs(r::LmResp{<:Any,<:FrequencyWeights}) = sum(r.wts)
function nobs(r::LmResp{<:Any,<:AbstractWeights})
return oftype(sum(one(eltype(r.wts))), length(r.y))
end

working_weights(r::LmResp) = r.wts

function loglikelihood(r::LmResp{<:Any,<:Union{UnitWeights,FrequencyWeights}})
n = nobs(r)
n = sum(weights(r))
return -n / 2 * (log(2π * deviance(r) / n) + 1)
end

Expand All @@ -106,7 +101,7 @@ function residuals(r::LmResp; weighted::Bool=false)
end
end

link(rr::LmResp) = IdentityLink()
distr(rr::LmResp) = Normal()

"""
LinearModel
Expand Down
46 changes: 46 additions & 0 deletions test/runtests.jl
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Expand Up @@ -2659,3 +2659,49 @@ end
x -0.502451 0.675377 -0.74 0.4982 -2.3776 1.3727
─────────────────────────────────────────────────────────────────────────"""
end

@testset "nobs, deviance & stderror with zero weights" begin
X = [ones(10) 1:10]
y = [1, 4, 6, 2, 3, 5, 6, 7, 1, 6]
wts = [1, 0, 4, 0, 5, 2, 6, 4, 2, 6]

lmod = lm(X, y)
glmod = glm(X, y, Normal())
@test nobs(lmod) == nobs(glmod) == 10
@test dof_residual(lmod) == dof_residual(glmod) == 8
@test deviance(lmod) ≈ deviance(glmod) ≈ 39.29696969696969
@test coef(lmod) ≈ coef(glmod) ≈ [2.6666666666666665, 0.2606060606060606]
@test stderror(lmod) ≈ stderror(glmod) ≈ [1.51404201801774, 0.24400996532360475]

lmod = lm(X, y, wts=uweights(10))
glmod = glm(X, y, Normal(), wts=uweights(10))
@test nobs(lmod) == nobs(glmod) == 10
@test dof_residual(lmod) == dof_residual(glmod) == 8
@test deviance(lmod) ≈ deviance(glmod) ≈ 39.29696969696969
@test coef(lmod) ≈ coef(glmod) ≈ [2.6666666666666665, 0.2606060606060606]
@test stderror(lmod) ≈ stderror(glmod) ≈ [1.51404201801774, 0.24400996532360475]

lmod = lm(X, y, wts=fweights(wts))
glmod = glm(X, y, Normal(), wts=fweights(wts))
@test nobs(lmod) == nobs(glmod) == sum(wts)
@test dof_residual(lmod) == dof_residual(glmod) == sum(wts) - 2
@test deviance(lmod) ≈ deviance(glmod) ≈ 91.87804878048782
@test coef(lmod) ≈ coef(glmod) ≈ [3.6707317073170724, 0.20731707317073195]
@test stderror(lmod) ≈ stderror(glmod) ≈ [0.9538283539174621, 0.13286974786560674]

lmod = lm(X, y, wts=aweights(wts))
glmod = glm(X, y, Normal(), wts=aweights(wts))
@test nobs(lmod) == nobs(glmod) == sum(!iszero, wts)
@test dof_residual(lmod) == dof_residual(glmod) == sum(!iszero, wts) - 2
@test deviance(lmod) ≈ deviance(glmod) ≈ 91.87804878048782
@test coef(lmod) ≈ coef(glmod) ≈ [3.6707317073170724, 0.20731707317073195]
@test stderror(lmod) ≈ stderror(glmod) ≈ [2.060504744176091, 0.2870314608599428]

lmod = lm(X, y, wts=pweights(wts))
glmod = glm(X, y, Normal(), wts=pweights(wts))
@test nobs(lmod) == nobs(glmod) == sum(!iszero, wts)
@test dof_residual(lmod) == dof_residual(glmod) == sum(!iszero, wts) - 2
@test deviance(lmod) ≈ deviance(glmod) ≈ 24.500813008130084
@test coef(lmod) ≈ coef(glmod) ≈ [3.6707317073170724, 0.20731707317073195]
@test stderror(lmod) ≈ stderror(glmod) ≈ [1.7617126628715203, 0.23455696986842048]

@nalimilan nalimilan Jan 11, 2026

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@gragusa I get slightly different standard errors with svyglm. Is this expected? Generally in my tests I got exactly the same values up to a least four decimals.

> X = 1:10
> y = c(1, 4, 6, 2, 3, 5, 6, 7, 1, 6)
> wts = c(1, 0, 4, 0, 5, 2, 6, 4, 2, 6)
> svyd <- svydesign(~1, weights=wts, data=data.frame(X=X, y=y, wts=wts))

> summary(svyglm(y ~ X, svyd))

Call:
svyglm(formula = y ~ X, design = svyd)

Survey design:
svydesign(~1, weights = wts, data = data.frame(X = X, y = y, 
    wts = wts))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)   3.6707     1.7371   2.113    0.079 .
X             0.2073     0.2313   0.896    0.405  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 3.500116)

@nalimilan nalimilan Apr 26, 2026

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@gragusa I'd appreciate your input on this one too.

@gragusa gragusa Apr 27, 2026

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Sorry for the late reply - I don't get the notifications from this repo (although I am subscribed).

I think they match to 4 digits (the one used by R to print the coefficient):

## GLM is master/main
using GLM, DataFrames
X = 1:10
y = [1, 4, 6, 2, 3, 5, 6, 7, 1, 6]
wts = [1, 0, 4, 0, 5, 2, 6, 4, 2, 6]
df = DataFrame(y=y, X=X, wts=wts)
julia> lm1 = lm(@formula(y~X), df, weights=GLM.pweights(df.wts))
LinearModel

y ~ 1 + X

Coefficients:
───────────────────────────────────────────────────────────────────────
                Coef.  Std. Error     t  Pr(>|t|)  Lower 95%  Upper 95%
───────────────────────────────────────────────────────────────────────
(Intercept)  3.67073     1.73707   2.11    0.0675  -0.334964   7.67643
X            0.207317    0.231276  0.90    0.3962  -0.326007   0.740641
───────────────────────────────────────────────────────────────────────

The variance returned by R on this example is

R> ss$cov.scaled
            (Intercept)           X
(Intercept)   3.0174195 -0.37802382
X            -0.3780238  0.05348872

which matches Julia's GMM:

julia> @show vcov(ll);
vcov(lm1) = [3.0174195202295895 -0.378023819721369; -0.3780238197213689 0.05348872288847028]

@gragusa gragusa Apr 27, 2026

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Actually, the problem is that the deviance reported by Julia and R differs.

- `GLM`: deviance = 30.626, dispersion = 3.828
- `svyglm`: deviance = 24.501, dispersion = 3.500

I'm unable to view the code for syvglm for the license. However, the ratio between the two is exactly n_all/n_nz = 10/8. The difference seems to be that syvglm normalizes the weights by the mean over non-zero observations, while GLM normalizes by the mean over all observations.

Let me try to fix this.

@nalimilan nalimilan Apr 27, 2026 •
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Thanks. The "problem" is that this PR changes the result. I get this:

LinearModel

y ~ 1 + X

Coefficients:
───────────────────────────────────────────────────────────────────────
                Coef.  Std. Error     t  Pr(>|t|)  Lower 95%  Upper 95%
───────────────────────────────────────────────────────────────────────
(Intercept)  3.67073     1.76171   2.08    0.0823  -0.640024   7.98149
X            0.207317    0.234557  0.88    0.4108  -0.366623   0.781257
───────────────────────────────────────────────────────────────────────

julia> vcov(lm1)
2×2 Matrix{Float64}:
  3.10363   -0.388825
 -0.388825   0.055017

julia> deviance(lm1)
24.50081300813008

This PR seems more correct to me as vcov uses the correct number of observations (skipping zero weights). But R's survey doesn't seem to do the same?

@gragusa gragusa Apr 27, 2026

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I'll try .... 🤞🏽

@gragusa gragusa Apr 27, 2026

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PR open: #648

@nalimilan nalimilan Apr 27, 2026 •
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Hmm so this works but are we sure it's right? :-) Do you think svyglm does not exclude observations with zero weights on purpose?

EDIT: and svyglm prints a warning when fitting a model with zero-weight observations, so it doesn't seem results are supposed to be trusted in that case.

1: In summary.glm(g) :
  observations with zero weight not used for calculating dispersion

@gragusa gragusa Apr 27, 2026 •
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Again, difficult to say what syvglm does internally. This is GPL code, so I'm not able to review it. Having weights equal to zero is a pathological case (observations with zero weights should not exist). The fix now handles this case by giving the same SE and deviance/dispersion as one would obtain by running the same model, while omitting observations with zero weights, which I think is the right thing to do. Throwing a warning is something we should do, since 0 weights may indicate an issue on the model's side.

@nalimilan nalimilan Apr 27, 2026

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The fix now handles this case by giving the same SE and deviance/dispersion as one would obtain by running the same model, while omitting observations with zero weights, which I think is the right thing to do.

This is was my goal with this PR, but I don't think that's the case with #648 at the moment, right?
Current state of this PR:

julia> lm1 = lm(@formula(y~X), df, weights=GLM.pweights(df.wts))
[ Warning: pweights is defined in StatsBase and is not public in GLM
LinearModel

y ~ 1 + X

Coefficients:
───────────────────────────────────────────────────────────────────────
                Coef.  Std. Error     t  Pr(>|t|)  Lower 95%  Upper 95%
───────────────────────────────────────────────────────────────────────
(Intercept)  3.67073     1.76171   2.08    0.0823  -0.640024   7.98149
X            0.207317    0.234557  0.88    0.4108  -0.366623   0.781257
───────────────────────────────────────────────────────────────────────

julia> df2 = df[df.wts .> 0,:];

julia> lm1 = lm(@formula(y~X), df2, weights=GLM.pweights(df2.wts))
LinearModel

y ~ 1 + X

Coefficients:
───────────────────────────────────────────────────────────────────────
                Coef.  Std. Error     t  Pr(>|t|)  Lower 95%  Upper 95%
───────────────────────────────────────────────────────────────────────
(Intercept)  3.67073     1.76171   2.08    0.0823  -0.640024   7.98149
X            0.207317    0.234557  0.88    0.4108  -0.366623   0.781257
───────────────────────────────────────────────────────────────────────

Current state of #648:

julia> lm1 = lm(@formula(y~X), df, weights=GLM.pweights(df.wts))
[ Warning: pweights is defined in StatsBase and is not public in GLM
LinearModel

y ~ 1 + X

Coefficients:
───────────────────────────────────────────────────────────────────────
                Coef.  Std. Error     t  Pr(>|t|)  Lower 95%  Upper 95%
───────────────────────────────────────────────────────────────────────
(Intercept)  3.67073     1.73707   2.11    0.0790  -0.579731    7.92119
X            0.207317    0.231276  0.90    0.4046  -0.358596    0.77323
───────────────────────────────────────────────────────────────────────

julia> df2 = df[df.wts .> 0,:];

julia> lm1 = lm(@formula(y~X), df2, weights=GLM.pweights(df2.wts))
LinearModel

y ~ 1 + X

Coefficients:
───────────────────────────────────────────────────────────────────────
                Coef.  Std. Error     t  Pr(>|t|)  Lower 95%  Upper 95%
───────────────────────────────────────────────────────────────────────
(Intercept)  3.67073     1.76171   2.08    0.0823  -0.640024   7.98149
X            0.207317    0.234557  0.88    0.4108  -0.366623   0.781257
───────────────────────────────────────────────────────────────────────

If that's useful I can look at the svyglm code for you and/or write to Thomas Lumley (I think he's responsive).

Zero weights should be supported without a warning IMO as they can arise sometimes. For example I have a survey where we have two different definitions of who is in scope, and it's convenient to have two different weighting columns, with zero weights for those who are out of scope in a given definition. We simply need to skip observations with zero weights everywhere and everything should be fine.

end
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