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arxiv: 1906.10125 · v1 · pith:KCAONCQBnew · submitted 2019-06-24 · 🧮 math.ST · stat.ME· stat.TH

A note on locally optimal designs for generalized linear models with restricted support

Osama Idais This is my paper

Pith reviewed 2026-05-25 17:06 UTC · model grok-4.3

classification 🧮 math.ST stat.MEstat.TH
keywords locally optimal designsgeneralized linear modelsrestricted supportPoisson modellogistic modelnonlinear modelsintercept
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The pith

At certain parameter values, locally optimal designs for generalized linear models without intercept can be derived from those with intercept under specific assumptions and vice versa.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that for generalized linear models with restricted support, particular assumptions on the regression parameters at certain values permit deriving a locally optimal design for the model without an intercept from the one for the model with an intercept, and the reverse. This relation is applied to Poisson and logistic models. The approach is also extended to nonlinear models. A reader would care because locally optimal designs for GLMs depend on unknown parameters, and this provides a way to relate designs across model specifications with and without intercept.

Core claim

At certain values of the parameters we propose particular assumptions which allow to derive a locally optimal design for a model without intercept from a locally optimal design for the corresponding model with intercept and vice versa. Applications to Poisson and logistic models and Extensions to nonlinear models are provided.

What carries the argument

The particular assumptions on the regression parameters enabling the derivation of locally optimal designs between models with and without intercept.

Load-bearing premise

The particular assumptions on the regression parameters are required to establish the mapping between the two classes of designs.

What would settle it

Observing a case where the parameter assumptions are satisfied but the derived design is not locally optimal for the model without intercept would falsify the claim.

read the original abstract

Optimal designs for generalized linear models require a prior knowledge of the regression parameters. At certain values of the parameters we propose particular assumptions which allow to derive a locally optimal design for a model without intercept from a locally optimal design for the corresponding model with intercept and vice versa. Applications to Poisson and logistic models and Extensions to nonlinear models are provided.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript claims that, at certain values of the regression parameters, particular (unspecified in the abstract) assumptions allow one to derive a locally optimal design for a GLM without intercept from the locally optimal design for the corresponding model with intercept, and vice versa. Applications to Poisson and logistic regression are given, together with extensions to nonlinear models.

Significance. If the claimed equivalence can be established under explicitly verifiable conditions on the parameters, the note would supply a modest but concrete shortcut for constructing locally optimal designs in GLMs whose support is restricted. The contribution is technical rather than conceptual; its value hinges on whether the required parameter restrictions are stated in a form that makes the proportionality of the two information matrices immediate and checkable.

major comments (1)
  1. [Introduction / main derivation (no numbered section or equation supplied in the abstract or visible structure)] The central claim rests on 'particular assumptions' on the regression parameters that are invoked to equate the two design problems. Because the GLM information matrix depends on the parameters through the weight function w(·), any such mapping requires an explicit algebraic relation between the linear predictors (or the weights) that renders the two matrices proportional. No such relation is stated in a form that can be verified, nor is a direct comparison of the information matrices supplied. This is load-bearing for the main result.
minor comments (1)
  1. [Abstract] The abstract asserts that 'derivations exist' but supplies neither the assumptions nor any equation; the reader cannot assess the claim from the abstract alone.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comment on the explicit verifiability of our parameter assumptions. We address this point below.

read point-by-point responses

  1. Referee: The central claim rests on 'particular assumptions' on the regression parameters that are invoked to equate the two design problems. Because the GLM information matrix depends on the parameters through the weight function w(·), any such mapping requires an explicit algebraic relation between the linear predictors (or the weights) that renders the two matrices proportional. No such relation is stated in a form that can be verified, nor is a direct comparison of the information matrices supplied. This is load-bearing for the main result.

    Authors: We agree that the assumptions must be stated in an explicit, verifiable algebraic form for the claim to be load-bearing. While the manuscript applies the assumptions to the Poisson and logistic cases, a general upfront statement of the relation between the linear predictors (or weights) that produces proportional information matrices is indeed missing. In the revision we will insert this relation at the beginning of the main derivation, together with a direct side-by-side comparison of the two information matrices under the stated parameter conditions. revision: yes

Circularity Check

0 steps flagged

No circularity: mapping between designs rests on external parameter assumptions, not self-definition or fitted inputs.

full rationale

The paper's central claim is that under particular (unspecified in abstract) assumptions on regression parameters, a locally optimal design for a GLM without intercept can be derived from the corresponding design with intercept (and vice versa). This is presented as following from algebraic relations in the information matrix induced by those parameter values, not as a redefinition or renaming of inputs. No self-citations are invoked as load-bearing uniqueness theorems, no fitted parameters are relabeled as predictions, and no ansatz is smuggled via prior work. The derivation is therefore self-contained; the assumptions function as external enabling conditions rather than tautological reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on unspecified particular assumptions about parameter values that enable the design mapping; no free parameters, invented entities, or additional axioms are mentioned in the abstract.

axioms (1)
  • domain assumption Particular assumptions on the values of the regression parameters allow derivation of the design mapping
    Invoked in the abstract as the condition under which the relation between designs holds.

pith-pipeline@v0.9.0 · 5566 in / 1226 out tokens · 23868 ms · 2026-05-25T17:06:35.934850+00:00 · methodology

discussion (0)

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Reference graph

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