arxiv: 2604.20743 · v1 · submitted 2026-04-22 · 📊 stat.ME · stat.CO

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ProfileGLMM: a R Package Extending Bayesian Profile Regression using Generalised Linear Mixed Models

Matteo Amestoy , Mark A. van de Wiel , Wessel N. van Wieringen

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Pith reviewed 2026-05-09 23:28 UTC · model grok-4.3

classification 📊 stat.ME stat.CO

keywords ProfileGLMMBayesian profile regressiongeneralized linear mixed modelsR packageclusteringhierarchical datalongitudinal datarandom effects

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The pith

ProfileGLMM extends Bayesian profile regression to hierarchical data by using GLMMs as the outcome model.

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

The paper introduces ProfileGLMM, an R package that integrates generalized linear mixed models into Bayesian profile regression. This approach simultaneously clusters observations based on interdependent covariates and models the outcome, now with random effects to handle hierarchical and longitudinal structures. It further permits direct examination of interactions between the resulting latent clusters and other observed covariates. The extension broadens applicability to complex data common in epidemiology, social sciences, and clinical research while supporting continuous or binary outcomes and both categorical and continuous clustering covariates. The package relies on efficient Rcpp implementation with few required parameters.

Core claim

Integrating GLMMs as the outcome model allows Bayesian profile regression to analyze hierarchical and longitudinal data through random effects and to study interactions between latent clusters and observable covariates, while still clustering observations on the basis of a specified set of interdependent covariates.

What carries the argument

The GLMM outcome model in which derived cluster memberships are included as explanatory variables together with random effects for hierarchical structure.

Load-bearing premise

That replacing the original outcome model with a GLMM preserves the statistical validity and clustering properties of Bayesian profile regression without creating new biases or identifiability problems.

What would settle it

Simulate hierarchical data with known true clusters, fit both the original profile regression and ProfileGLMM, and check whether cluster recovery accuracy declines under the GLMM extension.

Figures

Figures reproduced from arXiv: 2604.20743 by Mark A. van de Wiel, Matteo Amestoy, Wessel N. van Wieringen.

**Figure 2.** Figure 2: Decomposition of the outcome based on the true parameters. Left panel isolates the [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Figure 3: Graphical representation illustrating variable dependencies within the ProfileGLMM [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

**Figure 4.** Figure 4: Profile LMM representative clustering centroids and variance estimates. Points represent [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

**Figure 5.** Figure 5: Left panel isolates the fixed effect contribution with blue being the true contribution red [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

**Figure 6.** Figure 6: Blue is the underlying true signal, red is the ProfileGLMM fit [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗

**Figure 7.** Figure 7: Trace of the DP concentration parameter after a burn-in of 200 iterations. [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗

read the original abstract

ProfileGLMM is an R package integrating Generalised Linear Mixed Models (GLMMs) as the outcome model for Bayesian profile regression. This statistical framework simultaneously i) explains the variation in the outcome and ii) clusters the observations based on a specified set of interdependent clustering covariates. The derived cluster memberships are then incorporated, alongside others, as explanatory variables in the regression to model the outcome. This framework efficiently handles complex, highly correlated covariate structures whose direct inclusion in a standard regression model would be statistically sub-optimal. ProfileGLMM significantly extends Bayesian profile regression's scope by resolving two key constraints of previous implementations: 1) it allows the analysis of hierarchical and longitudinal data structures through the inclusion of random effects, and 2) it enables the study of interactions between latent clusters and other observable covariates. ProfileGLMM accommodates various data types, supporting both continuous or binary outcomes and both categorical and continuous clustering covariates. Built on fast Rcpp code with minimal mandatory parameters, ProfileGLMM offers a flexible analytical tool. It significantly enhances the utility of profile regression for researchers in fields such as epidemiology, social sciences, and clinical studies dealing with complex data.

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.

Desk Editor's Note private letter to a colleague

This is a software paper for an R package that adds GLMMs to Bayesian profile regression to handle random effects and cluster-covariate interactions, but the abstract gives no equations or checks to confirm the extension keeps the original clustering properties intact.

read the letter

This paper is announcing an R package, ProfileGLMM, that extends Bayesian profile regression by using generalised linear mixed models for the outcome. The main additions are random effects to deal with hierarchical and longitudinal structures, and the ability to include interactions between the latent clusters and other covariates. The package keeps the simultaneous clustering based on interdependent covariates and then uses those clusters in the GLMM outcome model. It works with continuous or binary outcomes and categorical or continuous clustering covariates. The implementation relies on Rcpp for speed and requires few mandatory parameters, making it straightforward for applied work. This is a practical extension of existing profile regression methods. It addresses two specific limitations in prior versions, which should make the approach more usable in fields like epidemiology where data often has clustering or repeated measures. The soft spot is that nothing in the abstract shows the math or any checks confirming that the GLMM integration does not introduce new biases or identifiability problems. When cluster indicators are used as predictors along with their interactions, it is not obvious that the clustering step stays independent from the outcome modeling. The stress-test note on this point holds up based on what is shown, since no likelihood factorization or constraints are provided. This work is aimed at researchers who already know profile regression and want a tool for more complex data. A reader needing an off-the-shelf solution for such analyses could benefit, but it is less useful for those seeking new theoretical insights. The thinking is clear in spotting the constraints and building a package around them. I would send this to peer review. A referee could check the implementation details, any validation, and whether the statistical properties are properly addressed.

Referee Report

2 major / 1 minor

Summary. The paper describes the ProfileGLMM R package for extending Bayesian profile regression with GLMMs as the outcome model. It simultaneously clusters observations using interdependent covariates and models the outcome incorporating cluster memberships, random effects for hierarchical/longitudinal structures, and interactions between clusters and covariates. The package handles continuous/binary outcomes and categorical/continuous clustering covariates using efficient Rcpp code with minimal parameters.

Significance. If the extension is implemented such that the clustering step remains valid and separate despite the added random effects and interactions, the package would meaningfully broaden the use of profile regression in applied fields dealing with complex data. The fast implementation and flexibility are positive features for practical use.

major comments (2)

[Abstract] The claim that ProfileGLMM resolves two key constraints of previous implementations lacks any equations or model details on how random effects and cluster-covariate interactions are incorporated into the GLMM while preserving the clustering properties, which is load-bearing for the central claim.
No results from simulations, real data applications, or comparisons to existing methods are provided to substantiate the assertions about handling various data types and avoiding statistical sub-optimality.

minor comments (1)

[Title] Grammatical error: 'a R Package' should be 'an R Package'.

Circularity Check

0 steps flagged

No significant circularity: software package description without derivations or predictions

full rationale

The document is a description of an R package (ProfileGLMM) that integrates GLMMs into Bayesian profile regression for handling hierarchical data and cluster-covariate interactions. It presents no equations, likelihoods, derivations, or statistical predictions. Claims concern software functionality, data type support, and scope extensions relative to prior profile regression implementations. No fitted parameters are renamed as predictions, no self-definitional steps exist, and no load-bearing self-citations or uniqueness theorems are invoked in the provided text. The central assertions are descriptive rather than derived, rendering the paper self-contained against external benchmarks with no reduction of outputs to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are introduced because the document is a package announcement rather than a theoretical derivation; the work relies on standard statistical assumptions from the GLMM and profile regression literature.

pith-pipeline@v0.9.0 · 5511 in / 1117 out tokens · 46288 ms · 2026-05-09T23:28:05.467544+00:00 · methodology

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