KGR-SKATER: Spatially clustered kernel graph regression for counting processes

Jeffrey Wu; Gareth W. Peters; Alex Franks

doi:10.1371/journal.pone.0348787

Peer Review History

Original SubmissionOctober 8, 2025
11 Feb 2026 Decision Letter - Laleh Tafakori, Editor -->PONE-D-25-54628-->-->KGR-SKATER: Spatially clustered kernel graph regression for counting processes-->-->PLOS One Dear Dr. Wu, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please submit your revised manuscript by Mar 28 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. 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If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise. [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions--> -->Comments to the Author 1. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. --> Reviewer #1: Yes Reviewer #2: Yes ******** -->2. Has the statistical analysis been performed appropriately and rigorously? --> Reviewer #1: Yes Reviewer #2: Yes ****** -->3. 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A graph is estimated to represent spatial dependence, and a locally periodic kernel is then estimated to represent temporal dependence. These two components are combined via a Kronecker product, producing a separable spatiotemporal covariance matrix that can account for multiple relevant variables and their dependencies at different time scales. In my opinion, the proposed model is interesting and certainly worthy of publication, and I think PLOS One is a good outlet for it. An illustrative example is provided in the form of monthly time series of respiratory-related deaths across California. Social deprivation indices are used to learn a graph structure, and surrogate variables constructed from exposure adjusted measures of air quality are used to learn time series regression relationships encoded by a kernel. This new model seems to do a decent job fitting the data. An additional synthetic case study is also presented to demonstrate how the proposed procedure makes better forecasts than the reference model in settings where time series exhibit less stationary amplitudes and periods. I am delighted to report that I found this manuscript a pleasure to read. The analysis is interesting and informative, and the text is well-written. The figures are thoughtfully designed and effectively illustrate the key points of the model. The main recommendation I have for the authors is to publish the model via GitHub or similar public website so others can easily try it out for themselves. Congratulations on an interesting and informative contribution to the literature. ****** -->6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. 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Attachments Attachment Submitted filename: Review of KGR-SKATER.pdf https://doi.org/10.1371/journal.pone.0348787.r001
Revision 1
5 Apr 2026 Author Response In the following, we outline the individual reviewer comments and questions, and the steps we took to address the comments or suggestions when required: Figures/Tables: - All of the maps included in figures for the main and supplemental documents were generated by the authors using publicly available geographic boundary data from the U.S. Census Bureau (https://catalog.data.gov/dataset/tiger-line-shapefile-2016-state-california-current-place-state-based). These datasets are produced by the U.S. federal government and are in the public domain (17 U.S.C. §105), and therefore do not require permission for reuse or publication. The figures were created by the authors in R using the maps, sf, and ggplot2 packages based on these public-domain shapefiles. Appropriate attribution to the U.S. Census Bureau TIGER/Line dataset has been added to the figure captions in the revised manuscript. - Table 1 and Figure 10 have been remade to be larger so they are more legible. Figure 1 has been reformatted and enhanced to be more detailed and legible. Reviewer #1 comments: - We agree with the reviewer that the novelty of the KGR-SKATER framework should be more clearly articulated. We have revised the Introduction to explicitly highlight the methodological contributions of the proposed framework. In particular, we now emphasize three key innovations: 1) The integration of spatial clustering with data-driven graph estimation. 2) The construction of a graph-filtered Gaussian process prior via the Kronecker product of spatial and temporal components. 3) Efficient estimation of the resulting model using INLA instead of MCMC. These clarifications have been added to the Introduction. - Figure 1 has been revised and reformatted to better illustrate the modeling workflow and the relationships between data inputs, clustering, graph estimation, kernel construction, and the final spatiotemporal model. The figure caption has also been expanded to explain each stage of the procedure. - We have added a new subsection in the Discussion titled “Computational Complexity and Scalability”, which provides an overview of the computational cost of each stage of the framework (clustering, graph estimation, kernel construction, and INLA inference) and discusses how the dimensionality reduction achieved through clustering improves scalability. - We have expanded the Introduction section to include references to additional kernel-based spatiotemporal models, including stochastic local interaction models proposed by Hristopulos (2015) and Hristopulos & Agou (2020). The revised text explains how these approaches differ from the proposed framework. - We have added a discussion of alternative kernel functions, including the Matérn family and recently proposed non-separable spatiotemporal kernels. We agree that exploring these kernels would be an interesting direction for future research. - A new subsection titled “Practical Implementation Considerations” has been added (see Section 6.1). This section outlines how practitioners may select clustering parameters, kernel structures, and hyperparameters when applying the framework. - We have revised and expanded the Discussion section to more clearly articulate the key modeling design choices underpinning the KGR-SKATER framework and their implications in applied settings. In particular, we clarify that the use of a separable spatiotemporal covariance structure is a deliberate structural decomposition that enables the model to disentangle and interpret distinct sources of spatial and temporal variation, rather than a restrictive assumption. We also emphasize that the specification of components such as the number of SKATER clusters, the graph learning procedure, the spectral filtering mechanism, and the temporal kernel design are not merely tuning parameters, but represent interpretable modeling choices that can be guided by domain knowledge to reflect application-specific dependence structures. Furthermore, we have expanded the discussion on how the resulting structured dependence representation improves uncertainty quantification, which in turn facilitates more reliable forecasting and supports actionable decision-making in applied contexts such as public health and policy planning. Finally, we comment on computational considerations in terms of scalability, framing them within the broader context of model resolution and structural complexity, which can be adjusted in a principled manner depending on the application. - We have clarified that spatial distances are computed using great-circle distances derived from geographic coordinates. - The notation has been clarified in Section 2.1. We now explicitly state that $x$ and $x'$ represent vectors of surrogate covariates rather than spatial locations, and that these variables are standardized prior to computing Euclidean distances. - We have added a paragraph discussing the potential effects of EM-based imputation of censored mortality counts and the extent to which this procedure may introduce additional uncertainty. - We have added a new subsection in the Discussion titled “Software Accessibility”, which explains that equivalent implementations are available in other programming environments (e.g., Python and MATLAB) and that the methodology itself is not restricted to R. - We have also: improved figure resolution, replaced map figures with publicly available data sources, reformatted Table 1, added direct links to the data sources, and provided a Github repository containing the code used in the analysis We believe that these revisions have substantially improved the clarity and accessibility of the manuscript, and we thank the reviewer again for their helpful suggestions. Attachments Attachment Submitted filename: Response_to_Reviewers.pdf https://doi.org/10.1371/journal.pone.0348787.r002
21 Apr 2026 Decision Letter - Laleh Tafakori, Editor KGR-SKATER: Spatially clustered kernel graph regression for counting processes PONE-D-25-54628R1 Dear Dr. Wu, We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. 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Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.--> Reviewer #1: Yes ****** -->5. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.--> Reviewer #1: Yes ****** -->6. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)--> Reviewer #1: The authors have addressed all of my comments in the revised version of the manuscript. The manuscript is well-written and organized. New sections and paragraphs have been added which help to understand the methodology and its potential applications/ The novelty of the research is clearly expressed. The reported results have not (to my knowledge) been presented anywhere else. The analysis of the data and the derived statistical description are state-of-the-art. The conclusions clearly state the main ingredients of the methodology, summarize the results, and discuss the scope of applications. The R code used to implement the application study is provided in a GitHub repository and the manuscript also discussed tools for implementation of the method in Python. Bith data and code are available at a DRYAD repository. ****** -->7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.--> Reviewer #1: No ******** https://doi.org/10.1371/journal.pone.0348787.r003
Formally Accepted
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