Robust small area estimation for unit level model with density power divergence

Xijuan Niu; Zhiqiang Pang; Zhaoxu Wang

doi:10.1371/journal.pone.0288639

Peer Review History

Original SubmissionOctober 27, 2022
2 Dec 2022 Decision Letter - Angelo Moretti, Editor PONE-D-22-29623Robust Small Area Estimation for Unit Level Model with Density Power DivergencePLOS ONE Dear Dr. Niu, 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. As you can see, the reviewers, who are experts in the field of small are estimation, have major concerns about your article, and I agree with all their comments. Please make sure that the article is proof read before resubmitting it in order to improve the English. The simulation study needs to be expended substantially following reviewer 1 in particular. I also believe that the application needs to be improved given the scope of the journal; the data is too old. Please make sure the the software is released. Please submit your revised manuscript by Jan 16 2023 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. Please include the following items when submitting your revised manuscript: A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'. If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter. If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols. We look forward to receiving your revised manuscript. Kind regards, Angelo Moretti, Ph.D. Academic Editor PLOS ONE Journal Requirements: When submitting your revision, we need you to address these additional requirements. 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf 2. We note that the grant information you provided in the ‘Funding Information’ and ‘Financial Disclosure’ sections do not match. When you resubmit, please ensure that you provide the correct grant numbers for the awards you received for your study in the ‘Funding Information’ section. 3. Thank you for stating the following in your Competing Interests section: "No" Please complete your Competing Interests on the online submission form to state any Competing Interests. If you have no competing interests, please state "The authors have declared that no competing interests exist.", as detailed online in our guide for authors at http://journals.plos.org/plosone/s/submit-now This information should be included in your cover letter; we will change the online submission form on your behalf. 4. In your Data Availability statement, you have not specified where the minimal data set underlying the results described in your manuscript can be found. PLOS defines a study's minimal data set as the underlying data used to reach the conclusions drawn in the manuscript and any additional data required to replicate the reported study findings in their entirety. All PLOS journals require that the minimal data set be made fully available. For more information about our data policy, please see http://journals.plos.org/plosone/s/data-availability. ""Upon re-submitting your revised manuscript, please upload your study’s minimal underlying data set as either Supporting Information files or to a stable, public repository and include the relevant URLs, DOIs, or accession numbers within your revised cover letter. For a list of acceptable repositories, please see http://journals.plos.org/plosone/s/data-availability#loc-recommended-repositories. Any potentially identifying patient information must be fully anonymized. Important: If there are ethical or legal restrictions to sharing your data publicly, please explain these restrictions in detail. Please see our guidelines for more information on what we consider unacceptable restrictions to publicly sharing data: http://journals.plos.org/plosone/s/data-availability#loc-unacceptable-data-access-restrictions. Note that it is not acceptable for the authors to be the sole named individuals responsible for ensuring data access. We will update your Data Availability statement to reflect the information you provide in your cover letter. 5. Please upload a copy of Supporting Information Figure which you refer to in your text. [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: Partly Reviewer #2: Yes ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: No Reviewer #2: Yes ****** 3. 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 Reviewer #2: Yes ****** 4. 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: No Reviewer #2: Yes ****** 5. 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 discussed a new methodology for dealing with outliers in the Small Area Estimation framework. The aim of the paper is attractive; however, there are many sentences with grammatical and spelling mistakes - which can all be corrected with a careful editing review of the manuscript. Moreover, there are also several aspects throughout the manuscript that are not so clear. In addition to the poor attention to the editing style (font size reduction from page 6), these aspects make the manuscript a little bit hard to read. Moreover, I think that a more concrete and recent application is necessary. In my opinion, the authors should also revise the simulation section. Comments are in the attached file. Reviewer #2: The authors proposed a robust small area estimation technique with unit-level models and density power divergence (DPD). The authors employs an objective function based on DPD applied to the marginal distribution of the observed values y_i and obtained asymptotic properties of the robust estimator. Furthermore, the authors derived a mean squared error estimator of the empirical best predictor. I think the paper is interesting and worth publishing. I have the following comments. 1. Estimation of random effects: While the model parameters are robustly estimated via DPD, the random effect prediction is derived in a standard way. As considered in Sugasawa (2020), is it possible to derive random effect estimator via Tweedie's formula? 2. Selection of the tuning parameter: although the authors adopted the selection method by Basak et al. (2021), using asymptotic mean squared errors. However, Sugasawa and Yonekura (2021) recently proposed a selection method based on the Hyvarinen score. This method is at least mentioned in the main text. 3. Simulation study: Under no contamination, the optimal value of gamma is ideally 0. However, the result indicates that the optimal value is considerably away from 0. Is there any reason or explanation for that? 4. Simulation study (line 323): The authors say ``According to the simulated data in the table 1, when tuning 323 parameter gamma = 0.026,... ", but I could not find the corresponding result in Table 1. 5. Table 3: It seems to show the results of bias and MSE of small area means according to the main text, but the caption indicates different results. 6. Real data: What is the optimal gamma here? Is there any reason for using only gamma=0.01 and 0.05 without selecting the optimal one? 7. I think the following two papers are closely related to the work, so it is worth mentioning in the main text (for example in Section 1). - Kurisu et al. (2021) employed the gamma-divergence (similar to density power divergence) for the Fay-Herriot model and discussed empirical Bayes confidence intervals rather than MSE. - Tang et al. (2018) proposed using global-local shrinkage priors for modeling random effects that allow potential outliers in the areal effect. Reference - Kurisu, D., T. Ishihara, and S. Sugasawa (2021). Adaptively robust small area estimation: Balancing robustness and efficiency of empirical Bayes confidence intervals. arXiv preprint arXiv:2108.11551. - Sugasawa, S. and S. Yonekura (2021). On selection criteria for the tuning parameter in robust divergence. Entropy 23(9), 1147. - Tang, X., M. Ghosh, N. S. Ha, and J. Sedransk (2018). Modeling random effects using global–local shrinkage priors in small area estimation. Journal of the American Statistical Association 113(524), 1476–1489. ****** 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. 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 Reviewer #2: No ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. Attachments Attachment Submitted filename: Review Manuscript Number PONE-D-22-29623.pdf https://doi.org/10.1371/journal.pone.0288639.r001
Revision 1
20 Apr 2023 Author Response Response to Reviewers I am very glad to receive comments from reviewers, who have provided many meaningful suggestions for further improvement of this paper. In view of the amendments of the articles, this article made the following changes. In view of the reviewer's main comments, this paper has been modified as follows: 1.For the first opinion, in the introduction part, the application background of DPD method is introduced in detail, and the advantages of this method compared with other methods are described, and some references are added. The changes in this section are between lines 90 and 108. 2.In section 5, the EBLUP can be obtained by substituting the estimated parameter values into the EBP, which is explained in section 5. 3.As for the third comments, the simulation part of the paper has been modified in detail. First, the Bias and MSE in the table become relative Bias and relative MSE. The parameter selection program is optimized and the values in the table are modified. This part is mainly in the numerical simulation part of the paper. It can be seen from the simulation results that the optimal adjustment parameters selected after modification can achieve the optimal estimation effect. 4.In the application of actual data, although the data used in this paper is relatively old, it can also illustrate the effect of the method proposed in this paper. For minor modification suggestions, the main contents are as follows: �In line 14, the difference between direct and model-based estimates is explained. �Modify "area random effect and model random effect" to" individual and area-specific random effect". �In line 156, subheading 3.1 has been added �In the definition of DPD, the meaning of parameter θ is given. �Adjust the content of Section 5.3 to Section 3.2. �Formula 16 and 17 in line 280 are numbered �The section 5 explains the relationship between EBP and EBLUP. �In the simulation part, the expression formulas of relative bias deviation and relative MSE are given, and the performance results of relative MSE are shown in the simulation table. �Huberm methods have been changed to RML methods in the simulation part of the images and tables. �In the discussion section, the applicability of other parameter selection algorithms and other robust estimation methods is pointed out. �Some references have been added. �Some inaccuracies in grammar and expression have been corrected. Attachments Attachment Submitted filename: Response to Reviewers.docx https://doi.org/10.1371/journal.pone.0288639.r002
16 May 2023 Decision Letter - Angelo Moretti, Editor PONE-D-22-29623R1Robust Small Area Estimation for Unit Level Model with Density Power DivergencePLOS ONE Dear Dr. Niu, 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. I am happy to see that the article has been improved considerably. However, there is still some room for improvements. Could you please go over Reviewer 1's report carefully? I agree with the reviewer decision. In particular, they asked for some comparisons which have not been carried out. I would like to see, at least, a careful discussion around that. Why did you decide not to provide such comparisons? Is there any literature available that you can include? Also, the issue related to the methods in Sinha and Rao needs to be addressed properly, given the importance of such paper in the literature. Please submit your revised manuscript by Jun 30 2023 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. Please include the following items when submitting your revised manuscript: A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'. If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter. If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols. We look forward to receiving your revised manuscript. Kind regards, Angelo Moretti, Ph.D. Academic Editor PLOS ONE Journal Requirements: Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation. Reviewer #1: (No Response) Reviewer #2: All comments have been addressed ******** 2. 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: Partly Reviewer #2: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: Yes ****** 4. 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 Reviewer #2: 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 Reviewer #2: 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 improved the manuscript. However, two of my questions remained unanswered: - In particular, I have asked for a comparison in the simulation study with other methods, such as the MQ approach and the bias corrected version of the REBLUP, why the authors decided to not provide any comparison? - the authors do not provide any code for running simulations; so my concern on why the results for variance of the random effects in two scenarios are different from the paper of Sinha and Rao remain unsolved, - in the simulation section, are the measure in the Tables expressed in percentage? beacuse in the formula seems that they are not in percentage, but the values in the tables seems very high. Please clarify this point. Reviewer #2: (No Response) ****** 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 Reviewer #2: No ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. https://doi.org/10.1371/journal.pone.0288639.r003
Revision 2
15 Jun 2023 Author Response 1.We have added a section on the MQ method and the REBLUP method for bias correction in the simulation experiments. 2.We have re-simulated the larger values in the tables using the same principle as Rao's method. Attachments Attachment Submitted filename: Response to Reviewers.docx https://doi.org/10.1371/journal.pone.0288639.r004
3 Jul 2023 Decision Letter - Angelo Moretti, Editor Robust Small Area Estimation for Unit Level Model with Density Power Divergence PONE-D-22-29623R2 Dear Dr. Niu, 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 for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org. If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. Kind regards, Angelo Moretti, Ph.D. Academic Editor PLOS ONE Additional Editor Comments (optional): Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation. Reviewer #1: All comments have been addressed ******** 2. 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 ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes ****** 4. 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: I think that the authors have adequately addressed the comments in the revised version of the manuscript. Therefore, I have no further comments. ****** 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.0288639.r005
Formally Accepted
7 Jul 2023 Acceptance Letter - Angelo Moretti, Editor PONE-D-22-29623R2 Robust Small Area Estimation for Unit Level Model with Density Power Divergence Dear Dr. Niu: I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org. If we can help with anything else, please email us at plosone@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Dr. Angelo Moretti Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0288639.r006

Open letter on the publication of peer review reports

PLOS recognizes the benefits of transparency in the peer review process. Therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. Reviewers remain anonymous, unless they choose to reveal their names.

We encourage other journals to join us in this initiative. We hope that our action inspires the community, including researchers, research funders, and research institutions, to recognize the benefits of published peer review reports for all parts of the research system.

Learn more at ASAPbio .