Decomposition of the mean absolute error (MAE) into systematic and unsystematic components

Scott M. Robeson; Cort J. Willmott

doi:10.1371/journal.pone.0279774

Peer Review History

Original SubmissionJune 20, 2022
26 Oct 2022 Decision Letter - Fabiana Zama, Editor PONE-D-22-17609 Decomposition of the mean absolute error (MAE) into systematic and unsystematic components PLOS ONE Dear Dr. Robeson, 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 Dec 10 2022 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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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 If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. Additional Editor Comments: Dear Prof. Scott M. Robeson, Based on the reviewers' comments, the decision is to accept your manuscript after minor revisions. Please follow the points raised by each reviewer. Kind Regards Fabiana Zama [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. 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: No 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: Yes 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: My areas of expertise focus on metrics to measure error and change, which is the exact topic of the submitted manuscript. I have thought about the concepts of the submitted manuscript for decades. Therefore, I report with confidence that the submitted manuscript is a brilliant major breakthrough. I inserted several comments in the PDF as I read. I ask the authors to consider those comments to increase clarity of the manuscript. The submitted manuscript is short, which is a strength. The manuscript states only what is necessary, which any scientific manuscript should do. The manuscript proposes a method to fix the flawed popular paradigm of squared deviations. The authors’ new method makes much better sense than the popular paradigm. Previous methods that have used Mean Absolute Error (Pontius Jr 2022) do not separate the Mean Absolute Error into as many helpful components as the proposed manuscript does. The manuscript illustrates how the new method has helpful practical implications. Below are ideas to make the manuscript even stronger than it already is. My browser could not activate the link where the authors have posted the data at https://www.ncdc.noaa.gov/dataaccess/paleoclimatology%E2%80%90data The example is helpful. It would be more helpful to have a column at the right in Table 1 to show the sum. It would be nicer to have the numbers be simpler such as all whole numbers for Pi and Oi, and to have n be a number that makes easier division than by 7. In figure 1d, it is not immediately clear to me why MAEb = 0.424 rather than \|-0.714\|, which is the absolute bias in figure 1c. The reader would understand better if the revised manuscript were to have a sentence to explain why \|Bias\| does not equal MAEb. Figures 1 and 2 should be consistent in the number of digits in the results. Report the % to the nearest whole number. The other numbers should have exactly two decimal places. I thank the authors for using sequential line numbers. In line 108, I think it would be clearer to eliminate “are conservative and must” In line 137, the meaning of the quotes around average is unclear. I find the language is imprecise when I see quotes like that. In line 155, replace “powerful” with “popular”. In lines 139-140, the implication is profound. Congratulations on the creation of a helpful method. Readers will be eager to have computer code, say in R, which would inspire more rapid adoption by researchers. I hope the authors find this review helpful, as I intend it to be. The authors have achieved a major accomplishment. LITERATURE Pontius Jr, Robert Gilmore. 2022. Metrics That Make a Difference: How to Analyze Change and Error. Advances in Geographic Information Science. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-70765-1. Reviewer #2: In the present paper, the authors propose the decomposition of the Mean Absolute Error into three components which represent the model bias, proportionality, and unsystematic components. The error components are clearly explained through a synthetic example and a data sample. Therefore, the present study improves the standard measures for evaluating model errors significantly. The analysis of the three components makes it possible to understand their different contribution. Overall, the paper is well written and well organized, hence the decision is to accept after minor revisions. Points of attention: • The data link is not working: https://www.ncdc.noaa.gov/dataaccess/ paleoclimatology‐data • Page 2 line 16. remove parenthesis • Page 2 line 41. remove parenthesis • Page 4 equation (14-16). Should be divided by n. • Page 5 equation (17) holds due to the definitions in (14)-(16). ****** 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: Yes: Robert Gilmore Pontius Jr 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/. 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Revision 1
9 Dec 2022 Author Response Decomposition of the mean absolute error (MAE) into systematic and unsystematic components Response to Reviews Reviewer #1 My areas of expertise focus on metrics to measure error and change, which is the exact topic of the submitted manuscript. I have thought about the concepts of the submitted manuscript for decades. Therefore, I report with confidence that the submitted manuscript is a brilliant major breakthrough. I inserted several comments in the PDF as I read. I ask the authors to consider those comments to increase clarity of the manuscript. The submitted manuscript is short, which is a strength. The manuscript states only what is necessary, which any scientific manuscript should do. The manuscript proposes a method to fix the flawed popular paradigm of squared deviations. The authors’ new method makes much better sense than the popular paradigm. Previous methods that have used Mean Absolute Error (Pontius Jr 2022) do not separate the Mean Absolute Error into as many helpful components as the proposed manuscript does. The manuscript illustrates how the new method has helpful practical implications. Below are ideas to make the manuscript even stronger than it already is. Thank you so much for your comments and the very useful feedback throughout your review. My browser could not activate the link where the authors have posted the data at https://www.ncdc.noaa.gov/dataaccess/paleoclimatology%E2%80%90data Our apologies. We have corrected the link, which now goes directly to the NOAA site for the particular data used. It also is given below: https://www.ncei.noaa.gov/access/paleo-search/study/28810 The example is helpful. It would be more helpful to have a column at the right in Table 1 to show the sum. It would be nicer to have the numbers be simpler such as all whole numbers for Pi and Oi, and to have n be a number that makes easier division than by 7. We modified our example to use a set of 6 numbers. We also added the summation column at the far right. The figure has been updated accordingly. In figure 1d, it is not immediately clear to me why MAEb = 0.424 rather than \|-0.714\|, which is the absolute bias in figure 1c. The reader would understand better if the revised manuscript were to have a sentence to explain why \|Bias\| does not equal MAEb. We have added the following explanation at the end of the section that discusses Fig. 1, as well as the additional recommendation to continue examining MBE: The constraints within the weighted decomposition of MAE diminish MAEb relative to the magnitude of MBE. MBE, therefore, remains a useful metric to be reported when analyzing model error. Figures 1 and 2 should be consistent in the number of digits in the results. Report the % to the nearest whole number. The other numbers should have exactly two decimal places. We made these corrections. I thank the authors for using sequential line numbers. In line 108, I think it would be clearer to eliminate “are conservative and must” In line 137, the meaning of the quotes around average is unclear. I find the language is imprecise when I see quotes like that. In line 155, replace “powerful” with “popular”. We made minor edits to address all of these comments. In lines 139-140, the implication is profound. Congratulations on the creation of a helpful method. Thank you! Readers will be eager to have computer code, say in R, which would inspire more rapid adoption by researchers. We now provide R and Matlab functions for these calculations in the Supporting Information. I hope the authors find this review helpful, as I intend it to be. The authors have achieved a major accomplishment. We found this review extremely helpful and appreciate your positive assessment. LITERATURE Pontius Jr, Robert Gilmore. 2022. Metrics That Make a Difference: How to Analyze Change and Error. Advances in Geographic Information Science. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-70765-1. This reference was added and we also made the suggested editorial changes that were in the annotated PDF. Reviewer #2 In the present paper, the authors propose the decomposition of the Mean Absolute Error into three components which represent the model bias, proportionality, and unsystematic components. The error components are clearly explained through a synthetic example and a data sample. Therefore, the present study improves the standard measures for evaluating model errors significantly. The analysis of the three components makes it possible to understand their different contribution. Overall, the paper is well written and well organized, hence the decision is to accept after minor revisions. Thank you very much for your comments and for the overall positive assessment of our work. Points of attention: • The data link is not working: https://www.ncdc.noaa.gov/dataaccess/ paleoclimatology‐data Our apologies. We have added the corrected link, which now goes directly to the NOAA site for the particular data used. It also is given below: https://www.ncei.noaa.gov/access/paleo-search/study/28810 • Page 2 line 16. remove parenthesis • Page 2 line 41. remove parenthesis We made these two corrections. • Page 4 equation (14-16). Should be divided by n. Thank you for catching this error. It has been corrected. • Page 5 equation (17) holds due to the definitions in (14)-(16). We changed the text here slightly to clarify this point. Attachments Attachment Submitted filename: Decomposition_MAE_Response_to_Review.pdf https://doi.org/10.1371/journal.pone.0279774.r002
14 Dec 2022 Decision Letter - Fabiana Zama, Editor Decomposition of the mean absolute error (MAE) into systematic and unsystematic components PONE-D-22-17609R1 Dear Dr. Robeson, 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, Fabiana Zama Academic Editor PLOS ONE Additional Editor Comments (optional): Reviewers' comments: https://doi.org/10.1371/journal.pone.0279774.r003
Formally Accepted
21 Dec 2022 Acceptance Letter - Fabiana Zama, Editor PONE-D-22-17609R1 Decomposition of the mean absolute error (MAE) into systematic and unsystematic components Dear Dr. Robeson: 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 Professor Fabiana Zama Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0279774.r004

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