Misspecification in Generalized Linear Mixed Models and Its Impact on the Statistical Wald Test
Round 1
Reviewer 1 Report
This paper has a certain degree of innovation and value, but before publication, the author needs to explain or revise the following problems:
1. The main contribution must be specified.
2. There are some tense errors in this paper. In the introduction section, when quoting studies of some researchers, the past tense should be used generally rather than the present tense. For example, the "are" should be corrected as "were". Please check the paper and revise them.
3. The research background needs to be richer.
4. Can we have a clear definition of the used notations? Perhaps as a listing table for the symbols and notations.
5. Add more description about Fig. (1-5).
6. The English of this paper is good, but there are still a few grammars and typing mistakes. Please examine them carefully.
7. The format of references is not completely unified.
Author Response
Medellin, December 05, 2022
Dear Prof. Dr. Takayoshi Kobayashi
Editor-in-Chief
Applied Sciences
Kind regards
According to the review of our article by the reviewers, the following changes were made, properly marked with green underline in the manuscript:
|
Reviewer |
Comment |
Response |
|
Reviewer 1 |
1. The main contribution must be specified. |
We made some modifications in the final part of the abstract, introduction and conclusions to highlight the contribution of the study. |
|
Reviewer 1 |
2. There are some tense errors in this paper. In the introduction section, when quoting studies of some researchers, the past tense should be used generally rather than the present tense. For example, the "are" should be corrected as "were". Please check the paper and revise them. |
The entire manuscript was carefully reviewed and corrections were made as necessary. |
|
Reviewer 1 |
3. The research background needs to be richer. |
Some ideas were included in the introduction section, and the summary and conclusions section were strengthened. |
|
Reviewer 1 |
4. Can we have a clear definition of the used notations? Perhaps as a listing table for the symbols and notations. |
All notation was reviewed, and clarification was provided where necessary, e.g., in the figures |
|
Reviewer 1 |
5. Add more description about Fig. (1-5). |
Figures 1 and 2 are simply illustrative so that the reader can recall some of the most important features of the distributions used for the random effects and can compare them with the normal distribution. At the beginning of the results section all the detail is given so that the reader can interpret all the figures and extract for himself the empirical evidence of the impact of the incorrect specification of the random effects distribution. |
|
Reviewer 1 |
6. The English of this paper is good, but there are still a few grammars and typing mistakes. Please examine them carefully. |
The entire manuscript was carefully reviewed and corrections were made as necessary. |
|
Reviewer 1 |
7. The format of references is not completely unified. |
References were reviewed and adjusted to the format suggested by the journal. |
|
Reviewer 2 |
The authors should re-read their manuscript thoroughly, since there are some typo errors (e.g. the “lonely” comma in the abstract). Figures 3-8 which document the achievements of the authors should be made larger (maybe the two-column setup instead of four-column one would be better for their legibility). |
The entire manuscript was carefully reviewed and corrected. We consider that the figures have a good resolution to look in detail making the corresponding zoom, and in addition, the choice of the different conventions to compare the 4 distributions was with the purpose of easily identifying the behavior of the normal distribution and the distributions that presented a greater distance from it. On the other hand, we consider that separating the graphs as suggested by the evaluator makes the interpretation and follow-up of the findings more difficult. |
|
Reviewer 3 |
Misprints in using bold fonts (e.g., θij in line 19; β’th in line 161, 220 etc.) should be corrected before publication. |
The entire manuscript was carefully reviewed, and corrections were made as necessary. |
We look forward to your comments and hope to hear from you soon.
Thank you very much
_
The authors
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The authors focus on the possibilities and limitations of Wald tests applied to generalized linear mixed models (GLMMs) used as statistical frameworks for data analysis. Wald tests are an alternative to likehood ratio tests, since they need lower computational burden, however the computation results, (in particular for smaller datasets) and their implications may be different. Wald tests are based on estimates from the model being estimated. The authors have carried out a simulation study to identify the effect of incorrect specification of distribution of random effects on type I errors and the power of Wald tests for several distributions of random effects in GLMMs. AS pointed out in the Conclusion (Future work) section, this manuscript is part of on-going research on the strengths and limitations of Wald statistical tests. In the present form the manuscript may be accepted “as it is”, since it offers a fresh perspective on a relatively simple-to-use tool, which may be useful for statistical inference. However the authors should re-read their manuscript thoroughly, since there are some typo errors (e.g. the “lonely” comma in the abstract). Figures 3-8 which document the achievements of the authors should be made larger (maybe the two-column setup instead of four-column one would be better for their legibility).
Author Response
Medellin, December 05, 2022
Dear Prof. Dr. Takayoshi Kobayashi
Editor-in-Chief
Applied Sciences
Kind regards
According to the review of our article by the reviewers, the following changes were made, properly marked with green underline in the manuscript:
|
Reviewer |
Comment |
Response |
|
Reviewer 1 |
1. The main contribution must be specified. |
We made some modifications in the final part of the abstract, introduction and conclusions to highlight the contribution of the study. |
|
Reviewer 1 |
2. There are some tense errors in this paper. In the introduction section, when quoting studies of some researchers, the past tense should be used generally rather than the present tense. For example, the "are" should be corrected as "were". Please check the paper and revise them. |
The entire manuscript was carefully reviewed and corrections were made as necessary. |
|
Reviewer 1 |
3. The research background needs to be richer. |
Some ideas were included in the introduction section, and the summary and conclusions section were strengthened. |
|
Reviewer 1 |
4. Can we have a clear definition of the used notations? Perhaps as a listing table for the symbols and notations. |
All notation was reviewed, and clarification was provided where necessary, e.g., in the figures |
|
Reviewer 1 |
5. Add more description about Fig. (1-5). |
Figures 1 and 2 are simply illustrative so that the reader can recall some of the most important features of the distributions used for the random effects and can compare them with the normal distribution. At the beginning of the results section all the detail is given so that the reader can interpret all the figures and extract for himself the empirical evidence of the impact of the incorrect specification of the random effects distribution. |
|
Reviewer 1 |
6. The English of this paper is good, but there are still a few grammars and typing mistakes. Please examine them carefully. |
The entire manuscript was carefully reviewed and corrections were made as necessary. |
|
Reviewer 1 |
7. The format of references is not completely unified. |
References were reviewed and adjusted to the format suggested by the journal. |
|
Reviewer 2 |
The authors should re-read their manuscript thoroughly, since there are some typo errors (e.g. the “lonely” comma in the abstract). Figures 3-8 which document the achievements of the authors should be made larger (maybe the two-column setup instead of four-column one would be better for their legibility). |
The entire manuscript was carefully reviewed and corrected. We consider that the figures have a good resolution to look in detail making the corresponding zoom, and in addition, the choice of the different conventions to compare the 4 distributions was with the purpose of easily identifying the behavior of the normal distribution and the distributions that presented a greater distance from it. On the other hand, we consider that separating the graphs as suggested by the evaluator makes the interpretation and follow-up of the findings more difficult. |
|
Reviewer 3 |
Misprints in using bold fonts (e.g., θij in line 19; β’th in line 161, 220 etc.) should be corrected before publication. |
The entire manuscript was carefully reviewed, and corrections were made as necessary. |
We look forward to your comments and hope to hear from you soon.
Thank you very much
_
The authors
Author Response File: Author Response.pdf
Reviewer 3 Report
Please correct fonts where they should be bold and where non-bold. Now it is some mixture.
Comments for author File: Comments.pdf
Author Response
Medellin, December 05, 2022
Dear Prof. Dr. Takayoshi Kobayashi
Editor-in-Chief
Applied Sciences
Kind regards
According to the review of our article by the reviewers, the following changes were made, properly marked with green underline in the manuscript:
|
Reviewer |
Comment |
Response |
|
Reviewer 1 |
1. The main contribution must be specified. |
We made some modifications in the final part of the abstract, introduction and conclusions to highlight the contribution of the study. |
|
Reviewer 1 |
2. There are some tense errors in this paper. In the introduction section, when quoting studies of some researchers, the past tense should be used generally rather than the present tense. For example, the "are" should be corrected as "were". Please check the paper and revise them. |
The entire manuscript was carefully reviewed and corrections were made as necessary. |
|
Reviewer 1 |
3. The research background needs to be richer. |
Some ideas were included in the introduction section, and the summary and conclusions section were strengthened. |
|
Reviewer 1 |
4. Can we have a clear definition of the used notations? Perhaps as a listing table for the symbols and notations. |
All notation was reviewed, and clarification was provided where necessary, e.g., in the figures |
|
Reviewer 1 |
5. Add more description about Fig. (1-5). |
Figures 1 and 2 are simply illustrative so that the reader can recall some of the most important features of the distributions used for the random effects and can compare them with the normal distribution. At the beginning of the results section all the detail is given so that the reader can interpret all the figures and extract for himself the empirical evidence of the impact of the incorrect specification of the random effects distribution. |
|
Reviewer 1 |
6. The English of this paper is good, but there are still a few grammars and typing mistakes. Please examine them carefully. |
The entire manuscript was carefully reviewed and corrections were made as necessary. |
|
Reviewer 1 |
7. The format of references is not completely unified. |
References were reviewed and adjusted to the format suggested by the journal. |
|
Reviewer 2 |
The authors should re-read their manuscript thoroughly, since there are some typo errors (e.g. the “lonely” comma in the abstract). Figures 3-8 which document the achievements of the authors should be made larger (maybe the two-column setup instead of four-column one would be better for their legibility). |
The entire manuscript was carefully reviewed and corrected. We consider that the figures have a good resolution to look in detail making the corresponding zoom, and in addition, the choice of the different conventions to compare the 4 distributions was with the purpose of easily identifying the behavior of the normal distribution and the distributions that presented a greater distance from it. On the other hand, we consider that separating the graphs as suggested by the evaluator makes the interpretation and follow-up of the findings more difficult. |
|
Reviewer 3 |
Misprints in using bold fonts (e.g., θij in line 19; β’th in line 161, 220 etc.) should be corrected before publication. |
The entire manuscript was carefully reviewed, and corrections were made as necessary. |
We look forward to your comments and hope to hear from you soon.
Thank you very much
_
The authors
Author Response File: Author Response.pdf
