Model Selection with Missing Data Embedded in Missing-at-Random Data

Round 1

Reviewer 1 Report

1. Section 2, the first paragraph: Why assume alpha=S*theta? It is better to present some explanation. 

2. Eq. (1): What is n? Which distribution is the expectation taken with respect to?

3. Page 4, the first paragraph: The authors consider a special case that is missing-data pattern. But in some applications, missing data may be not any pattern as is assumed in Ibrahim et al. (2008). In this case,  how to select model?

4.   Page 4, the last line: Omit the "trace".

5. Eq. (3): When assumption (3) is not correct, how is the result?

6. When the asymptotic normality of estimator of theta does not hold, how is result?

7. The considered IC should be investigated theoretically as done in Ibrahim et al. (2008). 

8.  Eq. (6): The first term is just that given in Ibrahim et al. (2008). Please compare the difference with that given in Ibrahim et al. (2008). In particular, I wonder in which case they have the same result. 

9. Simulation studies: It is better to consider a case that the missing data are created based on missing values such as Tang et al. (Statistica Sinica, 2014). I wonder comparing the results for Ibrahim et al. (2018) with those for the presented IC. From Table 3, the presented IC behaves unsatisfactorily for the true models 1 and 2. The authors did not consider patterns in simulation studies. Whether is it possible to consider different patterns?

10.  It is better to present some examples to illustrate the presented method. 

Author Response

We would like to express appreciation again the associate editor and reviewers for providing further feedback on our manuscript. The latest version of the manuscript reflects all suggestions kindly pointed by them. The following is a list of correction.

• p3. We delete description about the observed log-likelihood in the representation of missing patterns. 
• p3,l8-. A phrase "and are a random sample" is added to make the assumption clearer.
• p6,l5. A phrase "Under the regularity condition assumed in [16]" is added to present the assumptions we rely on.
• p9,l4. Description of trivariate normal distibution is corrected. 
• p9. The equations of missing mechanism are corrected because of lack of parameter $\omega_y$ and $\omega_{x_1}$.
• p10., Three sentences are added at the last part of the second paragraph in Section 5. They refer how to estimate H-function.

We believe that the presentation of the re-reviewed manuscript is improved in terms of readability and consistency.

Attached is each response to all comments.

We again appreciate the editor and reviewers' useful comments that would improve our manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript entitled "Model Selection with Missing Data Embedded in MAR Data" has been prepared by the authors. It needs improvement and correction. Note the following;

1- Writing and grammar need to be corrected. e.g. Do not use the "we" pronoun.

2- References must be developed.

3- results should be developed.

4- The introduction is very short. it is recommended to review the literature in the introduction.

Author Response

We would like to express appreciation to the associate editor and reviewers for providing significative feedback on our manuscript. The revised manuscript reflects all suggestions kindly pointed by them. We believe that the presentation of the reviewed manuscript becomes clearer to understand.

Attached is each response to all comments.

We again appreciate the editor and reviewers' useful comments that would improve our manuscript.

Author Response File: Author Response.docx

Reviewer 3 Report

Please find the attached PDF. In addition, it is better for the authors to do some English edits to improve readership.

Comments for author File: Comments.pdf

Author Response

We would like to express appreciation to the associate editor and reviewers for providing significative feedback on our manuscript. The revised manuscript reflects all suggestions kindly pointed by them. We believe that the presentation of the reviewed manuscript becomes clearer to understand.

Attached is each response to all comments.

We again appreciate the editor and reviewers' useful comments that would improve our manuscript.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

I don't think that the authors have completely revised this paper according to my previous comments. I have the following comments.

1. The previous comment 3: Ibrahim et al. (2008) did not consider missingness pattern and use the widely used notations, which are better than the current paper due to the fact that they did not need specifying special distribution and can be available for any likelihood function.

2. The previous comment 7: It is better to present theories. 

3. The previous comment 8: The authors did not understand the method given in Ibrahim et al. (2008) in that Ibrahim et al. (2008) considered two methods to deal with the criterion including approximation to H function and omitting H function. 

4. The previous comment 9: I want to compare the data generated as done in Tang et al. (2014). 

Author Response

We would like to express appreciation again the associate editor and reviewers for providing further feedback on our manuscript. The latest version of the manuscript reflects all suggestions kindly pointed by them. The following is a list of correction.

• p3. We delete description about the observed log-likelihood in the representation of missing patterns. 
• p3,l8-. A phrase "and are a random sample" is added to make the assumption clearer.
• p6,l5. A phrase "Under the regularity condition assumed in [16]" is added to present the assumptions we rely on.
• p9,l4. Description of trivariate normal distibution is corrected. 
• p9. The equations of missing mechanism are corrected because of lack of parameter $\omega_y$ and $\omega_{x_1}$.
• p10., Three sentences are added at the last part of the second paragraph in Section 5. They refer how to estimate H-function.

We believe that the presentation of the re-reviewed manuscript is improved in terms of readability and consistency.

Attached is each response to all comments.

We again appreciate the editor and reviewers' useful comments that would improve our manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

The reviewer's concerns remain.

Author Response

We would like to express appreciation again the associate editor and reviewers for providing further feedback on our manuscript. The latest version of the manuscript reflects all suggestions kindly pointed by them. The following is a list of correction.

• p3. We delete description about the observed log-likelihood in the representation of missing patterns. 
• p3,l8-. A phrase "and are a random sample" is added to make the assumption clearer.
• p6,l5. A phrase "Under the regularity condition assumed in [16]" is added to present the assumptions we rely on.
• p9,l4. Description of trivariate normal distibution is corrected. 
• p9. The equations of missing mechanism are corrected because of lack of parameter $\omega_y$ and $\omega_{x_1}$.
• p10., Three sentences are added at the last part of the second paragraph in Section 5. They refer how to estimate H-function.

We believe that the presentation of the re-reviewed manuscript is improved in terms of readability and consistency.

Attached is each response to all comments.

We again appreciate the editor and reviewers' useful comments that would improve our manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors have been responsive to the revision. I don't have additional comments.

Author Response

We are very grateful to the Reviewer 3 for providing a feedback on our manuscript.Our manuscript was further revised in accordance with other reviewers. We believe that the latest version of the manuscript is improved in terms of readability and consistency.

 

Thank you again for the reviewer's continued engagement with our work.