See attached decision letter.

I would like to thank you for taking the first round of recommendations to heart. I believe that this has greatly improved the manuscript, and has made it accessible to a wider audience. Reviewer 4's assessment of the revised paper raises only a few minor issues, plus one more serious one. The reviewer points out that the example shown in Figure 7 of the manuscript ('0708.txt') contains no evidence of non-normality in the residuals. Can you find an example that does show evidence for non-normal residuals?

The thought experiment in Appendix A is very useful. But I wonder why it only compares SPINE with model 1 and model 2. Why not also include model 3? The fact that the residuals of your example are normal strengthens my conviction that excess dispersion can be reliably modelled using a random effects approach.

1. I agree with your comment that an MSWD>1 does not automatically mean that a dataset is overdispersed, because the MSWD follows a positively skewed distribution around its expected value. Note that, for small datasets, the mode of this distribution is considerably less than 1. A better way to assess the significance of the dispersion is to use a chi-square test.

However none of this reduces the usefulness of model-3 regression. In fact model-3 regression can also be applied to non-dispersed datasets with only a small penalty in the precision of the fit parameters.

2. You are correct that outliers can result in incorrect estimates of the model-3 dispersion. So if one really cares about the amount of dispersion, then one would have to apply some kind of outlier detection algorithm prior to fitting the isochron. Without outlier detection, the presence of outliers will lead to an overestimated dispersion parameter. However in most situations this is a good thing because the main purpose of the dispersion parameter is to serve as a measure of 'geological precision'. Therefore, an overestimation of the dispersion 'protects' the user from over-interpreting the isochron age. My concern is that the SPINE algorithm lacks such a protection mechanism.

3. Despite this limitation, which is acknowledged in the revised manuscript, I agree that your robust regression approach is a welcome addition to the geochronological toolbox. Your manuscript adequately addresses the second round of comments from Reviewer 4's. Therefore, I am happy to accept your manuscript for publication in Geochronology.

I would just like to request one more small but important change. In my decision letter of the first version, I had requested that you update the abstract of your paper according to the guidelines provided at:

https://www.caam.rice.edu/~symes/CAAM600/abstract_scrutiny.pdf

You have not yet addressed this issue. The last three sentences of your abstract read like an outline rather than a "condensation and concentration of the essential information in the paper". Feel free to expand the abstract if necessary.

Thank you for choosing GChron to publish your work.

Thank you for modifying the abstract. I have now formally accepted the paper for publication in GChron.

I agree with the associate editor's decision.