Discussion of SSD Toolbox software. Log-transformed data can be fit by six distributions: normal, logistic, triangular, Gumbel, Weibull, and Burr. It is also interesting that four different fitting methods are available. These are maximum likelihood, moment matching, cdf linearization, and Bayesian methods. The authors question the inclusion of the triangular distribution as having tail characteristics not often seen in practice. I agree with that criticism. It would be valuable to expand this section to indicate what these methods do. At present, they offer little beyond dismissing linearization and favoring maximum likelihood. It would be really interesting, for example, to have a discussion of what Bayesian methods offer.
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No change. In view of existing papers on Bayesian methods in ecotox. and the fact we are over word count and have already added new material in response to earlier comments we do not feel this is warranted.
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Use following response from JT:
We have expanded the table on software tools and rewritten the section to allow more comparisons between tools. Model averaging is only available for SSD Toolbox and (shiny)ssdtools. Ultimately the user can select which models to include however the purpose of model averaging is to downweight detrimental models. We are unaware of an example where the AICc criteria is insufficient.
Note the current version of ssdtools soft-deprecated burr III because “poorly defined” where it means unclear which parameterization to use and because issues with convergence.
Some wordsmithing needed. Maximum likelihood, method of moments, or non-linear fits using the cdf are ways to estimating the parameters of the underlying distribution. This is a wealth of statistical literature on the pros and cons of each (computations simplicity, unbiased estimates of parameters etc) and I don’t think we want to go there.
Cdf linearization is method of finding se for the quantiles. This is different from fitting the distributions.
Bayesian methods are overlaid on maximum likelihood methods. Key advantages is the ability to incorporate prior information (e.g. you may have prior information based on other chemicals), or for more complex situation (e.g. individual endpoints have uncertainty, are censored) for which MLE are numerically complex to define (require integration) but MCMC does a numerical integration.
Given we’re already over the word count and that we’ve been asked to expand on qute a few topics, I suggest we just point to some references on Bayesian methods. Fox (2010) is already in our references but we could add one or two more.