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I have to say most of the comments I received made a lot of sense and were extremely helpful. In particular, when I was thinking about how I should address them, I realised that I was much better off by modelling all the prior distributions on the scale of the mean and standard deviation of the cost variable, rather than using the original scale (e.g. rate & shape for the Gamma distribution).
This is true in general, of course, but it is quite helpful in this case, because I want to impose a very informative prior for the subjects for whom a 0 has been observed (so that in the posterior the mean cost is identically 0, a fortiori). I have updated the software webpage, which now reports the full list of inputs required by the main function bces0.
In particular, I have modified the original code so that:
- a treatment-specific threshold for the default Uniform prior on the mean and standard deviation of the costs for the non-null component (previously, I was assuming a single value to be applied to both treatment being compared);
- a “robust” option, which by default is set to TRUE, which implies that “minimally informative” Cauchy priors are specified on the coefficients for the pattern model for the zero cost indicator. If robust is set to FALSE, then BCEs0 will use a vague Normal prior instead;
- a “model.file” option, which allows you to specify the name of the .txt file to which the JAGS model code is saved. This is not quite fundamental, but as I was testing the package I kind of got annoyed that every time I run it, it would overwrite previous versions of the model file, which I may need for future tests. And so I changed this.
I think the paper in its current (hopefully final!) version looks much better and the more I think about the overall problem and how the model deals with it, the more I kind of like it. But then again, as we say in Italian: “ogni scarrafone e’ bello a mamma sua“, which poorly translates into English as “every cockroach is beatiful to its own mother’s eyes”…
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