I am currently writing up an experiment where we asked people on a 0-10 scale how much they expected three different beverages, water, decaf, and coffee, to reduce their caffeine withdrawal symptoms. Initially, using Bayesian parameter estimation, I modelled this as a within-subjects regression beve…

Sorry for taking so long to respond. I agree with you that log-odds are hard to understand, but odds-ratio on the natural scale are also not great as the skew makes it hard to appreciate when the difference is actually symmetric. I.e. the plot can look quite differently if you choose to make the co…

It does. That is a very neat way to do it. Thank you!

So you think that point estimates are not the right way to do it? If you had a gun to your head and the terrorist demanded a point estimate for the distribution of odds ratios, would you pick the mean or the mode? A strange kind of terrorist who was concerned with this kind of thing I admit.

[image] llewmills: So you think that point estimates are not the right way to do it? If you had a gun to your head and the terrorist demanded a point estimate for the distribution of odds ratios, would you pick the mean or the mode? I wouldn’t put is so strongly and would generally beware of …

Let’s look at the second row. On the log-odds scale, the mean advantage of water over coffee is -1.3 which translates to an odds ratio of .27. The mean of odds ratios is .4. Because the skew of the odds ratios pulls the mean upwards, I think working on the log odds scale is better. You could still o…

Thank you @tjmahr that is well put. So you think a good way would be to find the mean or mode of the distribution of log-odds and then exponentiate that to get the odds ratio? Do you think a similar strategy for the HPDI, i.e. get the upper and lower bounds of the HPDI for the distribution of log o…

Thank you for your thoughtful answer @martinmodrak . It is always difficult in science to serve one’s desire to present a balanced, precise picture while simultaneously presenting the results in a way a reader can understand. I am writing up these data in an article intended for psychologists, most o…

[image] llewmills: Do you think a similar strategy for the HPDI, i.e. get the upper and lower bounds of the HPDI for the distribution of log odds and then exponentiate those values? Or do you think it’s safe to exponentiate the difference in estimated log-odds at each step in the mcmc chain and …

[image] llewmills: I am writing up these data in an article intended for psychologists, most of whom will be non-Bayesians. I would like to try and find a way of presenting the results of my Bayesian analysis in a way that is easy to understand, and hence I have decided to give point estimates. …

Strategies for graphing distributions of log-odds estimates and the corresponding odds ratios

Modeling

mike-lawrence December 5, 2019, 2:06pm 9

Note that there are good arguments against HPDIs. If you used straight quantiles, they’ll be transformation invariant.

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Strategies for graphing distributions of log-odds estimates and the corresponding odds ratios

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