Odds ratios in a posterior parameter plot

[Paul Lantos]

Hey Paul,
 I've used the mcmc_intervals function in bayesplot to generate this figure. I'm trying to present the x axis in the most comprehensible way to my readers.

I think it's an effective graphic, but I'm not entirely clear on the units of the x axis. I am assuming it is logit scale, and it is change in log odds for each change in my parameters.

Is this something I can change into something more comprehensible to non-statistician readers, like an odds ratio?

[Paul Buerkner]

I don't know exactly what kind of model you fitted, but I assume it is a binomial model, right?

You could try exponentiating the posterior samples of the coefficients to arrive at odds ratio changes and then pass the exponentiated samples to mcmc_interval.

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[Paul Lantos]

Right, its a binomial model.

So if this is model$fit could I just do exp(param - mean(param)) for each column?

On Wednesday, August 30, 2017 at 2:25:49 PM UTC-4, Paul Buerkner wrote:

I don't know exactly what kind of model you fitted, but I assume it is a binomial model, right?

You could try exponentiating the posterior samples of the coefficients to arrive at odds ratio changes and then pass the exponentiated samples to mcmc_interval.

2017-08-30 20:22 GMT+02:00 Paul Lantos <paul....@gmail.com>:

Hey Paul,
 I've used the mcmc_intervals function in bayesplot to generate this figure. I'm trying to present the x axis in the most comprehensible way to my readers.

I think it's an effective graphic, but I'm not entirely clear on the units of the x axis. I am assuming it is logit scale, and it is change in log odds for each change in my parameters.

Is this something I can change into something more comprehensible to non-statistician readers, like an odds ratio?

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[Paul Buerkner]

Why do you want to subtract the mean?

Otherwise yes, you can just exponentiate the posterior samples.

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[Paul Lantos]

Because that would make it an odds ratio rather than just odds, right?

[Paul Buerkner]

Let me think about that. So lets say we have two predictors, one with coefficient 1 and one with coefficient 0 (logit-scale).

exp(param) would yield 2.7 and 1 in those two cases. Let's say both parameters have roughly the same distribution (just shifted by 1 in comparison).

However, exp(param - mean(param)) whould yield the same odds ratio for both coefficients, although the first clearly has a higher association with the response than the second. Does that makes sense?

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[Paul Lantos]

I see, yeah that makes sense.

Well, I'm not opposed to keeping the chart in the original units (am I correct that it's logit scale and x represents change in log-odds per change in parameter?). I just want to make sure it's labeled correctly. Is my original label (see the first post) accurate enough as long as I specify in the caption that it's on the log odds scale?

[Paul Buerkner]

It seems accurate to me, yes.

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[Paul Lantos]

Thanks!