Posterior sampling of beta difference

[Edward Patzelt]

Hi brms-users,

I'm new to Bayesian approaches, but I'm trying to do the following. In the graph below we want to examine "the difference between differences". In other words, we want to find the posterior proportion of "the comparison of the beta difference (low vs high stakes) between young and old", where young has a greater stakes difference than old.

This would tell us the posterior probability that the stakes effect is larger for young than for old.

The graph below comes from a simple model with the default settings and is plotted using marginal_effects().

mod <- brm(W~stakes*ageFactor+IQ+gender, data=dat2)

[Paul Buerkner]

I suggest you take a look at the "hypothesis" method, which allows you to specify and compute exactly the contrasts you need.

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[Edward Patzelt]

Thanks Paul, just so I'm crystal clear on using hypothesis. The default for factors is to dummy code them. So hypothesis(model, "stakeshighStakesW:ageFactoryoung < 0") is telling me the evidence ratio that "highStakesW - lowStakesW is greater for young than for old"?

With the results indicating there is not a significant difference in "stakes" between young and old.

W ~ stakes * ageFactor

Hypothesis Tests for class b:

                         Estimate Est.Error l-95% CI u-95% CI Evid.Ratio Star

(stakeshighStakes... < 0    -0.07      0.08     -Inf     0.06       4.38   

On Friday, April 13, 2018 at 9:46:18 AM UTC-4, Paul Buerkner wrote:

I suggest you take a look at the "hypothesis" method, which allows you to specify and compute exactly the contrasts you need.

2018-04-12 19:46 GMT+02:00 Edward Patzelt <pat...@g.harvard.edu>:

Hi brms-users,

I'm new to Bayesian approaches, but I'm trying to do the following. In the graph below we want to examine "the difference between differences". In other words, we want to find the posterior proportion of "the comparison of the beta difference (low vs high stakes) between young and old", where young has a greater stakes difference than old.

This would tell us the posterior probability that the stakes effect is larger for young than for old.

The graph below comes from a simple model with the default settings and is plotted using marginal_effects().

mod <- brm(W~stakes*ageFactor+IQ+gender, data=dat2)

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[Paul Buerkner]

This interpretation seems correct to me.

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[Edward Patzelt]

Thanks Paul!