Group-level effects integrated over or set to zero in conditional_effects()? or neither?

Interfaces brms
1

This may be a dumb question, but here it goes.

Let’s say I have a model like this: fit<-brm(outcome ~ time + (time|state/county/town))

If I run conditional_effects(fit, re_formula=NA), then the uncertainty in the group-level effects is not included. So does that mean they are set to zero (ie a value of zero offset from the population level intercept and slope)? If I run conditional_effects(fit, re_formula=~(1+time|state)), then the uncertainty in the state level effect is included but not the county and town. So are county and town set to zero?

I tried looking at the dataframe from which the conditional_effects call was plotting, but it just said “NA” for any group level effects in the dataframe.

I also saw this comment by @bgoodri that mentioned that a group left out of the re_formula was “integrated over”.

Could someone shed some light on this? When I call conditional_effects(fit, re_formula=~(1+time|state)) in my above example am I conditioning on state but integrate over county/town? Or is county/town set to zero (zero offset from the state level)? Or neither?

What is the difference between integrating over and setting to zero?

I am a bit confused.

Thanks!

2

Here @paul.buerkner says that setting re_formula=NA sets the group level effects to zero. So it seems in my example above, specifying re_formula=~(1+time|state) would set county/town effects to zero but include the uncertainty in state.

So, I don’t understand @bgoodri comment linked above about integrating over the random effect left out of the re_formula() call.

The reason I would like to clarify this, is that I am working on an analysis where I would particularly like to show that much of the variation in my outcome is seen in the hierarchical group level effects. A good way to demonstrate this is by a series of conditional_effects() plots showing the trend over time when the uncertainty for time|state, time|state/county, and time|state/county/town is included for each plot (the plots show increasing uncertainty for the trend over time as the effects are included).

I would like to get the figure legend correctly written for those plots.

Any insight is appreciated. Thanks!

3

When using re_formula = NA or leaving out certain groups, we indeed set them to zero (that is, condition on a level with average parameter values) and don’t integrate over them. The latter will eventually be possible as well but is not yet supported.

4

Thanks so much for the clarification @paul.buerkner !
What is the practical difference between setting them to zero and integrating over them? I have been reading this article to try to understand (particularly the R code in the supplement). If someone has a brief practical explanation, that would be helpful.

5

When you use non-linear transformations, the difference matters. For example:

exp(0)
mean(exp(rnorm(1000, 0, 1)))

Both have the same mean before transformation (i.e. before exp()) but because of the non-linearity, the mean after transformation is different.

6

Ahh ok, thanks @paul.buerkner !! I think I understand - so when one “integrates over the random effects”, then one is averaging over the random effects on the outcome scale (transform and then average over; like make predictions across the distribution of random effects and then average over all of these predictions); which is quite different than taking the average value of the random effects (zero), conditioning on that value, and then making predictions. Correct?

7

Yeah, that sounds correct to me.

8

Thanks again for all of your help! Your responses cleared up all of the questions that I had in this post.
Also, I love the brms package. Really an amazing tool. Thanks