Using group-level parameters as predictors

[John Flournoy]

Hi all,

I was hoping to be able to use the group-level estimates of a parameter from the model of one variable as predictors in the model of a second variable. This seems to have some relation to the idea of using variables without measurement error (i.e., the `se` function) but with the added bonus (?) that the predictor is shrunk a bit toward the population mean.

I'm envisioning something like:

```
m1 <- brm(y1 ~ 1 + x1 + (1 + x1 | g))
m2 <- brm(y2 ~ 1 + bx1 + (1 | g))
```

Where bx1 is the vector of per-group parameters for the relation between y1 and x1.

Thanks for your help, and thanks for pardoning my somewhat noob-ish phrasing of the question.

~J

[Paul Buerkner]

Hi John,

this is certainly possible in a two-step approach you seem to have in mind. Consider the following sample code:

```R

m1 <- brm(y1 ~ 1 + x1 + (1 + x1 | g))

bx1 <- coef(m1)$g[, "Estimate", "x1"]

# or ranef instead of coef to get the centered estimates

<put bx1 into your data.frame>

m2 <- brm(y2 ~ 1 + bx1 + (1 | g))

```

If you want to include the measurement / estimation error in bx1, add:

```R

sdbx1 <- coef(m1)$g[, "Est.Error", "x1"]

<put sdbx1 into your data.frame>

m2 <- brm(y2 ~ 1 + me(bx1, sdbx1) + (1 | g))

```

All the best,

Paul

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[John Flournoy]

Hi Paul,

Thank you very much for the quick reply. Your solution will work nicely, I think. I was hoping to find a way to do it in a one-step process, though I'm not sure if I gain much from that except perhaps aesthetically. I have a sense of how I could accomplish this by either modifying or writing some Stan code from scratch, but again, perhaps without much potential gain.

Thanks again,
~j

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[Paul Buerkner]

I think it would be slightly better to model it in a one-step approach, but by how much will depend on the particular data and model.

In any case, the Stan code generated by brms should allow you making it a one-step approach with not too much effort.

-Paul

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