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- Operating System: Windows 10
- brms Version:

I am currently trying to fit a multilevel model and am having some troubles with understanding the exact use of || in brms syntax.

I read the vignettes but am somehow still confused about it.

**1. Here I read the following:**

The / operator indicates nested grouping structures and expands one grouping

factor into two or more when using multiple / within one term. If, for instance, you write (1 | g1/g2),

it will be expanded to (1 | g1) + (1 | g1:g2). Instead of | you may use || in grouping terms to prevent group-level correlations from being modeled.

So, for example, if we have

A ~ 1 + (1|g1/g2)

This would mean that A has a fixed effect + two random effects, 1|g1 and 1|g1:g2, and these two random effects of A can potentially be correlated,

but if we use

A ~ 1 + (1||g1/g2)

this would mean that 1|g1 and 1|g1:g2 random effects for A will NOT be correlated.

Is this a correct way to interpret it?

**2.** Here it says

Group-level terms are of the form (coefs | group), where coefs

contains one or more variables whose effects are assumed to vary with the levels of the grouping factor given in group. Multiple grouping factors each with multiple group-level coefficients are possible…

By default,

group-level coefficients within a grouping factor are assumed to be correlated. Correlations can be set to zero by using the (coefs || group).

So, for example, if we have two variables

A ~ 1+ (1|g1)

G ~ 1+ (1|g1)

this would mean that the group effect A|g1 is potentially correlated with G|g1, but if we write

A ~ 1+ (1||g1)

G ~ 1+ (1||g1)

this would mean that the random effect A|g1 is NOT correlated with G|g1?

I think my confusion comes from the fact that || seems to mean

**no correlation between two different group effects on the same variable** in (1),

and

**no correlation between the same group effect of the same grouping factor on two different variables.**

Now, if we make it even more complicated, if we have

A ~ 1+ (1||g1+g2)

G ~ 1+ (1||g1+g2)

This would mean that A|g1 is NOT correlated with A|g2, but also

A|g1+g2 is NOT correlated with G|g1+g2?

Is this correct?