[R-sig-ME] meaning of lmer formula

[Ben Bolker]

On 17-09-06 03:57 PM, Don Cohen wrote:
> 
> My current understanding is that something like (input2 | group)
> means the same as (1 + input2 | group) which means to estimate
> for each group an intercept, a slope and a correlation between the two.

  Yes.
> 
> Does (input1 + input2 | group) mean the same as
> (input1 | group) + (input2 | group) or does it also include a 
> correlation between input1 and input2 ?

  The latter.

> 
> Back to my question about additive shifts, is that extra correlation 
> required in order to maintain invariance over additive shifts?

  Yes.

> 
> Is there some way in the formula language to control more precisely
> which correlations are to be included/excluded?
> 

  Unfortunately not.
  I gave an example here
https://stackoverflow.com/questions/38976189/syntax-of-pdblocked-to-specify-covariance-matrix-in-mixed-effects-model-nlme
about how to specify some structural zeros in the covariance matrix, but
it's not easy ...

http://rpubs.com/bbolker/varcov_equiv may be useful as well.