meaning of lmer formula
On 17-09-06 05:17 PM, Don Cohen wrote:
Ben Bolker writes:
> > 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.
It occurred to me after I wrote the questions that (input1 | group) + (input2 | group) might also include that correlation between input1 and input2 - I gather now it does not.
It does not. Separate terms in lme4 formulas are always independent. (input1|group) + (input2|group) is problematic because both terms include an intercept. (0+input2|group) can be helpful, but doesn't do what you think when the variable on the LHS (e.g. input2) is a factor.
> > Back to my question about additive shifts, is that extra correlation > > required in order to maintain invariance over additive shifts?
> Yes.
One more question (so far): If there are two different groupings, would (input1 + input2 | group1) + (input1 + input2 | group2) involve correlations between group1 and group2 ?
No.
If I think of (1+input1 | group) as a 2x2 matrix, and (1+input1+input2 | group) as 3x3 then is (1+input1+input2 | group1)+(1+input1+input2 | group2) two independent 3x3's or a full 6x6 (or something else) ?
If input1 and input2 are both numeric (or 2-level factors) then they're two independent 3x3s.