[R-sig-ME] Random vs Fixed effect correlations

[Mike Lawrence]

Possibly a clue:

After playing with a few data sets, It seems that the fixed effects
correlation between B & D obtained from "A ~ B + D + (B + D | C)" is
consistently quite close to the value computed using the more
rudimentary "compute the score independently for each level of C"
approach. So maybe the fixed effects correlations report what you'd
likely see from the independent score method while the random-effects
correlations are what you get when you let the model shrink the
estimates?

On the other hand, it also seems that correlations involving the
intercept seem to differ dramatically between the fixed effects
correlations and the independent scores correlations.


On Tue, Jun 8, 2010 at 2:25 PM, Shujuan Feng <fengsj at mail.utexas.edu> wrote:
> I was confused about the correlation between fixed coefficients. I am still
> not very sure about it.....
>
> One thing is that the correlations between fixed coefficients also exist in
> the model without random effects. It is more like: how one coefficient
> estimate influence the other coefficient estimate. (We get point fixed
> estimate, but a fixed coefficient have a distribution and can vary (CIs).)
> Strong correlations between fixed coefficients may show there is
> collinearity between the predictors.
>
> I may be totally off. I am in the process of learning, too.
>
>
>
>
>
> ----- Original Message ----- From: "Mike Lawrence" <Mike.Lawrence at dal.ca>
> To: <r-sig-mixed-models at r-project.org>
> Sent: Tuesday, June 08, 2010 11:30 AM
> Subject: [R-sig-ME] Random vs Fixed effect correlations
>
>
>> Hi Folks,
>>
>> I'm in the process of learning mixed modelling, and I'm having trouble
>> getting my head around the meaning of the correlations produced for
>> fixed effects when you do something like print( my_lmer_model , corr=T
>> ). To possibly help you help me, I'll try to explain what I think I
>> *do* understand.
>>
>> I understand that when you fit a model like "A ~ B + (1|C)", you're
>> letting each level of C have it's own intercept, but specify that
>> levels of C should be fit to a common slope for the effect of B.
>> Furthermore, I understand that when you fit a model like "A ~ B +
>> (1+B|C)", you're letting each level of C have it's own intercept *and*
>> it's own slope for the effect of B. I understand that this differs
>> from simply fitting individual models to each level of C in that in
>> mixed effects modelling, the variance observed in the data at each
>> level of C affects your confidence in that level's estimate of the
>> slope of B, and thus estimates with low confidence are shrunk towards
>> the mean estimate of B across levels of C. Finally, I understand that
>> when you have multiple random effects like "A ~ B + D + (1+B+D|C)",
>> you can compute a correlation between the per-Ss estimates of B and D
>> that take into account the shrinkage applied to the estimates.
>>
>> What I don't understand is the fixed effects correlations obtained
>> when you fit a model like "A ~ B + D + (1|C)". In that model, I
>> thought that Ss are fit to common estimates of the slope for B and D,
>> so I don't understand over what these estimates are being correlated.
>>
>> Could it be that the fixed-effects correlation between B & D is the
>> correlation across trials, ignoring levels of C? If so, would it then
>> be accurate to describe this correlation as a measure of the degree to
>> which measurement error in B & D are correlated? Furthermore, if there
>> are true correlations at the random effects level between B & D (for
>> example: such that levels of C with high B's also have high D), would
>> a model like "A ~ B + D + (1+B+D|C)" take this random effects
>> correlation into account when reporting the fixed effects correlation
>> between B & D? If not, I can imagine that in presence of correlations
>> at the random effects level would confound investigation of
>> correlations at the fixed effects level.
>>
>> Would anyone care to attempt to ameliorate my confusions?
>>
>> Mike
>>
>> --
>> Mike Lawrence
>> Graduate Student
>> Department of Psychology
>> Dalhousie University
>>
>> Looking to arrange a meeting? Check my public calendar:
>> http://tr.im/mikes_public_calendar
>>
>> ~ Certainty is folly... I think. ~
>>
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>
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-- 
Mike Lawrence
Graduate Student
Department of Psychology
Dalhousie University

Looking to arrange a meeting? Check my public calendar:
http://tr.im/mikes_public_calendar

~ Certainty is folly... I think. ~