[R-sig-ME] High correlation among random effects for longitudinal model

[Joshua Rosenberg]

Dear Stuart and Ben,

Thank you, this worked to significantly reduce the correlations between the
intercept and the linear and quadratic terms (though still quite high
between the linear and quadratic term):

Random effects:
 Formula: ~time + I(time^2) | student_ID
 Structure: General positive-definite, Log-Cholesky parametrization
            StdDev    Corr
(Intercept) 18.671959 (Intr) time
time        11.029842 -0.262
I(time^2)    8.359834 -0.506  0.959
Residual    29.006598

Could I ask if that correlation between the linear (time) and quadratic
I(time^2) terms is cause for concern - and if so, how to think about
(potentially) addressing this?
Josh

On Sun, Apr 1, 2018 at 12:34 PM Ben Bolker <bbolker at gmail.com> wrote:

> On Sun, Apr 1, 2018 at 12:20 PM, Stuart Luppescu <lupp at uchicago.edu>
> wrote:
> > On Sun, 2018-04-01 at 12:55 +0000, Joshua Rosenberg wrote:
> >> lme(outcome ~ time + I(time^2),
> >>     random = ~ time + I(time^2),
> >>     correlation = corAR1(form = ~ time | individual_ID),
> >>     data = d_grouped)
> >>
> >> I have a question / concerns about the random effects, as they are
> >> highly
> >> correlated (intercept and linear term = -.95; intercept and quadratic
> >> term
> >> = .96; linear term and quadratic term = -.995):
> >
> > I think this is an ordinary occurrence for the intercept and time trend
> > to be negatively correlated. The way to avoid this is to center the
> > time variable at a point in the middle of the series, so, instead of
> > setting the values of time to {0, 1, 2, 3, 4} use {-2, -1, 0, 1, 2}.
> >
>
>   Agreed.  This is closely related, but not identical to, the
> phenomenon where the
> *fixed effects* are highly correlated.
>
> > --
> > Stuart Luppescu
> > Chief Psychometrician (ret.)
> > UChicago Consortium on School Research
> > http://consortium.uchicago.edu
> >
> > _______________________________________________
> > R-sig-mixed-models at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
> _______________________________________________
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>
-- 
Joshua Rosenberg, Ph.D. Candidate
Educational Psychology ​&​ Educational Technology
Michigan State University
http://jmichaelrosenberg.com

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