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

[Ben Bolker]

  It's not much of a concern (in my book).

  You could use poly(time,degree=2) (instead of (1 + ) time + I(time^2))
to construct orthogonal polynomials ...

On 18-04-02 05:32 PM, Joshua Rosenberg wrote:
> 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
> <mailto:bbolker at gmail.com>> wrote:
> 
>     On Sun, Apr 1, 2018 at 12:20 PM, Stuart Luppescu <lupp at uchicago.edu
>     <mailto: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
>     >
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> -- 
> Joshua Rosenberg, Ph.D. Candidate
> Educational Psychology ​&​ Educational Technology
> Michigan State University
> http://jmichaelrosenberg.com <http://jmichaelrosenberg.com/>