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High correlation among random effects for longitudinal model

7 messages · Stuart Luppescu, Joshua Rosenberg, Ben Bolker +1 more

Original
Joshua Rosenberg
# 
Hi R-sig-mixed-models, I am using the nlme package (and lme() function) to
estimate a longitudinal model for ~ 270 individuals over five time points.
Descriptively, the data seems to take a quadratic form, so I fit a model
like the following:

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):

Random effects:
 Formula: ~time + I(time^2) | individual_ID
 Structure: General positive-definite, Log-Cholesky parametrization
            StdDev    Corr
(Intercept) 34.836512 (Intr) time
time        39.803783 -0.959
I(time^2)    8.342256  0.969 -0.995
Residual    28.920368

Is this a concern in terms of interpreting the model? Is this a concern
technically in terms of how the model is specified?

Thank you for pointing me in the right direction. Happy to answer any
follow-up questions or to share additional details and information.


Josh
Stuart Luppescu
#
On Sun, 2018-04-01 at 12:55 +0000, Joshua Rosenberg wrote:
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}.
Ben Bolker
#
On Sun, Apr 1, 2018 at 12:20 PM, Stuart Luppescu <lupp at uchicago.edu> wrote:
Agreed.  This is closely related, but not identical to, the
phenomenon where the
*fixed effects* are highly correlated.
1 day later
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:

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Ben Bolker
    

    

      
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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:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Thierry Onkelinx
    

    

      
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Dear Joshua,

I wrote a blog post on a similar issue a few months ago. You can read
it here: https://www.muscardinus.be/2018/02/highly-correlated-random-effects/

In case you have one observation per time point per individual, then
the random effects structure and correlation structure is probably too
complex for the data.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
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not ensure that a reasonable answer can be extracted from a given body
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2018-04-01 14:55 GMT+02:00 Joshua Rosenberg <jrosen at msu.edu>:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Joshua Rosenberg
    

    

      
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Thank you Thierry and Ben,
Josh

On Tue, Apr 3, 2018, 4:10 AM Thierry Onkelinx <thierry.onkelinx at inbo.be>
wrote: