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

Joshua Rosenberg jrosen at msu.edu
Sun Apr 1 14:55:34 CEST 2018

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.


Joshua Rosenberg, Ph.D. Candidate
Educational Psychology ​&​ Educational Technology
Michigan State University

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