[R-sig-ME] Longitudinal covariation parameter estimate does not match average association over time

[Ben Pelzer]

Hi Matthew,

Could this be the difference between a within and a between regression 
effect?

What if you "group-center", i.e., calculate the subject means (Pmean) 
over time for each of the 140 subjects and subtract these group-means 
from your original P values so that the Pdev = P - Pmean and then try:

long <- lmer (N ~ Pdev + Pmean + (1 | ID), data = lip)

The parameter of Pdev could be positive and the one of Pmean negative, 
showing that the (negative) within-subject effect of P differs from the 
(positive) between-subject effect. This is e.g. discussed by Snijders 
and Bosker, chapter 4.

Best, Ben.



On 7-4-2016 19:37, Matthew Boden wrote:
> Hello,
>
> I am thoroughly perplexed and could greatly benefit from your feedback
> (thanks in advance!).
>
> I am examining the longitudinal covariation between two variables (N, P)
> measured each month for 26 months among 140 subjects. I am interested in
> determining the average relation between these two variables when
> accounting for dependencies due to repeated measures. Thus, I am interested
> in between-subject variation more so than within-subject variation. Yet,
> there exists considerable variation in both trajectories and intercepts for
> individual subjects.
>
> The issue is that the average association between N and P at each time
> point is negative (e.g., r = -.29).  Yet, in most LMM models I run, the
> fixed effects estimate for P predicting N is positive.
>
> For example, including random effects for both intercept and slope (to
> account for within subject variation in each) using the following code
> yields a positive estimate for P.  This is also true if I include only a
> random effect for the intercept or a random effect for the slope.
>
> long <- lmer (N ~ P + (1 + P | ID), data = lip)
>
> Fixed effect estimate (SE), Z
> Intercept = 46.9 (4.38), 10.68
> P = 2.99 (.57), 5.19
>
> The only way I obtain a negative estimate for P is when I include
> duration/time in the model and a random effect for duration/time, but
> exclude the random effect for P AND exclude the random intercept.
>
> long <- lmer (N ~ P + time +  (1 + time | ID), data = lip)
>
> Fixed effect estimate (SE), Z
> Intercept = 73.99 (2.17), 34.09
> Time = .18 (.06), 2.84
> P = -1.01 (.28), -3.51
>
> Besides the fact that I'm not really interested in the structure of N over
> time, and thus seemingly do not need a duration/time parameter, there is
> substantial variation in the intercept and slope for N by P for which
> random effects would be needed.
>
> It is my understanding, perhaps wrong, that the fixed effect parameter
> estimate for P should be akin to the average association between N and P
> across time. Thus, this parameter estimate should be negative, regardless
> of whether or not duration/time is included in the model. Indeed, plotting
> N by P without consideration of duration/time reveals a negative average
> regression slope.
>
> I'm at a loss and could use some help.
>
> Thank you,
>
> Matt
>
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