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

[Matthew Boden]

Thank you, Thierry and Ben!  I will do this immediately.

Matt

On Fri, Apr 8, 2016 at 3:58 AM, Ben Pelzer <b.pelzer at maw.ru.nl> wrote:

> Hi Matthew,
>
> There was a type in my previous mail, at the end. I switched "negative"
> and "positive", so it should:
>
> The parameter of Pdev could be positive and the one of Pmean negative,
> showing that the (***positive) within-subject effect of P differs from the
> (***negative) between-subject effect.
>
> Ben.
>
>
> On 8-4-2016 12:04, Ben Pelzer wrote:
>
>> 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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>>>
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>>>
>>
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