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

[Matthew Boden]

Ben and Theirry,

You were both absolutely correct.  Thank you much for the help!

Matt

On Fri, Apr 8, 2016 at 7:54 AM, Matthew Boden <matthew.t.boden at gmail.com>
wrote:

> 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
>>>>
>>>>     [[alternative HTML version deleted]]
>>>>
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>>>>
>>>
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>>
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