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

[Ben Pelzer]

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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