Longitudinal covariation parameter estimate does not match average association over time
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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