-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-
bounces at r-project.org] Namens Giancarlo Sadoti
Verzonden: maandag 17 oktober 2011 8:40
Aan: r-sig-mixed-models at r-project.org
Onderwerp: [R-sig-ME] longitudinal analysis of nested samples
Greetings list,
I'm helping a colleague with an analysis of spatially-clustered longitudinal
data. ?She is interested in testing for change in vigor (V) in a set of trees over
time.
In each of 5 years (YR), 4 trees (TR) were measured per point, 10 points (PT)
were measured along a transect. There may be two additional levels (transect
and site), but let's just consider one site on one transect for now. ?V is normally-
distributed, fyi.
My (basic) understanding of longitudinal models suggests I use the following
model formulation (using lme4):
lmer(V ~ YR + (YR|TR), data=TREES)
Linear mixed model fit by REML
Formula: V ~ YR + (YR | TR)
? ?Data: TREES
? AIC ?BIC logLik deviance REMLdev
?1423 1449 -705.5 ? ? 1415 ? ?1411
Random effects:
?Groups ? Name ? ? ? ?Variance ? Std.Dev. Corr
?TR ? ? ? (Intercept) 0.00247886 0.049788
? ? ? ? ? YR ? ? ? ? ?0.00081403 0.028531 -0.065
?Residual ? ? ? ? ? ? 0.71588684 0.846101 Number of obs: 560, groups: TR, 1
Fixed effects:
? ? ? ? ? ? ?Estimate Std. Error t value
(Intercept) 206.17857 ? 35.89736 ? 5.744 YR ? ? ? ? ? -0.10107 ? ?0.03367 ?-3.002
Correlation of Fixed Effects:
? ?(Intr)
YR -0.531
The model indicates a negative trend in vigor over time. However, this only
addresses the first level in the hierarchy (TR), if I wanted to address within-point
variance in vigor, would I simply add a random intercept for point (1|PT)? (see
below) Likewise, if I had additional levels of sampling (e.g. transect [TR]), would
adding (1|TR) be appropriate?
lmer(V ~ YR + (YR|TR) + (1|PT), data=TREES)
Linear mixed model fit by REML
Formula: V ~ YR + (YR | TR) + (1 | PT)
? ?Data: TREES
? AIC ?BIC logLik deviance REMLdev
?1326 1356 -655.8 ? ? 1309 ? ?1312
Random effects:
?Groups ? Name ? ? ? ?Variance ? Std.Dev. ?Corr
?PT ? ? ? (Intercept) 1.4817e-01 0.3849224
?TR ? ? ? (Intercept) 2.8743e-03 0.0536120
? ? ? ? ? YR ? ? ? ? ?1.2003e-06 0.0010956 0.271
?Residual ? ? ? ? ? ? 5.7145e-01 0.7559429 Number of obs: 560, groups: PT, 11; TR,
1
Fixed effects:
? ? ? ? ? ? ?Estimate Std. Error t value
(Intercept) 206.16368 ? 32.07247 ? 6.428 YR ? ? ? ? ? -0.10107 ? ?0.01601 ?-6.313
Correlation of Fixed Effects:
? ?(Intr)
YR -0.998
It appears V varies between points (PT), and the model is much improved. ?Is this
the correct route?
Many thanks, and pardon me if this has been asked previously.
Giancarlo