[R] Random intercept-slope correlation (nlme)

[Spencer Graves]

      I'm not certain I understand your question.  Consider the 
following modification of an example in the 'nlme' help file: 

 > fm1 <- nlme(height ~ SSasymp(age, Asym, R0, lrc),
+    data = Loblolly, fixed = Asym + R0 + lrc ~ 1,
+    random = Asym ~ 1,
+    start = c(Asym = 103, R0 = -8.5, lrc = -3.3))
 > fm2.0 <- update(fm1, random = Asym+lrc~1)
 > intervals(fm2.0)
Approximate 95% confidence intervals

 Fixed effects:
         lower       est.      upper
Asym 96.628100 101.641181 106.654262
R0   -9.190750  -8.639571  -8.088392
lrc  -3.306517  -3.234895  -3.163273
attr(,"label")
[1] "Fixed effects:"

 Random Effects:
  Level: Seed
                    lower        est.      upper
sd(Asym)       3.09405131  5.86255879 11.1082824
sd(lrc)        0.03826032  0.07513534  0.1475502
cor(Asym,lrc) -0.95852796 -0.80525713 -0.2906845

 Within-group standard error:
    lower      est.     upper
0.5309562 0.6386604 0.7682122 

      Does this answer your questions?  If no, please provide commented, 
minimal, self-contained, reproducible code, as suggested in the posting 
guide "www.R-project.org/posting-guide.html".  If you are not already 
fairly familiar with Pinheiro and Bates (2000) Mixed-Effects Models in S 
and S-Plus (Springer), I suggest you spend more quality time with that 
book;  it will likely answer these questions and many more.  I also 
suggest you make a local copy of 'simulate.lme' and modify it so it will 
simulate model(s) of interest to you and save the results you care about. 

      Hope this helps. 
      Spencer Graves

Antonio Revilla wrote:
> Dear list members,
>
> I am working with a multilevel growth curve, that in its simplest form goes 
> like follows:
>
> Yit = Ai + Bi t + eit   (the error term is assumed to follow an AR(1) 
> autorregressive process)
>
> One major topic in my research is the convergence in the values of Y over 
> time. Thus, I am interested in the relationship between the random effects 
> for the intercept and the slope, and I have a couple of questions about 
> this:
>
> First, I have fitted the model using the nlme library in R, and the 
> estimates for the random effects yield a correlation of -0.27. However, if I 
> take values for random intercepts and slopes from the lme model, and run a 
> correlation (or a regression) between them, I get a slightly positive 
> relationship (R~ 0.02). How can this difference be explained?
>
> Second, I am also interested in the size of the relationship between 
> intercept and slope. In other terms, in the rate of convergence. In order to 
> analyze this, does it make any sense if use the values from my 
> random-effects model and run an OLS regression using subject-specific 
> intercepts as a covariate to explain subject-specific slopes? The results I 
> mention above meake me suspicious about this, but I still do not know if it 
> would be correct from a statistical standpoint.
>
> Thanks a lot,
>
> Antonio
>
> _________________________________________________________________
> Moda para esta temporada. Ponte al día de todas las tendencias.
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>