# [R-sig-ME] help interpreting variance estimate in nlmer

robert denham rjadenham at gmail.com
Tue Oct 16 02:19:48 CEST 2012

```Hi,
just a quick question to try and help me understand the
interpretation of the variance part of a non-linear mixed effects
model.
If I use the orange tree example like:

nm1 <- nlmer(circumference ~ SSlogis(age,Asym, xmid, scal) ~ Asym|Tree,
Orange, start=c(Asym=192,xmid=770, scal=120),
corr=FALSE)

I get:

> summary(nm1)
Nonlinear mixed model fit by the Laplace approximation
Formula: circumference ~ SSlogis(age, Asym, xmid, scal) ~ Asym | Tree
Data: Orange
AIC  BIC logLik deviance
1901 1908 -945.3     1891
Random effects:
Groups   Name Variance  Std.Dev.
Tree     Asym 53986.025 232.349
Residual         52.868   7.271
Number of obs: 35, groups: Tree, 5

Fixed effects:
Estimate Std. Error t value
Asym   192.04     104.09   1.845
xmid   727.89      31.97  22.771
scal   347.97      24.42  14.252

So a single random effect for the asymptote. The values of these for
each tree are:
> ranef(nm1)
\$Tree
Asym
3 -37.925218
1 -30.143951
5  -5.299054
2  32.352094
4  41.016208

But the estimated variance/sd of this seems very large (sd=232.349).
Should we be able to interpret the estimates as the random effect term
for the asymptote is distributed N(0,232.349) and that the estimated
random effects should look like they come from this distribution?

Basically, I don't really understand the relationship between the
distribution of ranef(nm1)\$Tree and the estimated std.dev of the tree
(232.349). I would love it if someone could help explain it.

Thanks
Robert

```