A logistic growth curve model with random effects;
A comparison with NLME



ADMB Files
Code: orange.tpl
Data: orange.dat
Initial values: orange.pin
Expected Results: orange.par

Model description

A growth curve model was fitted to the "orange tree" data by Pinheiro & Bates (2000, Ch.8.2) as an illustration of the R (S-Plus) routine nlme. The logistic growth curve is given as

y = f1 /(1 + exp[-(t-f2)/f3]) ] + e,

where y is the response and t is the age of the three. The regression parameters to be estimated are: f1, f2 and f3, and e is the residual error term. A random effect u is added to the parameter f1. A full description of the model can be found here: orange.pdf.

Comparison with nlme

Parameter estimates are shown in the following table.
  f1 f2 f3 SD(e) SD(u)
ADMB-RE 192.1 727.9 348.1 7.843 31.65
Std. dev. 15.658 35.249 27.08 1.013 10.26
nlme 191.0 722.6 344.2 7.846 31.48
The difference between the estimates obtained with ADMB-RE and nlme is small. The difference is caused by the fact that the two approaches use different approximations to the likelihood function. (ADMB-RE uses the Laplace approximation, and for nlme the reader is referred to (Pinheiro & Bates, 2000, Ch. 7).