# 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).