
Model description
The orange data were considered by
Millar (2004, Aust NZ J. Stat, 46, p. 543554).
A "day effect" (v) was added to the original model formulation, yielding
y_{ij} = f_{1,ij}
/(1 + exp[(tf_{2})/f_{3}])
] + e_{ij},
f_{1,ij}
= f_{1} + u_{i} + v_{j}
where u is a treeeffect and v is a dayeffect. This is an example of a model where
the random effects u and v are crossed. Such models cannot easily be fit in nlme
(Pinheiro & Bates, 2000), while the inclusion
of the random effect v requires only 23 lines of extra code in the ADMBRE program.
Comparison with Millar (2004)
Millar (2004) used simulated likelihood to evaluate the marginal likelihood.
The following table shows a comparison of point estimates and standard deviations (SD):

Millar 
SD 
ADMBRE 
SD 
f_{1} 
195.9 
14.5 
196.2 
19.4 
f_{2} 
747.6 
59.1 
748.4 
62.3 
f_{3} 
352.7 
32.0 
352.9 
33.3 
Var(e 
28.1 
8.2 
28.1 
8.2 
Var(u) 
1059.8 
684.5 
1061.0 
687.6 
Var(v) 
109.1 
88.8 
109.9 
90.7 
The differences between the two approaches are minor.
