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Model description
The orange data were considered by
Millar (2004, Aust NZ J. Stat, 46, p. 543-554).
A "day effect" (v) was added to the original model formulation, yielding
yij = f1,ij
/(1 + exp[-(t-f2)/f3])
] + eij,
f1,ij
= f1 + ui + vj
where u is a tree-effect and v is a day-effect. 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 2-3 lines of extra code in the ADMB-RE 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 |
ADMB-RE |
SD |
f1 |
195.9 |
14.5 |
196.2 |
19.4 |
f2 |
747.6 |
59.1 |
748.4 |
62.3 |
f3 |
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.
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