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ADMB Files for simpler model
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Running ADMB-executables
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In a DOS window
Under linux
Command line options:
-l1 10000000 -l2 100000000
-l3 10000000 -nl1 10000000
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Results: Computation times
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ADMB-RE: 27 seconds.
WinBUGS: 700 seconds.
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Model Description
The negative binomial mixed model can be used instead of the poisson regression
to investigate whether there is overdispersion in the data, that is whether the
variance of the obsevations is greater than that which would be
expected for a poisson distributed random variable. Parameter estimation for such models is generally claimed to be difficult. See for example
R-help the mailing list archives of the statistical modeling language R.
The data used in this example are the epilepsy data considered in
Venables and Ripley
Modern applied statics with S 4th edition.
and by Booth et al.
Negative Binomial Loglinear Mixed Models.
Comparison with SAS NLMIXED
Booth et al. attempt to fit two negative binomial loglinear
mixed models to the data, the "full model" and a simpler
model. for the full model they report:
The fit of the full negative binomial model using NLMIXED was very unstable. Different starting values led to different estimates and very different standard errors.
Booth et al also apply a "Monte Carlo EM algorithm to the full model
and report:
Application of the MCEM algorithm in this problem suggest that the random slope is 0.
The MCEM algorithn was run for a large number of iterations with all of
the estimates except for slope variance and the covariance converging quickly.
These latter two estimates appear to be slowly convergin toward 0.
We coded the full model in ADMB-RE and noted quick convergence (15 seconds) with
the slope parameter converging to 0. However if the variance of the slope parameter is 0 then the covariance parameter is undefined so we removed that parameter
and fit the model again. This model converged quickly (15 seconds) to
the ML estimates. We used different starting values to investigate the
stability of the model and found that it conveged to the same values
each time. Thus is would appear that the performance of
ADMB-RE is superior to SAS NLMIXED
for this problem.
The ADMB-RE code
The R (S-Plus) script used to generate data in the input
format for both WinBUGS and ADMB-RE can be found here: logistic.s.
You can modify this script to generate new datasets.
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