Many thanks to all those who offered their advice regarding my problem
concerning differences in parameter estimates when a replicated-data node was
included. My apologies to David, Andrew, Finn, and others that asked
for a simple version of my model, though I am happy to say that I was
unsuccessful in constructing a simple version that illustrated my problem
because the in the interim, Finn Krogstad passed on a message that led me to the
answer. Here is the message he sent:
If it is true that "I've found that in
my complex model, the inclusion
of the "generated data" node seriously
affects the estimates of the
parameters" then you are doing something
seriously wrong. Inclusion of
the generated data nodes should have no
impact on the assympotic
distribution of the model parameters.
Either
-your generated data nodes are not just generated data, and you
are
doing something that you are not describing, or more likely
-you
are not achieving convergence, and what you are really seeing is
two
equally valid but different simulation paths for converging on the
true
distribution. The further you run them, the more similar they
should
become, but they will become identical only in asymtopia.
In such
situations, I like to run a 'stripped down' version of the
problem (below)
so I can study the question (e.g. does adding
uninstantiated posterior
predictive nodes alter the posterior parameter
distributions?).
If the two models converge with longer runs, then the second
explanation
is true, if not then the first is true, and you should probably
take
another look at the structure of your model (you might want to send
a
copy).
I think the latter is true - my model had
not converged. It was a matter of both running longer chains
(unfortunately, BUGS tends to crash for me when I run long chains of complex
models and then ask for stats) and having a longer burn-in
sequence. Altering either chain length or burn-in length had
little effect, but increasing both led me to see the theoretically-expected
results.
Again, my thanks to those
who offered their time and thoughts, and of course to those who make
the BUGS mailing list possible.
Roy Levy
Graduate Student
Department of Measurement, Statistics,
and Evaluation
University of Maryland
College Park, MD USA
20742