Using the 'line' example as a a context, I recently asked whether there
was a way to weight GLMs by sample sizes. David Spiegelhalter kindly
suggested that the precisions be made to incorporate the weight
information, such that:
y[i] ~ dnorm(mu[i], tau.y[i]) #Note: precision names must be changed
tau.y[i] <- weight[i]*tau #slightly to allow compilation
A brief analysis shows that this indeed does seem to solve the problem.
The point estimates appear below (he BUGS runs follow the oft-used 1000
burn-in, 5000 iterations format).
Case I: unweighted line data
BUGS SPSS
intercept .5968 .6000
slope .7952 .8
Case II: weighted line data - each data point weighted to have an
effective N of 1000
BUGS SPSS
intercept .5968 .6000
slope .7952 .8
Case III: weighted line data - first data point weighted to have an
effective N of 10, remaining weighted to have an effective N of 1000
BUGS SPSS
intercept 1.367 1.380
slope .6045 .605
The dispersion estimates were generally comparable as well. Many thanks
to David!
Best,
-Gene Hahn
George Washington University
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