I have a question about constructing the likelihood function where there
is censoring at level 1 in a two-level random effects sum.
In a conventional solution, the likelihood function is constructed using
the density for failures and the survivor function for (in this case,
right) censored results. Within (for example) an R environment, this is
easy to do and gives the same solution as survreg even if it is a little
heavy.
But where there is an hierarchical situation, we need to consider the
contributions at level 2.
y_ij=X_ij.beta'+err2_i+err1_ij
If all the units at level 1 for a given level 2 are censored, then the
information we have for the level 2 is itself censored and we should
presumably use the survivor function. Conversely if none of the units at
level 1 are censored, then the information at level 2 is complete and the
density should be used.
But what do we do if only some of the level 1 units for a given level 2
are censored? My instinct is to weight the density and survivor functions
for that given level 2 case according to the proportion of level 1
failures.
Am I right?
For a number of reasons I don't want to code for specific distributions
and I am quite happy to use a sledge hammer to crack a walnut with
optim().:)
Best wishes
John
John Logsdon "Try to make things as simple
Quantex Research Ltd, Manchester UK as possible but not simpler"
j.logsdon at quantex-research.com a.einstein at relativity.org
+44(0)161 445 4951/G:+44(0)7717758675 www.quantex-research.com
