[R] Random effects and level 1 censoring

[John Logsdon]

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