# Re: st: What is this problem called?

 From "Austin Nichols" To statalist@hsphsun2.harvard.edu Subject Re: st: What is this problem called? Date Sat, 17 Nov 2007 12:30:21 -0500

```Kieran McCaul <kamccaul@meddent.uwa.edu.au> :

This is an interesting problem, and I have been thinking about a
related one.  Let me rephrase your question, and you can see if I
correctly understand your research problem.  You observe outcome y_t
at times {1,2,...T}, possibly for a set of individuals {1,2,...N}
making up NT observations y_it in a panel regression of y on no
covariates.  Now you want to estimate both the mean of y_i and the
variance of y_i at each point in time t. Yes?

Presumably in your example of operation times, the mean and variance
are both falling over time, perhaps exponentially with a form like
mean(y_t)=a+b*exp(-c*t) and var(y_t)=d+e*exp(-f*t) so both are
asymptotically approaching some lower bound>0.  In this case, I'm not
sure we can speak of the operation time having "stabilized" at some
level, but we can speak of the variance reaching some percentage of
its average perhaps.

Assuming you have panel data, I think you can use -xtmixed- to
estimate the mean and var of y at each point in time (see
http://www.stata-journal.com/abstracts/st0095.pdf for discussion).  If
you have only time-series data on one doctor's surgeries, or you
believe each doctor has an essentially independent trajectory and
therefore do not want to exploit the panel structure, it becomes
harder.

Before I ramble on, perhaps you can clarify the nature of the data you
will have and what kinds of assumptions you are willing to make about
the DGP.

On 11/16/07, Kieran McCaul <kamccaul@meddent.uwa.edu.au> wrote:
> ... The interest
> is not in the time it takes to perform a procedure, but the variation in
> procedure times.  For example, if 200 procedures were performed, there
> might be little difference in the average time for the first 50
> procedure compared to the last 50 procedures.  I suspect, though, that
> there might be a large difference in the variance of these times.  It's
> the change in variance as more procedures are performed that's of
> interest.
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