On 13/07/19 10:54 AM, Spencer Graves wrote:
Hello:
What do you suggest I do about modeling random truncation?
Good question! Probably the best answer is "Give up and go to the pub!" :-)
But seriously, there is a package DTDA on CRAN which purports to analyse
randomly truncated data.
I have data on a variable Y in strata S[0], S[1], ..., S[n],
where Y is always observed in S[0] but is less often observed in the
other strata. I assume that the probability of observing Y is a
monotonically increasing function of Y and a monotonically decreasing
function of d[i] = the distance from S[0] to S[i].
There is a section on "random truncation" in the Wikipedia
article on "Truncated distribution".[1] It would be nice if I had an R
package that would make it relatively easy to model the truncation as a
function of "d" and / or publication that described someone doing it in
R. (I also have a couple of other variables that influence the
distribution of Y.)
Thanks,
Spencer Graves
[1] https://en.wikipedia.org/wiki/Truncated_distribution#Random_truncation
I'd just like to add that many many years ago, probably back before you
were born, I struggled mightily for a while with random truncation,
modelling the truncation variable to have a density that was uniform on
some interval [a,b].
I took the underlying ("untruncated") variable to have a Gaussian
distribution N(mu,sigma^2).
The distribution of the randomly truncated variable has thus four
parameters: a, b, mu and sigma. I was able to write down the likelihood
and attempted to maximise it, but this was a nightmare since the partial
derivatives of the log likelihood are undefined for b=x_i where x_1,
..., x_n are the i.i.d. observations from the randomly truncated
distribution. I fought with this for a long while, could not get
estimates based on simulated data to agree at all well with the true
values, and eventually chucked it all in.
This all happened back before there was R, or even S!!!
Let us hope that the authors of DTDA are far clever than I. (Not at all
unlikely!)
cheers,
Rolf
--
Honorary Research Fellow
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276
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