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st: Confidence intervals for rates (dependent events)


From   Dirk Enzmann <dirk.enzmann@jura.uni-hamburg.de>
To   statalist@hsphsun2.harvard.edu
Subject   st: Confidence intervals for rates (dependent events)
Date   Wed, 09 Feb 2005 16:57:01 +0100

This is not a specific stata question, but I don't know where to look for an answer to the following problem (perhaps it is too easy but I can't see it):

In a sample a part of the respondents have experienced victimizing events. Only a part of these events have been reported to the police. The rate of events reported to the police is

number of reported events / number of experienced events.

For example, 13 of 267 respondents have experienced a victimizing event, none of them did report it to the police, thus the rate of events reported is 0 % (here I am talking of events, not individuals!)

Because the events cannot be assumed to be independent (some victims have a high rate of vicitimization because they are more prone to become a victim) the construction of a confidence interval for the rate of events reported becomes difficult (to me).

Question 1: If nevertheless a use a binomial test to construct a confidence interval (say: 0 of 13 events reported, 95% CI = 0 to 24.7%), is it correct that the width of this interval is a lower bound and thus a conservative estimate?

Question 2: (a) My intuition tells me that multilevel modeling could be a solution to obtain a correct confidence interval by treating the events and the events reported as the first level and the victims as the second. Is this correct and how should I specify this model to obtain a confidence interval?

(b) Alternatively, could I treat the events (and events reported?) as coming from a negative binomial distribution and use this for constructing a confidence interval? How can this be done technically?

(Apart from constructing confidence intervals I would like to test the rate of reporting for different subgroups or different kind of events.)

Thanks in advance,
Dirk

*************************************************
Dr. Dirk Enzmann
Institute of Criminal Sciences
Dept. of Criminology
Schlueterstr. 28
D-20146 Hamburg
Germany

phone: +49-040-42838.7498 (office)
+49-040-42838.4591 (Billon)
fax: +49-040-42838.2344
email: dirk.enzmann@jura.uni-hamburg.de
www: http://www2.jura.uni-hamburg.de/instkrim/kriminologie/Mitarbeiter/Enzmann/Enzmann.html
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