[R] Confidence intervals for rates (dependent events)

[Dirk Enzmann]

I need advice or opinions for the following problem:

In a sample a part of the respondents has 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 experienced events / number of reported events.

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,

binom.test(0,13,0/13)

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?

(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, 
for example by using nb.glm?

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 at jura.uni-hamburg.de
www: 
http://www2.jura.uni-hamburg.de/instkrim/kriminologie/Mitarbeiter/Enzmann/Enzmann.html