st: Modeling repeated events with a continuous outcome

[Ian Sue Wing <isw@bu.edu>]

Dear Statalisters,

This posting is as much a plea for basic statistical advice as it is for 
assistance with Stata, so I apologize in advance.

I am trying to model the correlates of the timing and severity of 
repeated events, in particular, how a particular type of investment at a 
number of locations responds to local economic conditions over several 
years. Investment occurs in "bursts". At given location there are 
typically intervals of several years with zero investment, followed by 
one year in which investment takes place. The quantity of investment, 
which I seek to model, varies both across locations, and, for the ~10% 
of locations where I investment occurs multiple times (< 4), over years. 
My covariates are measured as panel data, with no censoring.

Is anyone familiar with a statistical model which is appropriate for 
this kind of process? I have looked for clues the medical literature, 
and the closest fit I could find is a survival model of headache 
incidence in which the outcome is classified into ordered categories:

Berridge D M; Whitehead J (1991). Analysis of failure time data with 
ordinal categories of response. Statistics in medicine 10:1703-10.

I am currently awaiting a copy of this article via interlibrary loan, 
but I fear that adapting such a framework to deal with continuous data 
is beyond my competence. Looking closer to home, I could use -heckman- 
or -selmlog- to estimate a linear model with site and year fixed effects 
that controls for selection, but I am unclear whether these methods are 
able to capture the *cumulative* impact of the covariates on the hazard 
of event occurrence over the span of the inter-investment intervals. I 
can also average my covariates over these intervals, convert my dataset 
to spell format, and estimate a survival model, but this only solves 
half the problem. The issue then is how to use the results of the 
survival analysis to account for fact that the covariates jointly 
influence both the selection hazard *and* the magnitude of investment 
once it occurs, e.g., through a quantity like the Inverse Mills Ratio in 
-heckman, twostep-.

Is this actually a simple problem that my own lack of statistical acumen 
is making too complicated? It is hard for me to imagine that someone 
hasn't dealt with a similar question before, and there must be something 
simple that can be done short of developing and estimating an entire 
structural DP model (which in this case is like Rust's (1987) bus engine 
replacement model with engines of different sizes!). Any guidance from 
more experienced and able researchers would be greatly appreciated.

Thanks,

-i

--
Ian Sue Wing                      675 Commonwealth Ave., Boston MA 02215
Associate Professor               Tel: (617) 353-5741
Dept. of Geography & Environment  Fax: (617) 353-5986
Boston University                 Web: http://people.bu.edu/isw

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