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st: Modeling repeated events with a continuous outcome


From   Ian Sue Wing <isw@bu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Modeling repeated events with a continuous outcome
Date   Thu, 04 Jun 2009 00:10:38 -0400

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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