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Re: st: Modeling repeated events with a continuous outcome


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Modeling repeated events with a continuous outcome
Date   Thu, 4 Jun 2009 11:54:26 -0400

Ian Sue Wing <isw@bu.edu> :
How about -poisson- or -glm- with location fixed effects (and cluster
by location)?

Who is doing the investing?  Multiple agents or one?  Are people
choosing from a finite set of locations to make a required investment,
or picking a level of investment in each place more or less
independently of their investments in other places?  Do you have
time-varying characteristics of locations and investors?  You might
want to hook up with an economist who runs this kind of model (there
are a lot of them in your town) and is willing to discuss empirical
strategies (fewer of those, I guess).  Or google "fdi location" or
somesuch to get a sense of what some folks do.  The trouble is, there
are a hundred different theoretical and statistical models that might
fit what you describe below, and the empirical strategy should fit
what you believe to be true about the data-generating process, and
that last part comes from theory.

You can relax the assumptions of -poisson- with fixed effects and
robust SE in several directions, but I assert without proof that it is
a good starting point.  You model expected investment in location i at
time t E(y_it) as a function exp(Xb) so you get estimates of point
elasticities or semi-elasticities. My guess is that a dollar of
investment is not much different than zero in your setting; if that is
not true, maybe a different type of model is in order.

On Thu, Jun 4, 2009 at 12:10 AM, Ian Sue Wing <isw@bu.edu> wrote:
> 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.
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