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st: How to model a positive continuous dependent variable with many zeros?


From   Adriaan Hoogendoorn <aw.hoogendoorn@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: How to model a positive continuous dependent variable with many zeros?
Date   Tue, 31 May 2011 09:24:01 +0200

Dear Statalisters,

I try to run regression models for two dependent variables that
concern the seclusions of psychiatric patients:
y1 = the number of seclusion incidents and y2 = the seclusion duration.
Fortunately (at least from the patients perspective), there are many zeroes.
I successfully applied a Poisson model (xtpoisson) to model the number
of seclusion incidents
for patients (level 1) in different clinics (level 2)
taking exposure time t (the time that a psychiatric patient spent in
the clinic) into account:
xtpoisson y1 x1 x2 x3, re exposure(t)

I am running into problems when I try modeling the duration of seclusions.
Because of the many zeroes (85%) and the successful analysis of the
number of seclusion incidents, I applied the xtpoisson model for the duration
variable as well. Obviously duration it is not exactly a count variable,
but I can count the number of hours within the duration, or the number
of days, can’t I? So I estimated the duration counting  the number of hours.

The problem appears when I alternatively estimate the duration by counting
the number of hours. I seem to get different model estimates for duration when
I count the number of days than when I count the number of hours. In fact,
not so much the parameter estimates change, but their significance levels
are very sensitive to the scale (days or hours or even minutes) on which
duration is measured.

It appears that in
xtpoisson y2 x1 x2 x3, re exposure(t)
it does not matter if “t” is measured in days or hours, but it does
matter if the duration “y2” is measured in days, hours or minutes.

So my trick of counting days or hours seems to fail, and modeling
seclusion duration by a poisson model seems not a good idea.
Therefore my question to you is: do you know of a model that can deal
with a positive continuous dependent variable (duration) with many
zeros?

Kind regards,
Adriaan Hoogendoorn
GGZ inGeest, Amsterdam

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