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Re: st: Fixed effects ordinal probit regression


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Fixed effects ordinal probit regression
Date   Fri, 05 Sep 2003 09:46:10 +0100 (BST)

James,

Quoting Joseph Coveney <jcoveney@bigplanet.com>:

> James Shaw wrote:
> 
> > I was wondering if there is such a thing as fixed effects ordinal
> probit
> > regression.  If so, could one simply add dummy variables for the
> panel
> > indicator (e.g., subject id) to the ordinal probit model to obtain
> fixed
> > effects estimates?  Also, when estimating a fixed effects
> regression model
> > with a subject-level effect, how problematic is it if there are
> missing
> > observations on the dependent variable for some subjects (i.e.,
> unbalanced
> > panels)?
> 
> -------------------------------------------------------------------------
---
> 
> By analogy to -areg , absorb()-, it seems feasible to create dummy
> (indicator) variables for the panel identifier with -oprobit-, but
> doing
> this in an ordered categorical regression risks having "note: [X]
> observations completely determined.  Standard errors questionable."
> at the
> bottom of the -oprobit- output.  This would raise suspicions about
> Wald
> tests, although in a test case that I tried out where this happens
> (see
> do-file below), the Wald test agrees well with the corresponding
> likelihood
> ratio test.  If panels are dropped due to collinearity in fitting
> the full
> model, then likelihood-ratio testing with the reduced (nested)
> models is
> problematic unless the same panels are fortuitously dropped in the
> latter.
> 
> When observations are missing, handling the panel as a fixed effect
> seems to
> be mechanically possible--in the test case, -oprobit- attained
> convergence
> and didn't seem to drop any panels with a missing value--but it
> might be
> worthwhile to perform Monte Carlo simulations in order to determine
> whether
> hypothesis testing and parameter estimates behave as expected in
> such a
> circumstance before using -oprobit- on an unknown dataset with
> missing
> observations.
> 
> -oprobit , cluster()- might serve as an alternative in some
> circumstances.
> With enough panels, another alternative would be to consider the
> panel as a
> random effect, and use -reoprob- or -gllamm-.
> 
> Joseph Coveney

There's another issue here as well, which is that a fixed effects ordered 
probit may not be consistent.

In a posting to the list back in June, Eduardo Nakasone quoted from the 
Stata manual:

"There is no command for a conditional probit fixed-effects model, as 
there does not exist a sufficient statistic allowing the fixed effects to 
be conditioned out of the likelihood. Unconditional fixed-effects probit 
models may be estimated with the probit command with indicator variables 
for the panels... However, unconditional fixed fixed-effect estimates are 
biased".

I haven't checked up on this, but I have strong suspicion that if a fixed 
effects probit is not consistent, then a fixed effects ordered probit 
won't be consistent either.

--Mark

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3008
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
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