[Limdep Nlogit List] Interpretation of Random coefficients ordered logit parameters
William Greene
wgreene at stern.nyu.edu
Thu Feb 21 23:51:45 AEDT 2019
Achilleas. It's misleading to consider the intervals in the centipede plot
"confidence intervals."
The "confidence" aspect of a confidence interval relates to type 1 error
induced by sampling
variability. The intervals in the centipede plot are probability intervals
from the conditional
distribution. In a Bayesian context, they would be called HPD intervals.
Regards
Bill Greene
On Thu, Feb 21, 2019 at 7:30 AM Achilleas' gmail via Limdep <
limdep at mailman.sydney.edu.au> wrote:
> Dear Prof. Greene,
>
> I agree about KDE but from its shape I (probably wrongly) expected that the
> confidence interval of some coefficients would be away from zero.
>
> The centipede plot is exactly what I need to show and actually it is the
> reason I started this thread. The plot shows observations around the
> horizontal axis and long lines (conf. intervals) that include zero in all
> observations. My worry was that this picture was not compatible with a
> stat.significant estimate unconditional standard deviation and might
> indicate random noise.
>
> I understand this is not the case so I will stick to individual-specific
> means and SD's to judge the effect of X1, X2.
>
> Thank you for your detailed reply.
>
> Best,
> Achilleas
>
> -----Original Message-----
> From: Limdep <limdep-bounces at mailman.sydney.edu.au> On Behalf Of William
> Greene via Limdep
> Sent: Thursday, February 21, 2019 13:04
> To: Limdep and Nlogit Mailing List <limdep at mailman.sydney.edu.au>
> Cc: William Greene <wgreene at stern.nyu.edu>
> Subject: Re: [Limdep Nlogit List] Interpretation of Random coefficients
> ordered logit parameters
>
> Achilleas. Your KDE is plotting the variation of the means of the
> conditional distributions across the individuals in the sample. From what
> you describe it sounds like you seek the range of variation of the within
> individual distributions (that is, the conditional distributions).
> There is a discussion of "centipede plots" in your manual that does this
> sort of thing. You might search for that material and see if it does what
> you are looking for. It uses the individual specific means and conditional
> standard deviations.
> Regards,
> Bill Greene
>
> On Thu, Feb 21, 2019 at 1:12 AM Achilleas' gmail via Limdep <
> limdep at mailman.sydney.edu.au> wrote:
>
> > Dear Prof. Green,
> >
> > Thank you for your reply. Indeed my statement was confusing the way I
> > worded it. What I meant is that the conf. intervals of the conditional
> > estimates include zero and the lower (upper) bounds are strictly
> > negative (positive) for all individuals.
> >
> > So your last statement " Some of the distribution may be near zero
> > while more of the distribution may be quite far from zero " (which was
> > what I also
> > expected) does not show itself in my data.
> >
> > When I plot the unconditional estimates with a kernel density plot, I
> > see that only a small part of the tail is below zero as expected.
> >
> > Could this be an indication of random noise that is captured by the
> > model as a distribution of population coefficients ?
> >
> > Best,
> >
> > Achilleas
> >
> > -----Original Message-----
> > From: Limdep <limdep-bounces at mailman.sydney.edu.au> On Behalf Of
> > William Greene via Limdep
> > Sent: Thursday, February 21, 2019 06:11
> > To: Limdep and Nlogit Mailing List <limdep at mailman.sydney.edu.au>
> > Cc: William Greene <wgreene at stern.nyu.edu>
> > Subject: Re: [Limdep Nlogit List] Interpretation of Random
> > coefficients ordered logit parameters
> >
> > Achilleas: Considering X1, your results suggest that the population
> > distribution of coefficients on X1 has a normal distribution with mean
> > of
> > 0.12776 and a standard deviation of 0.62482.
> > Interpretations of "statistical significance" in this context are
> > ambiguous.
> > The statement
> >
> > However, when I look at the individual specific (conditional)
> > estimates, I find a strong indication of their effect being zero for all
> (i.e.
> > confidence
> > intervals for all individuals are way far from zero on both ends)
> >
> > is contradictory. It seems to state that the effects are close to
> > zero, but confidence intervals are far from zero. What is true is
> > that the conditional estimates will vary around the mean of 0.12276.
> > The mean of the conditional estimates should equal the unconditional
> > estimate.
> > The conditional standard deviations that are estimable will all be
> > less than the 0.62482, and the average of these conditional standard
> > deviations will also be strictly less than 0.62482.
> > Characterizations of the distribution of random parameters should not
> > be based on "confidence intervals." Some of the distribution may be
> > near zero while more of the distribution may be quite far from zero.
> >
> > /Bill Greene
> >
> >
> >
> > On Wed, Feb 20, 2019 at 2:07 PM Achilleas' gmail via Limdep <
> > limdep at mailman.sydney.edu.au> wrote:
> >
> > > Dear all,
> > >
> > >
> > >
> > > I'm estimating a Random Coefficients Ordered Logit Model with Y an
> > > ordered variable and X1 and X2 independent dummy vars:
> > >
> > >
> > >
> > > SETPANEL; GROUP=ID; PDS=ROUNDS $
> > >
> > > ORDERED ; PANEL ; Lhs = Y
> > >
> > > ; Rhs = ONE, X1, X2
> > >
> > > ; MODEL= LOGIT $
> > >
> > > ORDERED ; PANEL; Lhs = Y
> > >
> > > ; Rhs = one, X1, X2
> > >
> > > ; RPM
> > >
> > > ; par
> > >
> > > ; Fcn = one(n), X1(n), X2(n)
> > >
> > > ; HALTON
> > >
> > > ; MODEL= LOGIT $
> > >
> > >
> > >
> > > My results are as follows:
> > >
> > >
> > >
> > > |Means for random parameters
> > >
> > > Constant| 8.33434*** .85987 9.69 .0000 6.64903
> 10.01966
> > >
> > > X1 | .12776 .32251 .40 .6920 -.50436
> .75988
> > >
> > > X2 | -.03393 .33030 -.10 .9182 -.68131
> .61344
> > >
> > > |Scale parameters for dists. of random parameters
> > >
> > > Constant| 3.26244*** .22798 14.31 .0000 2.81560
> 3.70927
> > >
> > > X1 | .62482*** .21928 2.85 .0044 .19503
> 1.05460
> > >
> > > X2 | .78015*** .22758 3.43 .0006 .33409
> 1.22621
> > >
> > >
> > >
> > > My intuition is that for the X's, the results of the unconditional
> > > estimates mean that their effect is non-significant (i.e. zero) on
> > > aggregate but with strong individual variability (i.e. showing that
> > > for some individuals it is different from zero).
> > >
> > >
> > >
> > > However, when I look at the individual specific (conditional)
> > > estimates, I find a strong indication of their effect being zero for
> > > all
> > (i.e.
> > > confidence
> > > intervals for all individuals are way far from zero on both ends)
> > >
> > >
> > >
> > > Is my interpretation mistaken? And if not, how I can possibly
> > > explain the different conclusions I get from conditional vs
> > > unconditional
> > estimates?
> > >
> > >
> > >
> > > Thank you,
> > >
> > >
> > >
> > > Achilleas
> > >
> > >
> > >
> > > _______________________________________________
> > > Limdep site list
> > > Limdep at mailman.sydney.edu.au
> > > http://limdep.itls.usyd.edu.au
> > >
> > >
> >
> > --
> > William Greene
> > Department of Economics
> > Stern School of Business, New York University
> > 44 West 4 St., 7-90
> > New York, NY, 10012
> > URL: https://protect-au.mimecast.com/s/a3s5CQnzP0t1M2O8uxJ5Ie?domain=people.stern.nyu.edu
> > Email: wgreene at stern.nyu.edu
> > Ph. +1.212.998.0876
> > Editor in Chief: Journal of Productivity Analysis Editor in Chief:
> > Foundations and Trends in Econometrics Associate Editor: Economics
> > Letters Associate Editor: Journal of Business and Economic Statistics
> > Associate
> > Editor: Journal of Choice Modeling
> > _______________________________________________
> > Limdep site list
> > Limdep at mailman.sydney.edu.au
> > http://limdep.itls.usyd.edu.au
> >
> >
> > _______________________________________________
> > Limdep site list
> > Limdep at mailman.sydney.edu.au
> > http://limdep.itls.usyd.edu.au
> >
> >
>
> --
> William Greene
> Department of Economics
> Stern School of Business, New York University
> 44 West 4 St., 7-90
> New York, NY, 10012
> URL: https://protect-au.mimecast.com/s/a3s5CQnzP0t1M2O8uxJ5Ie?domain=people.stern.nyu.edu
> Email: wgreene at stern.nyu.edu
> Ph. +1.212.998.0876
> Editor in Chief: Journal of Productivity Analysis Editor in Chief:
> Foundations and Trends in Econometrics Associate Editor: Economics Letters
> Associate Editor: Journal of Business and Economic Statistics Associate
> Editor: Journal of Choice Modeling
> _______________________________________________
> Limdep site list
> Limdep at mailman.sydney.edu.au
> http://limdep.itls.usyd.edu.au
>
>
> _______________________________________________
> Limdep site list
> Limdep at mailman.sydney.edu.au
> http://limdep.itls.usyd.edu.au
>
>
--
William Greene
Department of Economics
Stern School of Business, New York University
44 West 4 St., 7-90
New York, NY, 10012
URL: https://protect-au.mimecast.com/s/a3s5CQnzP0t1M2O8uxJ5Ie?domain=people.stern.nyu.edu
Email: wgreene at stern.nyu.edu
Ph. +1.212.998.0876
Editor in Chief: Journal of Productivity Analysis
Editor in Chief: Foundations and Trends in Econometrics
Associate Editor: Economics Letters
Associate Editor: Journal of Business and Economic Statistics
Associate Editor: Journal of Choice Modeling
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