[Limdep Nlogit List] Interpretation of Random coefficients ordered logit parameters

[Achilleas' gmail]

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
>
>
>
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>
>

--
William Greene
Department of Economics
Stern School of Business, New York University
44 West 4 St., 7-90
New York, NY, 10012
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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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