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Re: st: Re: rank regression


From   John Antonakis <John.Antonakis@unil.ch>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Re: rank regression
Date   Mon, 24 Feb 2014 20:53:18 +0100

Rank ordering does not assume that the distance between the 1st and 2nd rank is equal to that of the 2nd and 3rd, and so on and so forth. That is what I mean by equidistant--if it were equidistant, it would make it "approximately" an interval measurement (instead of ordinal).

See:  http://en.wikipedia.org/wiki/Level_of_measurement

See also:

Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. 2012. When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3): 354-373.


Best,
J.

__________________________________________

John Antonakis
Professor of Organizational Behavior
Director, Ph.D. Program in Management

Faculty of Business and Economics
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor:
The Leadership Quarterly
Organizational Research Methods
__________________________________________

On 24.02.2014 19:32, R Zhang wrote:
Hi John,

what do you mean by rank ordering to be roughly equidistant? please
excuse my ignorance.

Rochelle

On Mon, Feb 24, 2014 at 2:05 AM, John Antonakis <John.Antonakis@unil.ch> wrote:
If the dependent variable is a rank, where rank ordering does not seem to be
roughly equidistant, then they should have used an ordinal probit or logisit
estimator: -oprobit- or -ologisit-. If the independent variables are in the
same boat (non equidistant), I would model them as dummies.

Best,
J.

__________________________________________

John Antonakis
Professor of Organizational Behavior
Director, Ph.D. Program in Management

Faculty of Business and Economics
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor:
The Leadership Quarterly
Organizational Research Methods
__________________________________________


On 24.02.2014 04:25, Joseph Coveney wrote:
Rochelle Zhang wrote:

a finance paper I was reading today uses rank regression , the author
states that they replace both the dependent variable and independent
variables by their respective ranks and evaluation the regression
using the ordinary least squares.

I searched "stata rank regression", and did not find anything. If you
have knowledge how to conduct such regression, please share.


--------------------------------------------------------------------------------

  From your description, it sounds like the authors of the finance paper
were just computing Spearman's correlation coefficient.  See the Spearman
section of the do-file's output below.

On the other hand, if there were two (or more) independent variables, then
they might have been doing what I call "Koch's nonparametric ANCOVA".  See
the last section of the output below.  You can read about it at this URL:
https://circ.ahajournals.org/content/114/23/2528.full and the references
cited there.  Scroll down until you come to the section that is titled,
"Extensions of the Rank Sum Test".

Joseph Coveney

. clear *

. set more off

. set seed `=date("2014-02-24", "YMD")'

. quietly set obs 10

. generate byte group = mod(_n, 2)

. generate double a = rnormal()

. generate double b = rnormal()

.
. *
. * Spearman's rho
. *
. egen double ar = rank(a)

. egen double br = rank(b)

. regress ar c.br

        Source |       SS       df       MS              Number of obs =
10
-------------+------------------------------           F(  1,     8) =
0.64
         Model |  6.13636364     1  6.13636364           Prob > F      =
0.4458
      Residual |  76.3636364     8  9.54545455           R-squared     =
0.0744
-------------+------------------------------           Adj R-squared =
-0.0413
         Total |        82.5     9  9.16666667           Root MSE      =
3.0896


------------------------------------------------------------------------------
            ar |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]

-------------+----------------------------------------------------------------
            br |   .2727273   .3401507     0.80   0.446    -.5116616
1.057116
         _cons |          4   2.110579     1.90   0.095    -.8670049
8.867005

------------------------------------------------------------------------------

. test br

   ( 1)  br = 0

         F(  1,     8) =    0.64
              Prob > F =    0.4458

. // or
. spearman a b

   Number of obs =      10
Spearman's rho =       0.2727

Test of Ho: a and b are independent
      Prob > |t| =       0.4458

.
. *
. * Koch's nonparametric ANCOVA
. *
. predict double residuals, residuals

. ttest residuals, by(group)

Two-sample t test with equal variances

------------------------------------------------------------------------------
     Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf.
Interval]

---------+--------------------------------------------------------------------
         0 |       5    1.018182    1.601497    3.581057   -3.428287
5.464651
         1 |       5   -1.018182    .8573455    1.917083   -3.398555
1.362191

---------+--------------------------------------------------------------------
combined |      10           0    .9211324    2.912876   -2.083746
2.083746

---------+--------------------------------------------------------------------
      diff |            2.036364    1.816545               -2.152596
6.225323

------------------------------------------------------------------------------
      diff = mean(0) - mean(1)                                      t =
1.1210
Ho: diff = 0                                     degrees of freedom =
8

      Ha: diff < 0                 Ha: diff != 0                 Ha: diff >
0
   Pr(T < t) = 0.8526         Pr(|T| > |t|) = 0.2948          Pr(T > t) =
0.1474

. // or
. pwcorr residuals group, sig

               | residu~s    group
-------------+------------------
     residuals |   1.0000
               |
               |
         group |  -0.3685   1.0000
               |   0.2948
               |

.
. exit

end of do-file


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