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Re: st: Re: rank regression


From   John Antonakis <[email protected]>
To   [email protected]
Subject   Re: st: Re: rank regression
Date   Mon, 24 Feb 2014 08:05:51 +0100

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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