Re: st: Re: rank regression

[John Antonakis <John.Antonakis@unil.ch>]

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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