Re: st: Re: rank regression

[R Zhang <r05zhang@gmail.com>]

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
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> __________________________________________
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>
> 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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>
>
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