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Re: st: Interpretation of Box-Cox Results


From   Yuval Arbel <yuval.arbel@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpretation of Box-Cox Results
Date   Fri, 7 Dec 2012 22:42:43 +0200

Dear Harris,

The box-cox is a problematic specification test. Note, that this theta
is highly susceptible to hetheroskedasticity and other econometric
problems in your data, particularly if this parameter appears in the
dependent variable. In addition, the problem you are talking about is
precisely the classical problem arises. In many cases, and as you can
also see in Nick's example, the 3 specifications (logarithmic, linear
and reciprocal) will be rejected.

Kmenta (1997), for example, suggests an alternative test, which is
based on only two competitive specifications (e.g., linear and
logarithmic). I suggest you take a look on:

Jan Kmenta, Elements of Econometrics, Second Addition (1997), pp. 518-521

On Fri, Dec 7, 2012 at 8:00 PM, Nick Cox <njcoxstata@gmail.com> wrote:
> Please send plain text only to Statalist. See
>
> <http://hsphsun3.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1212/date/article-258.html>
>
> for how your posting will appear to many list members. The importance
> of sending plain text is explained in the FAQ.
>
> My guess is that you have a large sample size and that the best
> transform is unclear. This is common enough. Consider the example
> below my signature. P-values necessarily depend on sample size. You
> are still at liberty to choose a transform indicated by low or even
> the lowest chi-square.
>
> However, note that P-values depend on other assumptions too (notably
> independence) and that for modelling the marginal distribution of the
> response is less important than is widely believed.
>
> Nick
>
> . sysuse auto, clear
> (1978 Automobile Data)
>
> . boxcox mpg
> Fitting comparison model
>
> Iteration 0:   log likelihood = -234.39434
> Iteration 1:   log likelihood = -228.26891
> Iteration 2:   log likelihood = -228.26777
> Iteration 3:   log likelihood = -228.26777
>
> Fitting full model
>
> Iteration 0:   log likelihood = -234.39434
> Iteration 1:   log likelihood = -228.26891
> Iteration 2:   log likelihood = -228.26777
> Iteration 3:   log likelihood = -228.26777
>
>                                                   Number of obs   =         74
>                                                   LR chi2(0)      =       0.00
> Log likelihood = -228.26777                       Prob > chi2     =          .
>
> ------------------------------------------------------------------------------
>          mpg |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>       /theta |  -.3533898    .391631    -0.90   0.367    -1.120972    .4141927
> ------------------------------------------------------------------------------
>
> Estimates of scale-variant parameters
> ----------------------------
>              |      Coef.
> -------------+--------------
> Notrans      |
>        _cons |   1.853957
> -------------+--------------
>       /sigma |   .0882471
> ----------------------------
>
> ---------------------------------------------------------
>    Test         Restricted     LR statistic      P-value
>     H0:       log likelihood       chi2       Prob > chi2
> ---------------------------------------------------------
> theta = -1      -229.60603         2.68           0.102
> theta =  0      -228.67835         0.82           0.365
> theta =  1      -234.39434        12.25           0.000
> ---------------------------------------------------------
>
>
> . expand 1000
> (73926 observations created)
>
> . boxcox mpg
> Fitting comparison model
>
> Iteration 0:   log likelihood = -234394.34
> Iteration 1:   log likelihood = -228268.91
> Iteration 2:   log likelihood = -228267.77
> Iteration 3:   log likelihood = -228267.77
>
> Fitting full model
>
> Iteration 0:   log likelihood = -234394.34
> Iteration 1:   log likelihood = -228268.91
> Iteration 2:   log likelihood = -228267.77
> Iteration 3:   log likelihood = -228267.77
>
>                                                   Number of obs   =      74000
>                                                   LR chi2(0)      =       0.00
> Log likelihood = -228267.77                       Prob > chi2     =          .
>
> ------------------------------------------------------------------------------
>          mpg |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>       /theta |  -.3533898   .0123845   -28.53   0.000    -.3776629   -.3291167
> ------------------------------------------------------------------------------
>
> Estimates of scale-variant parameters
> ----------------------------
>              |      Coef.
> -------------+--------------
> Notrans      |
>        _cons |   1.853957
> -------------+--------------
>       /sigma |   .0882471
> ----------------------------
>
> ---------------------------------------------------------
>    Test         Restricted     LR statistic      P-value
>     H0:       log likelihood       chi2       Prob > chi2
> ---------------------------------------------------------
> theta = -1      -229606.03      2676.51           0.000
> theta =  0      -228678.35       821.17           0.000
> theta =  1      -234394.34     12253.13           0.000
> ---------------------------------------------------------
>
>
> On Fri, Dec 7, 2012 at 2:40 PM, Charalambos Karagiannakis
> <karagiannakis.charalambos@ucy.ac.cy> wrote:
>> Dear Statalist users,
>>
>>
>>
>> Hello. I run a Box-Cox transformation for only the dependent variable
>> using
>> the command boxcox and I would appreciate some help with the
>> interpretation
>> of the results.
>>
>> The Box-Cox transform parameter ‘theta’ turns out to be very close to zero
>> and statistical significant (namely, -0.0730 with a s.e. of 0.0091).
>> However, at the bottom table where different null hypotheses for theta are
>> tested, all three cases (H0:theta=-1, H0:theta=0, H0:theta=1) return a
>> 0.000
>> p-value, rejecting all the possible specifications (reciprocal, log and
>> linear specification respectively). How could one interpret this result?
>>
>>
>>
>> Thank you in advance.
>>
>> Harris Karagiannakis
>>
>>
>
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-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: yuval.arbel@carmel.ac.il
e-mail2: yuval.arbel@gmail.com

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