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# Re: st: Interpretation of Box-Cox Results

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: Interpretation of Box-Cox Results Date Fri, 7 Dec 2012 18:00:40 +0000

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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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```