Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: st: Interpretation of Box-Cox Results
From
Nick Cox <[email protected]>
To
[email protected]
Subject
Re: st: Interpretation of Box-Cox Results
Date
Fri, 7 Dec 2012 18:00:40 +0000
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
<[email protected]> 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
>
>
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/faqs/resources/statalist-faq/
* http://www.ats.ucla.edu/stat/stata/