Re: st: Understanding Factor variables - is order significant ?

["Michael N. Mitchell" <Michael.Norman.Mitchell@gmail.com>]

Dear Richard

  I think I need to use my glasses!

  Yes, Richard, you are exactly on target. It relates to the use of -#- instead of -##- .

  My previous answer is still true, in the sense that when you do a#b and b#a, that you 
get a different reference "cell", and thus it is re-scrambling the coding.

  However, doing a##b and b##a will be the same, as shown in the example below using the 
auto dataset with a simple regression...

. sysuse auto
(1978 Automobile Data)
. generate bigtrunk = trunk > 15
. generate biglen   = length > 190

. regress mpg bigtrunk##biglen

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  3,    70) =   23.21
       Model |  1218.59972     3  406.199906           Prob > F      =  0.0000
    Residual |  1224.85974    70  17.4979963           R-squared     =  0.4987
-------------+------------------------------           Adj R-squared =  0.4772
       Total |  2443.45946    73  33.4720474           Root MSE      =  4.1831

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  1.bigtrunk |  -1.939394    2.52248    -0.77   0.445    -6.970323    3.091535
    1.biglen |  -7.806061   1.509981    -5.17   0.000    -10.81762   -4.794499
             |
    bigtrunk#|
      biglen |
        1 1  |    1.35368   2.955949     0.46   0.648    -4.541775    7.249134
             |
       _cons |   25.60606   .7281774    35.16   0.000     24.15376    27.05836
------------------------------------------------------------------------------

.
. regress mpg biglen##bigtrunk

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  3,    70) =   23.21
       Model |  1218.59972     3  406.199906           Prob > F      =  0.0000
    Residual |  1224.85974    70  17.4979963           R-squared     =  0.4987
-------------+------------------------------           Adj R-squared =  0.4772
       Total |  2443.45946    73  33.4720474           Root MSE      =  4.1831

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    1.biglen |  -7.806061   1.509981    -5.17   0.000    -10.81762   -4.794499
  1.bigtrunk |  -1.939394    2.52248    -0.77   0.445    -6.970323    3.091535
             |
      biglen#|
    bigtrunk |
        1 1  |    1.35368   2.955949     0.46   0.648    -4.541775    7.249134
             |
       _cons |   25.60606   .7281774    35.16   0.000     24.15376    27.05836
------------------------------------------------------------------------------

I hope that helps,

Michael N. Mitchell
Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html
A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html
Stata tidbit of the week         - http://www.MichaelNormanMitchell.com



On 2010-05-25 8.06 PM, Richard Williams wrote:
> At 08:32 PM 5/25/2010, Michael N. Mitchell wrote:
> > Extend that idea to your interaction... Suppose you flip the coding of
> > your "ra" and "dm" variables. Note that the test of the interaction,
> > the p value, will remain the same (assuming both are dummy variables).
> > The coefficients of "ra" and "dm" will change as well, due to the
> > change in coding. The details get more complicated, but are explained
> > in section 3.5 of
> > http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter3/statareg3.htm
> > . It is explained using the old "xi" terminology, but the issues still
> > are the same.
>
> He is not changing the coding though. He is just flipping the placement
> of the terms, i.e. b1.ra#b0.dm in one model and b0.dm#b1.ra. Like using
> female * race versus using race * female.
>
> I'd be curious to know if the two models did produce identical fits.
> That would indicate whether the parameterizations are equivalent. If
> not, then something is getting screwed up.
>
> I suspect using ## instead of # might solve the problem -- and that
> would be my preference anyway.
>
> The following code also produces inconsistent results, with the 3rd
> model being wrong. It isn't clear to me why that is the case.
>
> use "http://www.indiana.edu/~jslsoc/stata/spex_data/ordwarm2.dta";, clear
> ologit warm yr89#male, nolog
> ologit warm b0.male#b1.yr89, nolog
> ologit warm b1.yr89#b0.male, nolog
>
> I hate to accuse Stata of having a bug, but I am starting to wonder...
>
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
> HOME: (574)289-5227
> EMAIL: Richard.A.Williams.5@ND.Edu
> WWW: http://www.nd.edu/~rwilliam
>
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