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Re: st: Dummy variable p value question


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: st: Dummy variable p value question
Date   Sun, 30 Nov 2008 20:18:46 -0500

At 07:52 PM 11/30/2008, Jimmy Verner wrote:
Suppose you have an interval dependent variable Y, an interval
independent variable B and a nominal variable C.  C has four
categories, C1, C2, C3 and C4.  C is coded by four dummy variables, C1
through C4, with the value 1 when "in play" and the value 0 otherwise.

One may regress Y on B and C1 through C4 by dropping the constant:

Model A:  reg Y B C1 C2 C3 C4, nocon

Alternatively, one may keep the constant but drop a category to avoid
falling into the dummy variable trap.  The constant replaces the
dropped category:

Model B:  reg Y B C1 C2 C3

If what I have said is correct, why are the p values different for C1
through C3 between the two models?  And should not the p value for C4
in Model A be the same as for the constant in Model B?

In Model A, you are testing whether the C coefficients equal 0. In Model B, you are testing whether the C coefficients equal the constant. In model A, testing whether C1, C2 or C3 = C4 is equivalent to the tests of C1, C2 and C3 in Model B. In other words, the P values differ because the hypotheses being tested are different. As for the C4 and constant P values being different -- can you give an example where that is the case? It isn't in the example I give below.

. use "http://www.indiana.edu/~jslsoc/stata/spex_data/ordwarm2.dta";, clear
(77 & 89 General Social Survey)

. quietly tab1 warm, gen(warm)

. reg ed  warm1 warm2 warm3 warm4, nocon

      Source |       SS       df       MS              Number of obs =    2293
-------------+------------------------------           F(  4,  2289) = 8936.13
       Model |  343220.884     4  85805.2209           Prob > F      =  0.0000
    Residual |  21979.1163  2289  9.60206042           R-squared     =  0.9398
-------------+------------------------------           Adj R-squared =  0.9397
       Total |      365200  2293  159.267335           Root MSE      =  3.0987

------------------------------------------------------------------------------
          ed |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       warm1 |   10.94613   .1798059    60.88   0.000     10.59353    11.29873
       warm2 |   11.85339   .1152426   102.86   0.000      11.6274    12.07938
       warm3 |   12.63435    .105912   119.29   0.000     12.42665    12.84204
       warm4 |   12.90168   .1517449    85.02   0.000     12.60411    13.19925
------------------------------------------------------------------------------

. test warm1 = warm4

 ( 1)  warm1 - warm4 = 0

       F(  1,  2289) =   69.08
            Prob > F =    0.0000

. reg ed  warm1 warm2 warm3

      Source |       SS       df       MS              Number of obs =    2293
-------------+------------------------------           F(  3,  2289) =   31.93
       Model |  919.856222     3  306.618741           Prob > F      =  0.0000
    Residual |  21979.1163  2289  9.60206042           R-squared     =  0.0402
-------------+------------------------------           Adj R-squared =  0.0389
       Total |  22898.9725  2292  9.99082571           Root MSE      =  3.0987

------------------------------------------------------------------------------
          ed |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       warm1 |  -1.955551     .23528    -8.31   0.000    -2.416935   -1.494166
       warm2 |   -1.04829    .190545    -5.50   0.000    -1.421949   -.6746312
       warm3 |  -.2673329    .185051    -1.44   0.149    -.6302181    .0955524
       _cons |   12.90168   .1517449    85.02   0.000     12.60411    13.19925
------------------------------------------------------------------------------

. test warm1 = 0

 ( 1)  warm1 = 0

       F(  1,  2289) =   69.08
            Prob > F =    0.0000



-------------------------------------------
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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