get matrix of all possible contrasts for a single factor variable after reg

Colin Peterson

Join Date: Apr 2019
Posts: 2

get matrix of all possible contrasts for a single factor variable after reg

11 Apr 2019, 22:09

I'd like to get a matrix showing all possible contrasts for a given factor variable after a regression. For example, let's say I have a factor variable with 4 levels.

Code:

sysuse census.data, clear
tab region

     Census |
     region |      Freq.     Percent        Cum.
------------+-----------------------------------
         NE |          9       18.00       18.00
    N Cntrl |         12       24.00       42.00
      South |         16       32.00       74.00
       West |         13       26.00      100.00
------------+-----------------------------------
      Total |         50      100.00

reg medage i.region

      Source |       SS       df       MS              Number of obs =      50
-------------+------------------------------           F(  3,    46) =    7.56
       Model |  46.3961903     3  15.4653968           Prob > F      =  0.0003
    Residual |  94.1237947    46  2.04616945           R-squared     =  0.3302
-------------+------------------------------           Adj R-squared =  0.2865
       Total |  140.519985    49   2.8677548           Root MSE      =  1.4304

------------------------------------------------------------------------------
      medage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      region |
    N Cntrl  |  -1.708333   .6307664    -2.71   0.009       -2.978   -.4386663
      South  |  -1.614583   .5960182    -2.71   0.009    -2.814306   -.4148606
       West  |  -2.948718    .620282    -4.75   0.000    -4.197281   -1.700155
             |
       _cons |   31.23333   .4768146    65.50   0.000     30.27356    32.19311
------------------------------------------------------------------------------

I know I can use contrasts r.region, contrast a.region, or contrast ar.region, to get the default, adjacent, or reverse adjacent contrasts, respectively. The r(table) matrix that's accessible after doing any one of these is half way to what I need.

Code:

contrast ar.region

Contrasts of marginal linear predictions

Margins      : asbalanced

-------------------------------------------------------
                    |         df           F        P>F
--------------------+----------------------------------
             region |
   (N Cntrl vs NE)  |          1        7.34     0.0095
(South vs N Cntrl)  |          1        0.03     0.8645
   (West vs South)  |          1        6.24     0.0161
             Joint  |          3        7.56     0.0003
                    |
        Denominator |         46
-------------------------------------------------------

---------------------------------------------------------------------
                    |   Contrast   Std. Err.     [95% Conf. Interval]
--------------------+------------------------------------------------
             region |
   (N Cntrl vs NE)  |  -1.708333   .6307664        -2.978   -.4386663
(South vs N Cntrl)  |   .0937502   .5462597     -1.005814    1.193314
   (West vs South)  |  -1.334135   .5341191     -2.409261   -.2590085
---------------------------------------------------------------------

matrix list r(table)

r(table)[9,3]
            ar2vs1.     ar3vs2.     ar4vs3.
            region      region      region
     b  -1.7083332   .09375016  -1.3341345
    se   .63076642   .54625975   .53411913
     t  -2.7083452   .17162194   -2.497822
pvalue   .00946336   .86448754   .01613433
    ll  -2.9780002  -1.0058137  -2.4092605
    ul  -.43866627    1.193314  -.25900847
    df          46          46          46
  crit   2.0128956   2.0128956   2.0128956
 eform           0           0           0

I'd like a single matrix like this one but with all possible contrasts, regardless of whether they are shown in the original results. That would be either 3 additional columns if 2vs1 and 1vs2, etc., are regarded as redundant (just sign differences, ultimately), or 9 if they are not. I would have a slight preference for the latter, but either would be great. How might I get such a matrix? Thank you.

Last edited by Colin Peterson; 11 Apr 2019, 22:15.

Tags: contrast, matrix, regression

ericmelse

Join Date: May 2014
Posts: 445

12 Apr 2019, 00:00

Dear Colin,
Possibly there is a more smart way of coding, but here is my blunt solution. You have to run seperate regressions looping through each base level of region:

Code:

forvalue i = 1(1)4 {
qui reg medage b`i'.region
qui contrast r.region
matrix C`i'=r(table)
mat list C`i'
matrix C`i't = C`i''
}
matrix drop C
matrix C = (C1t \ C2t \ C3t \ C4t)
mat list C

The matrix has the result that you are looking for:

Code:

C[12,9]
                       b          se           t      pvalue          ll          ul          df        crit       eform
r2vs1.region  -1.7083332   .63076642  -2.7083452   .00946336  -2.9780002  -.43866627          46   2.0128956           0
r3vs1.region  -1.6145831   .59601825  -2.7089491   .00944857  -2.8143056  -.41486056          46   2.0128956           0
r4vs1.region  -2.9487176   .62028204  -4.7538335   .00001998  -4.1972806  -1.7001546          46   2.0128956           0
r1vs2.region   1.7083332   .63076642   2.7083452   .00946336   .43866627   2.9780002          46   2.0128956           0
r3vs2.region   .09375016   .54625975   .17162194   .86448754  -1.0058137    1.193314          46   2.0128956           0
r4vs2.region  -1.2403843   .57263581  -2.1660964   .03552209  -2.3930404  -.08772825          46   2.0128956           0
r1vs3.region   1.6145831   .59601825   2.7089491   .00944857   .41486056   2.8143056          46   2.0128956           0
r2vs3.region  -.09375016   .54625975  -.17162194   .86448754   -1.193314   1.0058137          46   2.0128956           0
r4vs3.region  -1.3341345   .53411913   -2.497822   .01613433  -2.4092605  -.25900847          46   2.0128956           0
r1vs4.region   2.9487176   .62028204   4.7538335   .00001998   1.7001546   4.1972806          46   2.0128956           0
r2vs4.region   1.2403843   .57263581   2.1660964   .03552209   .08772825   2.3930404          46   2.0128956           0
r3vs4.region   1.3341345   .53411913    2.497822   .01613433   .25900847   2.4092605          46   2.0128956           0

but in the process the correct region strings to indicate the contrast get lost.
The only solution to this, which I know (I assume they can be retrieved from somewhere more easy), is hard coding, like:

Code:

matrix rownames C = NCvsNE SOvsNE WEvsNE NEvsNC SOvsNC WEvsNC NEvsSO NCvsSO WEvsSO NEvsWE NCvsWE SOvsWE
mat list C

which will result in:

Code:

C[12,9]
                 b          se           t      pvalue          ll          ul          df        crit       eform
NCvsNE  -1.7083332   .63076642  -2.7083452   .00946336  -2.9780002  -.43866627          46   2.0128956           0
SOvsNE  -1.6145831   .59601825  -2.7089491   .00944857  -2.8143056  -.41486056          46   2.0128956           0
WEvsNE  -2.9487176   .62028204  -4.7538335   .00001998  -4.1972806  -1.7001546          46   2.0128956           0
NEvsNC   1.7083332   .63076642   2.7083452   .00946336   .43866627   2.9780002          46   2.0128956           0
SOvsNC   .09375016   .54625975   .17162194   .86448754  -1.0058137    1.193314          46   2.0128956           0
WEvsNC  -1.2403843   .57263581  -2.1660964   .03552209  -2.3930404  -.08772825          46   2.0128956           0
NEvsSO   1.6145831   .59601825   2.7089491   .00944857   .41486056   2.8143056          46   2.0128956           0
NCvsSO  -.09375016   .54625975  -.17162194   .86448754   -1.193314   1.0058137          46   2.0128956           0
WEvsSO  -1.3341345   .53411913   -2.497822   .01613433  -2.4092605  -.25900847          46   2.0128956           0
NEvsWE   2.9487176   .62028204   4.7538335   .00001998   1.7001546   4.1972806          46   2.0128956           0
NCvsWE   1.2403843   .57263581   2.1660964   .03552209   .08772825   2.3930404          46   2.0128956           0
SOvsWE   1.3341345   .53411913    2.497822   .01613433   .25900847   2.4092605          46   2.0128956           0

I hope that this is helpfull.
Eric

http://publicationslist.org/eric.melse

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Joseph Coveney

Join Date: Apr 2014

Posts: 4540
#3

12 Apr 2019, 00:06

Are you looking for all pairwise contrasts? If so, then

Code:

sysuse auto regress gear_ratio i.rep78 margins rep78, pwcompare // <= here matrix list r(table_vs)
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Colin Peterson

Join Date: Apr 2019

Posts: 2
#4

12 Apr 2019, 18:21

Joseph, yes, that's exactly what I need. Thank you!
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get matrix of all possible contrasts for a single factor variable after reg

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