t-testing the same parameter over different groups

[Daniele Ravasi]

Hello everyone and thanks in advance for the help,
I have a database which is divided in 4 groups, captured by a variable which takes values 1-4.
I have to run a regression a check if the parameter of the variable X takes different values between the groups
My idea is to to run the regression with the option by(group_var). With this, I get the same regression over the 4 sub-samples.
Then I must find a way to tell Stata to t-test the difference between the _b[X] of each group.
Any advice?

[Carlo Lazzaro]

Daniele:
welcome to this forum.
If you have a four-level categorical variable and you want to -test- its level each other, the simplest way is the following one:

. use "C:\Program Files\Stata17\ado\base\a\auto.dta"
(1978 automobile data)

. regress price mpg i.rep78

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(5, 63)        =      4.39
       Model |   149020603         5  29804120.7   Prob > F        =    0.0017
    Residual |   427776355        63  6790100.88   R-squared       =    0.2584
-------------+----------------------------------   Adj R-squared   =    0.1995
       Total |   576796959        68  8482308.22   Root MSE        =    2605.8

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -280.2615   61.57666    -4.55   0.000    -403.3126   -157.2103
             |
       rep78 |
          2  |   877.6347   2063.285     0.43   0.672     -3245.51     5000.78
          3  |   1425.657   1905.438     0.75   0.457    -2382.057    5233.371
          4  |   1693.841   1942.669     0.87   0.387    -2188.274    5575.956
          5  |   3131.982   2041.049     1.53   0.130    -946.7282    7210.693
             |
       _cons |   10449.99   2251.041     4.64   0.000     5951.646    14948.34
------------------------------------------------------------------------------

. test 2.rep78=3.rep78

 ( 1)  2.rep78 - 3.rep78 = 0

       F(  1,    63) =    0.28
            Prob > F =    0.5990

.

Conversely, if your gìresearch goal is to compare four different linear regression, see -suest-.

[Felix Bittmann]

Adding to Carlo's helpful suggestion, you could also like the command

margins rep78, pwcompare(pv)

To get all pairwise effects.

. margins rep78, pwcompare(pv)

Pairwise comparisons of predictive margins      Number of obs     =         69
Model VCE    : OLS

Expression   : Linear prediction, predict()

-----------------------------------------------------
             |            Delta-method    Unadjusted
             |   Contrast   Std. Err.      t    P>|t|
-------------+---------------------------------------
       rep78 |
     2 vs 1  |   877.6347   2063.285     0.43   0.672
     3 vs 1  |   1425.657   1905.438     0.75   0.457
     4 vs 1  |   1693.841   1942.669     0.87   0.387
     5 vs 1  |   3131.982   2041.049     1.53   0.130
     3 vs 2  |   548.0223   1037.044     0.53   0.599
     4 vs 2  |   816.2063   1118.251     0.73   0.468
     5 vs 2  |   2254.347   1312.785     1.72   0.091
     4 vs 3  |    268.184   788.9719     0.34   0.735
     5 vs 3  |   1706.325   1040.229     1.64   0.106
     5 vs 4  |   1438.141   1057.152     1.36   0.179
-----------------------------------------------------

[Rich Goldstein]

I'm interpreting #1 slightly differently and I suggest interacting X with your 4-category variable; using Carlo's example, as you did not supply any example data, this would be:

 
 regress price c.mpg##i.rep78