Interpreting nestreg output / Stata manual

[Kathleen Carluzzo]

Hello, I am using the nestreg command and want to be sure I’m interpreting the output correctly. The Stata manual (https://www.stata.com/manuals/rnestreg.pdf) explains this, but I’m not quite grasping it. Specifically, on page 4 they show the following output:

…with the explanation of what is in the table at the bottom on page 5

However, I’m not grasping what is explained here and what the F statistics in the box at the bottom convey as compared to the F statistic for each of the models listed in the table above. I.e., the difference between the F(5, 44) = 100.63 reported for block 3 above vs. F(3, 44) = 8.85 in the table at the bottom. Any advice would be greatly appreciated!

[Andrew Musau]

nestreg: regress brate (medage) (c.medage#c.medage) (i.region)

So you have 3 models with the following regressors:

1. medage
2. medage & medage^2
3. medage & medage^2 & region dummies

1 and 2 are nested in 3, and 1 is nested in 2. Now, when you have nested models, an important question is whether the added variables contribute to the model (in other words, is the change in R-squared resulting from the addition of the variables significant?). To determine this, you test for their joint significance (or whether they are jointly equal to 0). If this is the case, they do not contribute to the model. That is exactly what the F-statistics at the foot of the table tell you.

the difference between the F(5, 44) = 100.63 reported for block 3 above vs. F(3, 44) = 8.85 in the table at the bottom. Any advice would be greatly appreciated!

100.63 is a test of the joint significance of all the variables and 8.85 is the joint significance of the regional dummies (added variables to model 2).

webuse census4
regress brate medage c.medage#c.medage
test c.medage#c.medage
regress brate medage c.medage#c.medage i.region
testparm i.region
testparm medage c.medage#c.medage i.region

Res.:

.   . webuse census4
(birth rate, median age)

. regress brate medage c.medage#c.medage

      Source |       SS           df       MS      Number of obs   =        50
-------------+----------------------------------   F(2, 47)        =    158.75
       Model |  36755.8566         2  18377.9283   Prob > F        =    0.0000
    Residual |  5440.96342        47  115.765179   R-squared       =    0.8711
-------------+----------------------------------   Adj R-squared   =    0.8656
       Total |    42196.82        49  861.159592   Root MSE        =    10.759

-----------------------------------------------------------------------------------
            brate |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
           medage |  -109.8926   15.96663    -6.88   0.000    -142.0133   -77.77189
                  |
c.medage#c.medage |   1.607334   .2707229     5.94   0.000      1.06271    2.151958
                  |
            _cons |   2007.073   235.4316     8.53   0.000     1533.445      2480.7
-----------------------------------------------------------------------------------

. test c.medage#c.medage

 ( 1)  c.medage#c.medage = 0

       F(  1,    47) =   35.25
            Prob > F =    0.0000

. regress brate medage c.medage#c.medage i.region

      Source |       SS           df       MS      Number of obs   =        50
-------------+----------------------------------   F(5, 44)        =    100.63
       Model |  38803.4208         5  7760.68416   Prob > F        =    0.0000
    Residual |  3393.39921        44  77.1227094   R-squared       =    0.9196
-------------+----------------------------------   Adj R-squared   =    0.9104
       Total |    42196.82        49  861.159592   Root MSE        =     8.782

-----------------------------------------------------------------------------------
            brate |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
           medage |  -109.0958   13.52452    -8.07   0.000    -136.3527   -81.83892
                  |
c.medage#c.medage |   1.635209   .2290536     7.14   0.000     1.173582    2.096836
                  |
           region |
         N Cntrl  |   15.00283   4.252067     3.53   0.001     6.433353    23.57231
           South  |   7.366445   3.953335     1.86   0.069    -.6009775    15.33387
            West  |   21.39679   4.650601     4.60   0.000     12.02412    30.76946
                  |
            _cons |   1947.611   199.8405     9.75   0.000     1544.859    2350.363
-----------------------------------------------------------------------------------

. testparm i.region

 ( 1)  2.region = 0
 ( 2)  3.region = 0
 ( 3)  4.region = 0

       F(  3,    44) =    8.85
            Prob > F =    0.0001

. testparm medage c.medage#c.medage i.region

 ( 1)  medage = 0
 ( 2)  c.medage#c.medage = 0
 ( 3)  2.region = 0
 ( 4)  3.region = 0
 ( 5)  4.region = 0

       F(  5,    44) =  100.63
            Prob > F =    0.0000

[Kathleen Carluzzo]

Thank you so much!