Number of Estimated Coefficients in a Regression

[Trevor Andrew]

Is there a way to display the number coefficients estimated in a regression? I am estimating different models by adding various covariates and would like to store the number of regressors from each regression in a local. I thought maybe I could use the number of columns of e(b) but I don't know how to obtain the number of columns of e(b).

[Jared Greathouse]

sysuse auto, clear


cls


qui reg price weight head

mat l e(b)

loc cols = colsof(e(b))

di `cols'

Or if you wanna know the number of predictors aside from the constant

sysuse auto, clear


cls


qui reg price weight head

mat l e(b)

loc cols = colsof(e(b))-1

di `cols'

[Clyde Schechter]

A perhaps simpler way to get the number of predictors other than the constant is

regress whatever
display e(df_m)

If you want to include the constant term, just add 1.

Added: An advantage of this approach is that it works correctly after, as far as I know, all Stata estimation commands. By contrast, with multi-level models, the approach based on columns of the e(b) matrix will include the random effects as well, which is probably not what you want in most situations.

[Jared Greathouse]

Oh yeah I forgot about df_m, yes this way is much better than mine

[Andrew Musau]

If you use e(df_m) or any other degrees of freedom based statistic, you need to be careful if there is clustering as this affects the reported degrees of freedom. In xtreg with the -fe- option, e(df_b) will give you the count excluding the fixed effects in the absence of clustering (the displayed coefficients). There are some macros which store the names of the regressors, so one can count the number of words, but this is complicated by factor variable expansion if factor variable notation is used. Adjustment for the degrees of freedom under clustering is always possible if you know what you are doing.

webuse grunfeld, clear
xtreg invest mvalue kstock i.time, fe
di e(df_m)
di e(df_b)
xtreg invest mvalue kstock i.time, fe cluster(company)
di e(df_m)
di e(df_b)

Res.:

. xtreg invest mvalue kstock i.time, fe

Fixed-effects (within) regression               Number of obs     =        200
Group variable: company                         Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.7985                                         min =         20
     between = 0.8143                                         avg =       20.0
     overall = 0.8068                                         max =         20

                                                F(21,169)         =      31.90
corr(u_i, Xb)  = -0.3250                        Prob > F          =     0.0000

------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |   .1177158   .0137513     8.56   0.000     .0905694    .1448623
      kstock |   .3579163    .022719    15.75   0.000     .3130667    .4027659
             |
        time |
          2  |  -19.19741   23.67586    -0.81   0.419    -65.93593    27.54112
          3  |  -40.69001   24.69541    -1.65   0.101    -89.44122    8.061213
          4  |   -39.2264   23.23594    -1.69   0.093    -85.09647    6.643667
          5  |  -69.47029   23.65607    -2.94   0.004    -116.1698   -22.77083
          6  |  -44.23507   23.80979    -1.86   0.065      -91.238     2.76785
          7  |  -18.80446     23.694    -0.79   0.429     -65.5788    27.96987
          8  |  -21.13979   23.38163    -0.90   0.367    -67.29748    25.01789
          9  |  -42.97762   23.55287    -1.82   0.070    -89.47334    3.518104
         10  |  -43.09876    23.6102    -1.83   0.070    -89.70766    3.510134
         11  |  -55.68303   23.89561    -2.33   0.021    -102.8554   -8.510689
         12  |  -31.16928   24.11598    -1.29   0.198    -78.77665    16.43809
         13  |  -39.39223   23.78368    -1.66   0.100    -86.34361    7.559141
         14  |  -43.71651   23.96965    -1.82   0.070    -91.03501    3.601991
         15  |   -73.4951   24.18292    -3.04   0.003    -121.2346   -25.75559
         16  |  -75.89611   24.34553    -3.12   0.002    -123.9566    -27.8356
         17  |   -62.4809   24.86425    -2.51   0.013    -111.5654   -13.39637
         18  |  -64.63233    25.3495    -2.55   0.012    -114.6748   -14.58987
         19  |  -67.71796   26.61108    -2.54   0.012    -120.2509   -15.18501
         20  |  -93.52622   27.10786    -3.45   0.001    -147.0399   -40.01257
             |
       _cons |  -32.83631   18.87533    -1.74   0.084     -70.0981    4.425483
-------------+----------------------------------------------------------------
     sigma_u |  91.798268
     sigma_e |  51.724523
         rho |  .75902159   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 169) = 52.36                     Prob > F = 0.0000

. 
. di e(df_m)
30

. 
. di e(df_b)
21

. 
. xtreg invest mvalue kstock i.time, fe cluster(company)

Fixed-effects (within) regression               Number of obs     =        200
Group variable: company                         Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.7985                                         min =         20
     between = 0.8143                                         avg =       20.0
     overall = 0.8068                                         max =         20

                                                F(9,9)            =          .
corr(u_i, Xb)  = -0.3250                        Prob > F          =          .

                               (Std. Err. adjusted for 10 clusters in company)
------------------------------------------------------------------------------
             |               Robust
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |   .1177158   .0108244    10.88   0.000     .0932293    .1422024
      kstock |   .3579163   .0478484     7.48   0.000     .2496757    .4661569
             |
        time |
          2  |  -19.19741   20.69857    -0.93   0.378    -66.02082    27.62601
          3  |  -40.69001   33.28318    -1.22   0.253    -115.9818    34.60179
          4  |   -39.2264   15.73649    -2.49   0.034    -74.82481   -3.627994
          5  |  -69.47029   26.99875    -2.57   0.030    -130.5457   -8.394865
          6  |  -44.23507    17.3723    -2.55   0.031    -83.53394    -4.93621
          7  |  -18.80446   17.84747    -1.05   0.320    -59.17824    21.56931
          8  |  -21.13979   14.16477    -1.49   0.170    -53.18273    10.90314
          9  |  -42.97762   12.54411    -3.43   0.008    -71.35436   -14.60088
         10  |  -43.09876   10.99586    -3.92   0.004    -67.97313    -18.2244
         11  |  -55.68303    15.2019    -3.66   0.005    -90.07212   -21.29394
         12  |  -31.16928   20.91692    -1.49   0.170    -78.48663    16.14807
         13  |  -39.39223   26.43707    -1.49   0.170    -99.19704    20.41257
         14  |  -43.71651   38.87861    -1.12   0.290     -131.666    44.23301
         15  |   -73.4951    38.2545    -1.92   0.087    -160.0328    13.04259
         16  |  -75.89611   36.79846    -2.06   0.069      -159.14    7.347783
         17  |   -62.4809   49.41812    -1.26   0.238    -174.2725    49.31066
         18  |  -64.63233   51.56208    -1.25   0.242    -181.2739     52.0092
         19  |  -67.71796   43.74465    -1.55   0.156    -166.6752    31.23932
         20  |  -93.52622   31.72632    -2.95   0.016    -165.2961   -21.75629
             |
       _cons |  -32.83631   19.78259    -1.66   0.131    -77.58765    11.91503
-------------+----------------------------------------------------------------
     sigma_u |  91.798268
     sigma_e |  51.724523
         rho |  .75902159   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
. di e(df_m)
8

. 
. di e(df_b)
9

[Clyde Schechter]

Good point. I didn't think about clustered vce. So it seems there is no simple solution that works for all estimation commands.

[Trevor Andrew]

Andrew, that is a great point. I was wondering why I get so few coefficients if I use e(df_m) or e(rank) with clustered standard errors. The best solutions is to use colsof(e(b)) as Jared suggested if you have clustered standard errors. It worked great for me.