Saving estimates from -margins-

[Karl Yesler]

Hi Statalisters,

I have a rather simple question. I am trying to save the estimate from margins after running margins multiple times to evaluate the margins of a 1 unit increase of age for different groups at the mean age of the group being evaluated. For example:

use http://www.stata-press.com/data/r13/margex, clear
logistic outcome i.sex c.age##i.group

foreach num of numlist 1/3 { 
margins if group==`num', at((mean)age) dydx(age)
}

Results below: 

 use http://www.stata-press.com/data/r13/margex, clear
(Artificial data for margins)

. logistic outcome i.sex c.age##i.group

Logistic regression                               Number of obs   =       3000
                                                  LR chi2(6)      =     596.53
                                                  Prob > chi2     =     0.0000
Log likelihood = -1067.8068                       Pseudo R2       =     0.2183

------------------------------------------------------------------------------
     outcome | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         sex |
     female  |   1.645435   .2217915     3.69   0.000     1.263414    2.142969
         age |   1.095059   .0092606    10.74   0.000     1.077058    1.113361
             |
       group |
          2  |    .524537   .3500767    -0.97   0.334     .1418022    1.940301
          3  |   .4550779   .4768744    -0.75   0.452     .0583599    3.548597
             |
 group#c.age |
          2  |   1.001389   .0140286     0.10   0.921     .9742675    1.029266
          3  |   .9852544   .0255426    -0.57   0.567     .9364425    1.036611
             |
       _cons |   .0037717   .0016669   -12.63   0.000     .0015862    .0089686
------------------------------------------------------------------------------

. 
. foreach num of numlist 1/3 { 
  2. margins if group==`num', at((mean)age) dydx(age)
  3. }

Average marginal effects                          Number of obs   =       1199
Model VCE    : OIM

Expression   : Pr(outcome), predict()
dy/dx w.r.t. : age
at           : age             =    46.71893 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0183786   .0015931    11.54   0.000     .0152562     .021501
------------------------------------------------------------------------------

Average marginal effects                          Number of obs   =       1118
Model VCE    : OIM

Expression   : Pr(outcome), predict()
dy/dx w.r.t. : age
at           : age             =     37.9025 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0064137   .0006617     9.69   0.000     .0051169    .0077105
------------------------------------------------------------------------------

Average marginal effects                          Number of obs   =        683
Model VCE    : OIM

Expression   : Pr(outcome), predict()
dy/dx w.r.t. : age
at           : age             =    30.75549 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0013779   .0004068     3.39   0.001     .0005805    .0021753
------------------------------------------------------------------------------

How would I save the dy/dx and the Std. Err.?

Thanks!

[Clyde Schechter]

-margins- returns the estimates in matrix r(b) and the squares of the standard errors are found in the diagonal elements of r(V). You can store those matrices immediately after -margins- runs and then store the parameters of interest in scalars or macros, or combine them in whatever way suits you using the various matrix commands in Stata.

[Clyde Schechter]

By the way, are you sure those are the marginal effects you want? A more usual approach would be:

margins group, dydx(age) at((mean) age)

The matrices r(b) and r(V) will contain the marginal effects and the squares of the standard errors for all of the values of group.

But these are different statistics from what your code generates. The loop gives you estimates restricted to three subsamples of the data, identified by the value of group. Note also that with this approach, the mean value of age differs: it is the mean value for observations with that value of group. The one-liner here gives you estimates using the entire sample, but with each observation treated as if it had age = (mean) age [meaning mean age in the entire sample], and group = particular value of group shown in output.

It's your call as to which set of statistics is the one you need for your purposes. I'm just noting that the statistics generated by the one-line version are more commonly wanted.

[Scott Merryman]

This

 
 foreach num of numlist 1/3 {  margins if group==`num', at((mean)age) dydx(age) }

can be rewritten as

margins , at((mean)age) dydx(age) over(group)

[Karl Yesler]

Clyde and Scott,

Thank you for your help. 2 points:

1) I do believe that

margins , at((mean)age) dydx(age) over(group)

gives me what I want since it gives me the effect of an additional year of age on the probability of outcome if the age was the mean age at the subgroup being predicted. And done for each subgroup. (A mouthful, but I think I got that right??)

2) Apologies, I am not very familiar with saving return matrices, I tried to look it up and tried to following to no avail. I am just trying to save the dy/dx and the Std. Err. for each subgroup with the subgroup identifier.

margins , at((mean)age) dydx(age) over(group)

Average marginal effects                          Number of obs   =       3000
Model VCE    : OIM

Expression   : Pr(outcome), predict()
dy/dx w.r.t. : age
over         : group
at           : 1.group
                   age             =    46.71893 (mean)
               2.group
                   age             =     37.9025 (mean)
               3.group
                   age             =    30.75549 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age          |
       group |
          1  |   .0183786   .0015931    11.54   0.000     .0152562     .021501
          2  |   .0064137   .0006617     9.69   0.000     .0051169    .0077105
          3  |   .0013779   .0004068     3.39   0.001     .0005805    .0021753
------------------------------------------------------------------------------

.
. gen dydx = r(b)
type mismatch
r(109);

[Clyde Schechter]

Yes, -gen dydx = r(b)- won't work because you are trying to create a variable, but r(b) is a matrix. So you have to do a little more work:

use http://www.stata-press.com/data/r13/margex, clear
logistic outcome i.sex c.age##i.group

margins, dydx(age) at((mean) age) over(group)

matrix B = r(b)
matrix list B // JUST SO YOU CAN SEE WHAT IT IS, NOT NECESSARY

matrix V = r(V)
matrix list V // AGAIN, JUST SO YOU CAN SEE IT

gen dydx = .
gen se_dydx = .
forvalues g = 1/3 {
    replace dydx = B[1, `g'] if group == `g'
    replace se_dydx = sqrt(V[`g', `g']) if group == `g'
}

[Karl Yesler]

Clyde,

Thank you. That worked perfectly.