Rewrite variance code so it is possible to get vcov across at

[leeper]

This is currently possible in Stata but not R:

sysuse auto
reg price c.mpg##i.foreign
margins, dydx(mpg) at(foreign=(0 1)) post
lincom _b[mpg:1bn._at] - _b[mpg:2._at]

The reason is that Stata produces a single Jacobian across all at values:

. matrix list e(V)

symmetric e(V)[2,2]
                  mpg:        mpg:
                    1.          2.
                  _at         _at
mpg:1._at   5622.8176
mpg:2._at  -1.819e-11   7029.2128

. matrix list e(Jacobian)

e(Jacobian)[2,6]
                                 0b.           1.  0b.foreign#   1.foreign#             
                   mpg      foreign      foreign       co.mpg        c.mpg        _cons
mpg:1._at            1            0            0            0            0            0
mpg:2._at            1            0            0            0            1            0

Whereas the current R code does everything separately across at specifications. We could simply return the Jacobian for each at, rbind() them together, and then sandwich the result to get a full variance-covariance matrix in the style of Stata's return value. This could be returned by vcov() but will require some generalization and possibly rewriting of summary().

[leeper]

Solution:

m <- lm(price ~ mpg * factor(foreign), data = auto)
# difference in AMEs
diff(summary(margins(m, at = list(foreign = c("0", "1")), variables = "mpg"))$AME)
##      mpg 
## 78.88826
# standard error of difference
vc <- vcov(margins(m, at = list(foreign = c("0", "1")), variables = "mpg"))
sqrt(sum(diag(vc)) - 2*vc[1,2])
## [1] 112.7029

which matches Stata:

. lincom _b[mpg:1bn._at] - _b[mpg:2._at]

 ( 1)  [mpg]1bn._at - [mpg]2._at = 0

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |  -78.88826   112.4812    -0.70   0.485     -303.225    145.4485
------------------------------------------------------------------------------