st: adjust vs. margins revisited

[Tim Wade <wadetj@gmail.com>]

Hello Statalisters:

Having recently upgradted to v. 11, I have been testing  -margins-
and, like others have discussed on Statalist, I am trying to reconcile
some results compared to the old -adjust-

Here is a simplified example


sysuse auto.dta
logistic foreign  price mpg weight
adjust price=4000 mpg weight, pr ci
margins, atmeans at(price=4000)

produces the following:


. adjust price=4000 mpg weight, pr ci

-----------------------------------------------------------------------------------------------------------------------------------------
     Dependent variable: foreign     Equation: foreign     Command: logistic
 Covariates set to mean: mpg = 21.297297, weight = 3019.4595
 Covariate set to value: price = 4000
-----------------------------------------------------------------------------------------------------------------------------------------

----------------------------------------------
      All |         pr          lb          ub
----------+-----------------------------------
          |    .005861    [.000219    .137016]
----------------------------------------------
     Key:  pr         =  Probability
           [lb , ub]  =  [95% Confidence Interval]


. margins, atmeans at(price=4000)

Adjusted predictions                              Number of obs   =         74
Model VCE    : OIM

Expression   : Pr(foreign), predict()
at           : price           =        4000
               mpg             =     21.2973 (mean)
               weight          =    3019.459 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   .0058613   .0097907     0.60   0.549    -.0133281    .0250508
------------------------------------------------------------------------------


I read the previous postings by Stata Corp's  Jeff Pitlblado
(http://www.stata.com/statalist/archive/2009-11/msg00199.html where he
stated:

"The -pr- confidence intervals from -adjust- are computed by transforming the
end-points of the CI limits from the linear prediction.

-margins- computes the CI limits using the normal approximation is valid."

but here margins produces negative confidence bounds on a probability
and also produces quite different results from -adjust-, which seems
to provide reasonable results. It does not seem plausible that both
results could be considered valid. Any thoughts?

Kind regards, Tim
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