st: Questions related to -predict-, -adjust-, and predictive margins

["Michael I. Lichter" <mlichter@buffalo.edu>]

Question 1: How do you calculate SEs for predicted probabilities for 
data that require weights or are from a complex sample design? I've seen 
the FAQ about how to do this in general, but I suspect that the FAQ's 
advice is not correct for weighted data/data from complex samples.

Question 2: -adjust, pr  ci- produces confidence intervals for 
proportions. Is it not the case that SE = (UB - LB)/(2 * 1.96) given a 
95% confidence interval (assuming that weights/design are not a problem)?

Question 3: I want to calculate predictive margins (predictions where 
every element is treated as if it belonged to a given group, but 
otherwise the elements' own values are used in the prediction), AND I 
want to be able to test for equality of predicted proportions. From what 
I glean from an recent article in NEJM, SUDAAN can do this, but I don't 
know how.

Here is an example that goes partway there:

. sysuse auto
. gen himpg = mpg > 25

. logit foreign himpg weight
------------------------------------------------------------------------------
    foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. 
Interval]
-------------+----------------------------------------------------------------
      himpg |  -2.079449    .998357    -2.08   0.037    -4.036193   
-.1227054
     weight |  -.0037159   .0009375    -3.96   0.000    -.0055534   
-.0018785
      _cons |   9.795139   2.632037     3.72   0.000     4.636442    
14.95384
------------------------------------------------------------------------------

. adjust himpg=0, pr ci
--------------------------------------------------------------------------------
    Dependent variable: foreign     Command: logit
   Variable left as is: weight
Covariate set to value: himpg = 0
--------------------------------------------------------------------------------
----------------------------------------------
     All |         pr          lb          ub
----------+-----------------------------------
         |    .193884    [.085888    .381067]
----------------------------------------------
    Key:  pr         =  Probability
          [lb , ub]  =  [95% Confidence Interval]

. adjust himpg=1, pr ci

--------------------------------------------------------------------------------
    Dependent variable: foreign     Command: logit
   Variable left as is: weight
Covariate set to value: himpg = 1
--------------------------------------------------------------------------------
----------------------------------------------
     All |         pr          lb          ub
----------+-----------------------------------
         |    .029187    [.003519    .203809]
----------------------------------------------
    Key:  pr         =  Probability
          [lb , ub]  =  [95% Confidence Interval]


What can I say about the relationship between the predictions (aside 
from the obvious facts that they seem to be very different but their CIs 
are wide and overlap)?

     All |         pr          lb          ub
----------+-----------------------------------
         |    .193884    [.085888    .381067]
         |    .029187    [.003519    .203809]
----------------------------------------------
    Key:  pr         =  Probability
          [lb , ub]  =  [95% Confidence Interval]
Thanks.

Michael

--
Michael I. Lichter, Ph.D.
Research Assistant Professor & NRSA Fellow
UB Department of Family Medicine / Primary Care Research Institute
UB Clinical Center, 462 Grider Street, Buffalo, NY 14215
Office: CC 125 / Phone: 716-898-4751 / E-Mail: mlichter@buffalo.edu

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