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

[Steven Samuels <sjhsamuels@earthlink.net>]

Michael would like a standard error for the weighted average of
           P(foreign|himpg =0, Z) - P(foreign | high mpg=1, Z)
with other covariates at their original values Z. In SUDAAN parlance,  
the weighted average of the individual estimated probabilities is a  
"predicted marginal" and the difference is a contrast in the  
predicted marginals. (SUDAAN 8.0 Manual, p. 266).

SUDAAN cam compute standard errors for the predicted marginals and  
their contrasts. Stata can compute the predicted marginals and  
contrasts, but not their standard errors.

To compute the predicted marginals and their contrasts in Stata, run - 
svy: logit- . Then compute the individual predicted values: -adjust-  
will do it easily with the -pr- and -gen- options. Once individual  
predictions are at hand, -generate- the difference between any two. A  
call to -svy: mean- will compute the average of the predicted values  
(i.e. the "predicted marginals" and of the differences. However the  
standard error produced by -svy: mean- will not account for  
uncertainty in the estimated coefficients, and so will be too small.

Despite this, it may be useful, and perhaps something is to be  
learned graphing the distribution of the differences for various  
groups, with -dotplot-.

Michael can also get an idea of the magnitude of error in individual  
predictions by computing confidence intervals for them; he can do  
this by running -predict- after his -svy: logit-. If he generates the  
linear predictor -xb- and its standard error -stdp-, he can compute a  
CI for the linear predictor, then endpoints for the predicted  
probability itself. He could then plot a histogram of the length of  
these intervals. -predictnl- run after -svy: logit- can also directly  
compute the difference in probabilities and will also produce a  
standard error for these differences.



-Steve



On Sep 24, 2008, at 3:53 PM, Michael I. Lichter wrote:


> 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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