Re: SV: S: SV: st: Survey - raking - calibration - post stratification - calculating weights

[Steven Samuels <sjhsamuels@earthlink.net>]

On Dec 8, 2008, at 2:55 AM, Kristian Wraae wrote:

> Ok, thanks.
>
> Now I understand how to do the raking procedure.
>
> I have one question though.
>
> Since I have a two step inclusion procedure wouldn't it be more  
> accurate to
> rake in two steps.
>
> Example:
> I know the distribution of medication amongst the 3745 men.
>
> But the 3745 men differs from the 4975 men by being slightly  
> younger and we
> know that the older you get the more medicin do you get. That also  
> goes for
> physical activity and smoking.
>
> So if I calculate the expected prevalences amongst the 4975 (in  
> order to
> rake the 600) from the 3750 I risk making a mistake  
> (underestimating the
> prevalences in the baclground population). I guess should be  
> calculating the
> all prevalences from the 4975, but I don't those data.
>
> So wouldn't it be more correct to:
>
> 1. Rake the 3750 so they match the 4975 on age and geography.
>
> 2. Calculate all the expected prevalences on age, medication, smoking,
> physical activity ect from the now raked 3750 (as we would expect  
> them to be
> had we had a 100% response rate).
>
> 3. Use these prevalences to rake the 600 as you showed me?


Your concern is a good one, Kristian.  However, the solution you  
propose is ad-hoc with no real theoretical justification. I've tried  
some complicated raking in the past, but I have never seen a  
reference to the method you propose. You have much questionnaire  
information on too many informative variables; raking can use only a  
small part of it.  There is a standard approach to this problem:   
model the probability of participating in the phone interview. I  
suggest you consult the text "Statistical Analysis with Missing Data"  
by Little & Rubin, especially Chapters 3 & 13.  In the parlance of  
that book, you must assume that data are "Missing at Random". This  
means that the probability of having a phone interview depends  
completely on characteristics known from the mail questionnaire or  
the census.

Here are the steps:

1. Estimate weight1 = N_i/n_i  as before for the 15 age groups.

2. You can use this weight on the second phase sample of 3,750 to  
estimate various properties of the population known such as  
proportions in categories of medication, physical activity smoking.   
These may be of interest in themselves.

3. Instead of raking, use -logistic- or -logit- (not the survey  
versions)  on the 3,750 men to predict who participated in the  
telephone interview.  Consider as covariates: age, geography,  
medication, physical activity, smoking and any others that might be  
of use.

4. Generate the predicted probability of participating in the  
telephone interview.   Call this p_r.  Your goal is to get a good  
prediction, so compute ROC curves, if possible.  (I don't recall if  
Stata 8 has the -lroc- command.)

5. For the 600 men in the telephone survey, compute:  weight2 =  
(weight1) x (1/p_r).

6.  Rake weight2 back to the age categories & geographic categories  
of  the 5,000 men.  Call the result "weight3".

7. Finally rake weight3 to the Danish Census age/geographical  
breakdowns: Call it "weight4".

7. Use this as your final analysis weight for -svymean-.

You are a long way from the simplicity of Stas's earlier suggestion  
to use "weight1" on your data.  Standard errors that you compute will  
be under-estimated, because they do not account for the uncertainty  
in the estimating "weight3", and you must state this in your report.   
If you wish to compute the proper standard errors, you must, I think,  
bootstrap the process starting no later than Step 3.  This is the  
price for using the complex sampling design.

-Steve

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