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

 From Steven Samuels To statalist@hsphsun2.harvard.edu Subject Re: SV: st: Survey - raking - calibration - post stratification - calculating weights Date Sun, 7 Dec 2008 13:20:33 -0500

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```Correction: "by age" in the code examples should have been "by agex".

On Dec 7, 2008, at 11:01 AM, Steven Samuels wrote:

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Kristian, raking on the two or more variables, with the totals coming from different populations, is easy.
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1. Create the initial weight1 =N/n with "population" N and sample n in age groups as Stas and I suggested in the previous email.
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2. Then, create categorized variables for age, medicin, smoke You will create counts for these categories (tot_age, tot_medicin, tot_smoke) from the control percentages, but with a "population size" of 10,000 across all.
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2.1 Age: These will be numbers based on percentages in the original 5,000 men, though it would be *much* better to base them on the Danish Census data. (If I were a journal reviewer, I would not accept a publication that did not do this unless there was a very good reason.) The data source (5,000 men or census) is known as the "external" or "control" population for age.
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I would suggest you create a variable with fewer than 15 categories, as too many categories can prevent the raking algorithm from working. I will call the variable agex
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You must compute the percentages of observations in each category of agex externally and merge them into the 600 man data set.
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For example, suppose that in the control population, the first few categories of agex have the following percentages
```
agex    pct_agex     tot_agex (= 100 x pct_agex, rounded to nearest 1)

1         8.23          823
2        10.41         1041
etc.

Total   100.00        10,000
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Important: If the totals do not add to 10,000 then adjust the counts of the largest few categories so they do.
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You can add tot_agex by hand to the 600 man data set, or create it externally and merge it in.
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2.2. For medicin, do the same kind of categorization, but base the percentages on the 3,750 man data set. Here I assume that medicin, has three categories.
```
medicin    pct_medicin    tot_medicin
1           30.23         3023
2           45.86         4586
3           23.93         2393
Total      100.02        10002

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The original totals must be adjusted so that they add up exactly to 10,000. In this case, for example I would subtract 1 from totals for the largest two groups. 3023->3022 and 4586 ->4585
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2.3. You can also do the same with smoking: create smoke categories and tot_smok as the totals in each which add to 10,000 exactly. In fact, if the number of smoking and medicin combinations is small (say 3 x 3 = 9), you can create a combined variable, with the percentages in each.
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med_smok     pct_med_smok    tot_medsmok
1
2
3
..
9

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If you do this, then you do not need the separate medicin adjustment and smoke margins.
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3. Rake the three control variables (agex, medicin, smoke) simultaneously.
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**************************CODE BEGINS**************************
survwgt rake  weight1,   ///
by(age medicin smoke) ///
totvars(tot_agex tot_medicin tot_smoke ///
gen(weight2)
***************************CODE ENDS***************************
Or, with a combined med_smok margin.
**************************CODE BEGINS**************************
survwgt rake  weight1,   ///
by(age med_smok) ///
totvars(tot_agex tot_med_smok ///
gen(weight2)
***************************CODE ENDS***************************

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(Note the comma in the first line, which was missing from my previous post.) Rarely will you need more than the default 10 iterations in -survwgt rake-. If you do, the program will issue an error message. You can increase the number by adding a -maxrep- option at the end: e.g. "maxrep(100)"
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If the number of sample observations in any control cell (agex, medicin, smoke (or medicin_smoke) is too small, then the program may not converge or will take a long time. In that case, you will need to merge sparse adjacent categories. Suppose, for example, that you start out with 9 medicin_smoke combinations, but two of them have few observations among the 600 men final sample. Then merge these into adjacent categories and create a new 7 category variable.
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4. Finally: -svyset- your data and run Stata's survey programs:

svyset _n [pweight=weight2], strata(age_gp)

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Here "age_gp" is your original age variable with 15 categories. You can probably omit the strata option at no loss. Be sure that if you want estimates for subpopulations, you do use the -subpop- option and not an "if" option.
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-Steven

On Dec 7, 2008, at 4:52 AM, Kristian Wraae wrote:

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```Thanks Stas & Steven

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What I would like to do is to calibrate on some of the measures from the
```first questionaire.

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I have data on 3750 men from that first questionnaire and I would like to transform my 600 man population into my 5000 man population so that the distribution of chronic diseases and medication is the same as we would
```expect it to be in the 5000 man population.

I know how the 5000 men differs from the 3750 men regarding age and
geaography. There was a slight effect of age, but geography was not
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important for non-responders. So adjusting for age is really the only thing
```needed at this step.

Then I know how the 600 differs from the 3750 men. The 600 are better
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educated, smoke less and do more exercise and then they are slightly less
```prone to have chronic diseases and then they are slightly younger.

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So I'd like to weight each of the 600 men so that I can compensate for education, smoking, physical activity, chronic diseases (and medication but they are closely related so I think I'll just adjust for medication as it is
```the most precise measure) and age.

So if I want to adjust for those, how do I go by that?

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I can see that the code below will adjust on age and geography since those data are present through the two steps, but the more detailed information on
```smoing, health and lifestyle is only present in step two.

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I don't know the tot_medgb (medicin) or tot_smokegp (smoking) amongst the
```5000 but only amongst the 3750.

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That is how do I incoorporate the two steps into the raking? Or should I use the post stratification command instead since I know these data on the
```individual level?

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As I see it running two rakings after each other: one for step 1 and one for step 2 would risk changing the what has been done in the first raking.
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I might be stupid but I don't really see how I can do this using the code
```below.

Also,how many variables is it adviseable to rake on?

Kristian

-----Oprindelig meddelelse-----
Fra: owner-statalist@hsphsun2.harvard.edu
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[mailto:owner-statalist@hsphsun2.harvard.edu] På vegne af Steven Samuels
```Sendt: Sunday, December 07, 2008 6:43 AM
Til: statalist@hsphsun2.harvard.edu
```
Emne: Re: SV: st: Survey - raking - calibration - post stratification -
```calculating weights

--

Stas, I am envious of statisticians who draw samples from those
lists.  This is a double sample and I agree with your advice: give
everyone the weight for their age stratum:
weight1 = N_i/n_i
where "N" denotes population and "n" denotes sample size.  Kristian
apparently thinks of the 5,000 person sample as his "population"; the
figure that he linked to does not show the initial sampling step at
all. He may not have access to  the one-year census counts. If he
does not, I suggest that he use the N's from the 5,000.  I  suggest
below that he also form  geographic categories and rake those, with
population counts, if possible, otherwise with counts from the
5,000.  I roughly calculate that with 5,000 in the first phase
sample, bias in estimates and in standard errors will be small.

Kristian, here is how to simultaneously match the age distribution
and the geographic distribution of the final sample to your
population. (This is called "sample balancing" or "raking".)  Form
age groups (agegp) and geographical groupings (geogp) and get the
population counts(or percentages, see below) in each cell.

**************************CODE BEGINS**************************
* tot_agep =  total for population in participant age group (agegp)
* tot_geogp = total for population in participant geographical group
(geogp)
**************************************************************

survwgt rake  weight1  ///
by(agegp geogp) ///
totvars(tot_agegp tot_geogp ///
gen(weight2)
***************************CODE ENDS***************************

Raking can present problems, so so I suggest that you read http://
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www.abtassociates.com/ presentations/raking_survey_data_2_JOS.pdf. If you
```cannot get
population counts, perhaps you can get population percentages,
multiply by 10 or 100 and  round to the nearest whole number (e.g.
5.12% = 51 or 512), so that the population "size" is 1,000 or 10,000.
For estimating means and proportions, these will yield nearly the
same results as actual population counts. The Denmark census counts
or percentages might be available only in larger age categories than
the ones you used to draw the sample: say (60-64, 65-70,70-74). If
so, use those for the raking calculations.

If you have, say, four geographical categories, you may be tempted to
use  4 x 15 =60 stratification combinations.  However, with only 600
people in the final sample, the numbers in individual cells will be
too small for reliable estimation.

Theory for double sampling can be found in WG Cochran, 1973, Sampling
Techniques, pp 117-119, 327-334,  or in most other texts.
Unfortunately, raking will not completely solve the problem of non-
response.

-Steven

On Dec 6, 2008, at 11:19 PM, Stas Kolenikov wrote:

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```Steven,

you might be shocked, but people in Nordic countries do have their
population completely enumerated. Putting NJC's hat on :)), let me
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remind you that this is an international list, and different countries have different standards of how they collect and store their official
```data. Denmark has a register with an equivalent of SSN that makes it
possible to combine the data three ways from economic, medical and
social perspectives. That's a survey statistician and a
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microeconometrician dream... and they actually do have the capacity of
```drawing SRS. That is, the first 5000 were SRS of the population, and
then Kristian continued a with stratified second phase sampling.

I would probably just give everybody the weight = # in age group
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across Denmark (in some meaningfully defined period of the study) / #
```in age in group in the sample. If you treat sample groups as
non-response adjustment cells, that's what this will probably boil
down to after multiplication of three or so fractions. ches and help
try:
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```*
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```
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