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

 From "Kristian Wraae" To Subject SV: SV: SV: st: Survey - raking - calibration - post stratification - calculating weights Date Sun, 7 Dec 2008 20:18:10 +0100

```Ok, I'll try do it as I understand you just to make sure I've got it right.

I will try to do the different steps here with the numbers I have.

1.
So you say I must define weight1 first.

Our imaginative background population is 10.000 individuals. And if we
assume that the sample of 4975 men we recieved from the register is
representative for the background population regarding age composition I get
(I can get the exact numbers for each age group for the paper but for now
I'll use the 4975 as the population):

weight1 = 10000 / 4975

Now let us just try to calibrate the dataset for age and smoking.

I will here keep the 15 age strata just to make it simple.

The 4975 men were distributed like this:

age_grp	n_age_grp	pct_age_grp	Cum.
1		450		9.05		9.05
2		438		8.80		17.85
3		395		7.94		25.79
4		375		7.54		33.33
5		376		7.56		40.88
6		370		7.44		48.32
7		344		6.91		55.24
8		315		6.33		61.57
9		306		6.15		67.72
10		299		6.01		73.73
11		275		5.53		79.26
12		271		5.45		84.70
13		263		5.29		89.99
14		241		4.84		94.83
15		257		5.17		100.00
Total		4975

So I create a variable called pct_age_grp = n_age_grp / 4975 and get the
values above.

Now I create the variable

gen tot_age_grp = round(pct_age_grp * 10000)

It looks like this

age_grp	tot_age_grp
1		904
2		880
3		794
4		754
5		756
6		744
7		691
8		633
9		615
10		601
11		553
12		545
13		529
14		484
15		517
Total		10001

So I subtract one from group 1 :

replace tot_age_grp = tot_age_grp - 1 if age_grp == 1

Now the total is 10000.

For smoking I have a variable based on packyear which has three categories.

smoke_grp	n_smoke_grp	pct_smoke_grp
1		801		23.45
2		1,272		37.24
3		1,343		39.31
Total		3416

So I generate tot_smoke_grp = round(pct_smoke_grp * 10000)

The totals are:

smoke_grp	tot_smoke_grp
1		2345
2		3724
3		3931
Total		10000

So the total is 10000. No need to do more here.

My dataset contains all 4975 men. I assume that I should drop all
observations except the ones for 600 men before running the survwgt ?

keep if sample == 1 (the 600 men all had sample == 1 and everybody
else has sample == 0)

So now I run the survwgt command:

survwgt rake  weight1,   ///
by(age_grp  smoke_gr) ///
totvars(tot_age_grp tot_smoke_grp) ///
gen(weight2)

If I have a binary variable called ed amongst the 600 men. And the
distribution amongst these men is that 23% have ed = 1 and the rest have
ed==0.

How do I estimate ed amongst the 10.000 men?

Is it:

svymean ed

I really appreciate all your help

Best regards
Kristian Wraae

-----Oprindelig meddelelse-----
Fra: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] På vegne af Steven Samuels
Sendt: Sunday, December 07, 2008 5:02 PM
Til: statalist@hsphsun2.harvard.edu
Emne: Re: SV: SV: st: Survey - raking - calibration - post stratification -
calculating weights

Kristian, raking on the two or more variables, with the totals coming
from different populations, is easy.

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.

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.

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.

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

You must compute the percentages of observations in each category of
agex externally and merge them into the 600 man data set.

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
Important: If the totals do not add to 10,000 then adjust the counts
of the largest few categories so they do.

You can add tot_agex by hand to the  600 man data set, or create it
externally and merge it in.

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

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

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.

med_smok     pct_med_smok    tot_medsmok
1
2
3
..
9

If you  do this, then you do not need the separate medicin adjustment
and smoke margins.

3. Rake the three control variables (agex, medicin, smoke)
simultaneously.

**************************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***************************

(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)"

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.

4. Finally: -svyset- your data and run Stata's survey programs:

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

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.

-Steven

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

> Thanks Stas & Steven
>
> What I would like to do is to calibrate on some of the measures
> from the
> first questionaire.
>
> 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
> 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
> educated, smoke less and do more exercise and then they are
> slightly less
> prone to have chronic diseases and then they are slightly younger.
>
> 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?
>
> 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.
>
> I don't know the tot_medgb (medicin) or tot_smokegp (smoking)
> amongst the
> 5000 but only amongst the 3750.
>
> 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?
>
> 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.
>
> 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?
>
> Thank you for your help
> Kristian
>
>
>
> -----Oprindelig meddelelse-----
> Fra: owner-statalist@hsphsun2.harvard.edu
> [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://
> 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:
>
>> Steven,
>>
>> you might be shocked, but people in Nordic countries do have their
>> population completely enumerated. Putting NJC's hat on :)), let me
>> 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
>> 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
>> 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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