# 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 14:56:22 -0500

```On Dec 7, 2008, at 2:18 PM, Kristian Wraae wrote:
```
```I'll use the 4975 as the population):

weight1 = 10000 / 4975

```
No: The advice was to use a different weight in each age group. weight1 = N/n where the N is in your list below and the "n" the corresponding number in the sample of 600 men. So, for example if, in age group 1 there were 30 men in the sample of 600, then weight1 would have the value (450/30) = 15 for that group. The population size "10,000" is purely a convenient fiction so that the total population counts will match for all the control variables (age and smoking, here). It's okay to use such a fiction because for estimating means and proportions, the population totals do not matter.
```
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.
```
```YES

```
```
```
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 ?

```
Yes--this is key. If your outcomes are only defined in the 600 man sample, then that is the analysis data set. I see above that you have missing values for smoking among the 3,750 men who responded to the second phase of the survey. You have a potential problem if any of the 600 men in the final sample are also missing the smoking variable.. For the purposes of raking you must assign these men to one of the three smoking categories. I suggest that you assign them as close to the known proportions as possible-about 23% to group1, 37% to group 2, and 39% to group 3.
```
```
```	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)
```
```
YES

```
```
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

```
No the command is " svy: mean ed" You must first -svyset- your data, as I outlined below. Don't use any finite population correction ("fpc") options.
```
```
At this point you should familiarize yourself with the different commands available. Try -help for "svy" and, from there, for -svy estimation-. Both the help and manual have good examples.
```
Good luck

Steven

```
```

-----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?

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:
```
```*
```
```
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```