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

 From Steven Samuels To statalist@hsphsun2.harvard.edu Subject Re: SV: SV: S: SV: st: Survey - raking - calibration - post stratification - calculating weights Date Mon, 8 Dec 2008 15:31:20 -0500

Kristian:

I was vague and I apologize: I mixed up the initial weights.

Step 1. Compute weight1x = N/n but now n is the number of the 3,750 in each age group. You will never use the original weight that Stas and I suggested for the 600.

Step 2. Rake age and geographical area to get new weights weight2x for the 3,750 people. To get estimates of population characteristics from the mail questionnaire, in the data set of 3,750,

Type: "svyset _n [pweight=weight1x], strata(age_grp) as before.

Then you can use -svymean- -svytab- (if available in Stata 8) to describe the population.

Step 3. For the logistic regression, you should use as many, predictors in the mail questionnaire data to predict who participated in the telephone survey, not just age and geography.

Steps 4 and beyond are now confined to the 600 men in the last phase sample. You completely ignore from this point on the 3,750 man phase.

Step 5 is correct, as long as you add more covariates to your logistic regression and check the model fit.

Step 6 is okay. You don't need to first compute the percentages, just the original totals in the age groups of the 5,000 men. You do not need the 10,000 person trick, because you are only matching to a single external population in this step.

Step 7. In Step 7, you can just provide the age group totals for the census groups, not the percentages.

Thank you for your kind of offer of acknowledgement. I think it appropriate to refer to help that you received on Statalist, but I do not wish to be acknowledged individually.

-Steve

On Dec 8, 2008, at 2:10 PM, Kristian Wraae wrote:

Ok. I'm a bit lost here. I really don't understand all the steps (especially
step 2) but I'll try to do them anyway.

*1:

Like before:
The 600:
age_grp	n_age_grp_s	pct_age_grp_s
1		38		6.33
2		47		7.83
3		41		6.83
4		41		6.83
5		44		7.33
6		38		6.33
7		44		7.33
8		48		8.00
9		43		7.17
10		41		6.83
11		42		7.00
12		35		5.83
13		39		6.50
14		33		5.50
15		26		4.33
Total 	600

And the 4975:
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 weight1 is defined as:

gen weight1=.
replace weight1 = 450 / 38 if age_grp == 1
replace weight1 = 438 / 47 if age_grp == 2
replace weight1 = 395 / 41 if age_grp == 3
replace weight1 = 375 / 41 if age_grp == 4
replace weight1 = 376 / 44 if age_grp == 5
replace weight1 = 370 / 38 if age_grp == 6
replace weight1 = 344 / 44 if age_grp == 7
replace weight1 = 315 / 48 if age_grp == 8
replace weight1 = 306 / 43 if age_grp == 9
replace weight1 = 299 / 41 if age_grp == 10
replace weight1 = 275 / 42 if age_grp == 11
replace weight1 = 271 / 35 if age_grp == 12
replace weight1 = 263 / 39 if age_grp == 13
replace weight1 = 241 / 33 if age_grp == 14
replace weight1 = 257 / 26 if age_grp == 15

*2:
?????
How do I estimate

*3:

*4:

Now I generate a variable called sample which is 1 for each of the 600 and 0
for the rest of the 3743.

.tab sample

sample	Freq.	Percent	Cum.

0		3,143	83.97		83.97
1		600	16.03		100.00

I now generate the probability of inclusion using just age and geography to
make things simple:

xi: logistic sample i.age_grp i.geo_grp

Predict p_r

*5:
gen weight2 = weight1 * (1/p_r)

*6:

Now I generate the totals for age and geography:

*age
gen pct_agex = .
replace pct_agex = 450 / 4975 if age_grp == 1
replace pct_agex = 438 / 4975 if age_grp == 2
replace pct_agex = 395 / 4975 if age_grp == 3
replace pct_agex = 375 / 4975 if age_grp == 4
replace pct_agex = 376 / 4975 if age_grp == 5
replace pct_agex = 370 / 4975 if age_grp == 6
replace pct_agex = 344 / 4975 if age_grp == 7
replace pct_agex = 315 / 4975 if age_grp == 8
replace pct_agex = 306 / 4975 if age_grp == 9
replace pct_agex = 299 / 4975 if age_grp == 10
replace pct_agex = 275 / 4975 if age_grp == 11
replace pct_agex = 271 / 4975 if age_grp == 12
replace pct_agex = 263 / 4975 if age_grp == 13
replace pct_agex = 241 / 4975 if age_grp == 14
replace pct_agex = 257 / 4975 if age_grp == 15

gen tot_agex = round(pct_agex * 10000)

replace tot_agex = tot_agex - 1 if agex ==1

*Geography
gen pct_geo =.
replace pct_geo = 2726 / 4975 if geo_gr==1
replace pct_geo = 2249 / 4975 if geo_gr==2

gen tot_geo = round(pct_geo * 10000)

* Now I rake weight2 back to the age categories & geographics

keep if sample==1

survwgt rake  weight2,   ///
by(age_grp  geo_grp) ///
totvars(tot_agex tot_geo) ///
gen(weight3)

*7

Here I make new variables for tot_agex and tot_grp from data from the Danish
Census (_DC) like this:

*age
gen pct_agex = .
replace pct_agex_DC = (DC population total in age_grp==1) / (DC population
total) if age_grp == 1
.
.
.
.
replace pct_agex_DC = (DC population total in age_grp==15) / (DC population
total) if age_grp == 15
gen tot_agex_DC = round(pct_agex_DC * 10000)

And the same for tot_geo_DC

Then I use the rake again

survwgt rake  weight3,   ///
by(age_grp  geo_grp) ///
totvars(tot_agex_DC tot_geo_DC) ///
gen(weight4)

svyset  [pweight=weight4], strata(agex)

So to estimate ed in the general populaion I would do:

svymean ed

Is it correct?

Steven if you give me your personal details I'll include you in the
acknowledgements of the paper if you'd like.

Best regards
Kristian

-----Oprindelig meddelelse-----
Fra: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] På vegne af Steven Samuels
Sendt: Monday, December 08, 2008 6:13 PM
Til: statalist@hsphsun2.harvard.edu
Emne: Re: SV: S: SV: st: Survey - raking - calibration - post stratification
- calculating weights

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

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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