calibrating survey weights in stata · syntax familiar work flow 1.use svyset to specify the...
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Calibrating Survey Weights in Stata
Jeff PitbladoStataCorp LLC
2018 Canadian Stata Users Group MeetingVancouver, Canada
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Outline
Motivation
Methods
Syntax
Stata Example
Summary
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Motivation
Survey data analysisWe collect data from a population of interest so that we candescribe the population and make inferences about thepopulation.
SamplingThe goal of sampling is to collect data that represents thepopulation of interest.
I If the sample does not reasonably represent the populationof interest, then we cannot accurately describe thepopulation or make inferences.
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Motivation
WeightingSampling weights provide a measure of how many individuals agiven sampled observation represents in the population.
I In simple random sampling (SRS), the sampling weight isconstant
wi = N/n
I N is the population sizeI n is the sample size
I Other, more complicated, sampling designs are also selfweighting, but this is more a special case than the norm.
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Motivation
WeightingSurvey methods employ sampling weights, in the computationof descriptive statistics and the fitting of regression models, inorder to describe the population and make inferences about thepopulation.
Sampling weights
I Correctly scaled sampling weights are necessary forestimating population totals.
I Typically provide for consistent and approximatelyunbiased estimates.
I Typically provide for more accurate variance estimationwhen used with the survey design characteristics.
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Motivation
Non-responseFailure to observe all the individuals that were selected for thesample.
I A common cause for some groups to be under-representedand other groups to be over-represented.
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Motivation
ExampleConsider a survey design that intends for individuals sampledfrom group g to have weight
wgi =Ng
ng
I Ng is the population size for group gI ng is the group’s sample size
If we observe mg < ng individuals, then wgi is smaller than itshould be. Group g is under-represented in the sample.
I Seems reasonable to adjust wgi by something that willmake them sum to Ng in the sample.
w̃gi = wging
mg=
Ng
mg
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Motivation
Weight adjustmentWeight adjustment tries to give more weight tounder-represented groups and less weight to over-representedgroups.
I The idea is to cut down on bias, thus make point estimatesmore consistent for the things they are estimating.
I Has been used to force estimation results to be numericallyconsistent with externally sourced measurements.
I Tends to result in more efficient point estimates.I The degree to which they are more efficient is a function of
the correlation between the analysis variable and theauxiliary information used to adjust the weights.
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Methods
PoststratificationAdjust weights so that the poststratum totals agree with“known” values.
I simple method for weight adjustmentI requires poststratum identifiers are present in the sample
informationI single categorical auxiliary variable
I requires population poststratum totalsI adjustment is a function of the sampling weights and
poststratum totalsI new feature in Stata 9
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Methods
CalibrationAdjust the sampling weights to minimize the difference between“known” population totals and their weighted estimates.
I postratification is a special caseI supports multiple categorical auxiliary variablesI supports count and continuous auxiliary variablesI adjustment is a function of the sampling weights and
auxiliary informationI new feature in Stata 15
I raking-ratio methodI general regression method (GREG)
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Syntax
Familiar work flow
1. Use svyset to specify the survey design characteristics.I Sampling unitsI Sampling and replication weightsI StrataI Finite population correction (FPC)I Poststratification, raking-ratio, or GREG
2. Use the svy: prefix for estimation.I Calibration is supported by the following variance
estimation methods:I LinearizationI Balanced repeated replication (BRR)I BootstrapI JackknifeI Successive difference replication (SDR)
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Syntax
svyset psu[weight
], options || ...
Poststratification options
I poststrata(varname) specifies variable containing thepoststratum identifiers
I postweight(varname) specifies variable containing thepoststratum totals
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Syntax
svyset psu[weight
], options || ...
Calibration options
I rake(calspec) specifies the raking-ratio methodI regress(calspec) specifies the GREG methodI calspec has syntax
varlist, totals(totals)
I varlist contains the list of auxiliary variables and allowsfactor variables notation
I totals specifies the population totals for each auxiliaryvariable
I var=# specify each population total separatelyI matname specify the population totals using a matrix
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Stata Example
Simulated population
frame count index variablestrata 2 h st1PSU 1,000 i su1SSU 100 jtotal 200,000
I y is the measurement of interestI µy , the mean of y, is the parameter of interestI a and b are continuous auxiliary variablesI f and g are categorical auxiliary variables
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Stata Example
Simulated population
ahij = µa + νahi + εahij
I νahi i.i.d. N(0, 100)I εahij i.i.d. N(0, 100)I ν and ε are independentI a has intraclass correlation ρ2
a = .5I µa = 10I total for a is 2,000,000I f categorizes a into 4 roughly-equal groups
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Stata Example
Simulated population
bhij = µb + νbhi + εbhij
I νbhi i.i.d. N(0, 100)I εbhij i.i.d. N(0, 300)I ν and ε are independentI b has intraclass correlation ρ2
b = .25I µb = 5I total for b is 1,000,000I g categorizes b into 2 roughly-equal groups
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Stata Example
Simulated populationCell and margin sizes of f and g:
. table f g, row col
gf 1 2 Total
1 23,238 22,693 45,9312 25,286 29,486 54,7723 27,618 25,059 52,6774 22,615 24,005 46,620
Total 98,757 101,243 200,000
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Stata Example
Simulated population
yhij = β0 + β1ahij + β2bhij + νyhi + εyhij
I νyhi i.i.d. N(0, 100)I εyhij i.i.d. N(0, 100)I ν and ε are independentI y has intraclass correlation ρ2
b = .5I β0 = 10, β1 = 4, β2 = 2I y has overall mean
µy = β0 + β1µa + β2µb
= 10 + 4 × 10 + 2 × 5 = 60
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Stata Example
Simulated populationStrength of association between y, a, and b:
. correlate y a b(obs=200,000)
y a b
y 1.0000a 0.8012 1.0000b 0.5655 0.0017 1.0000
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Stata Example
Simulated populationStrength of association between y, f, and g:
. correlate y f g(obs=200,000)
y f g
y 1.0000f 0.5774 1.0000g 0.2560 -0.0022 1.0000
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Stata Example
Sample from the populationStratified two-stage design:
1. select 20 PSUs within each stratum2. select 10 individuals within each sampled PSU
With zero non-response, this sampling scheme yielded:I 400 sampled individualsI constant sampling weights
pw = 500
Other variables:I w4f – poststratum weights for fI w4g – poststratum weights for g
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Stata Example
Sample weighted cell totals for f. table f [pw=pw], c(freq min w4f) format(%9.0gc)
f Freq. min(w4f)
1 50,000 45,9312 75,000 54,7723 59,000 52,6774 16,000 46,620
I Over-represented: 2I Under-represented: 4
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Stata Example
Sample weighted cell totals for g. table g [pw=pw], c(freq min w4g) format(%9.0gc)
g Freq. min(w4g)
1 105,000 98,7572 95,000 101,243
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Stata Example
Work flow
1. Specify the survey design characteristics:
svyset su1 [pw=pw], strata(st1) ...
2. Estimate the population parameter of interest:
svy: mean y
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Stata Example
PostratificationI Using fsvyset su1 [pw=pw], strata(st1) ///
poststrata(f) postweight(w4f)
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Stata Example
Raking-ratio using factor variable f
I Without population size, need bn.svyset su1 [pw=pw], strata(st1) ///
rake(bn.f, totals(1.f=45931 ///2.f=54772 ///3.f=52677 ///4.f=46620))
I With population size, i. is sufficientsvyset su1 [pw=pw], strata(st1) ///
rake(i.f, totals(1.f=45931 ///2.f=54772 ///3.f=52677 ///4.f=46620 ///
_cons=200000))
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Stata Example
zero non-response sample, using f
Variable orig post rake regress
y 53.005247 62.788326 62.788326 62.7883267.4721232 5.3039955 5.3039955 5.3039955
N_pop 200,000 200,000 200,000 200,000
legend: b/se
I Reminder: µy is 60I Weight adjustment changed the point estimate.I Smaller variance estimates indicate a more efficient mean
estimate.
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Stata Example
zero non-response sample, using g
Variable orig post rake regress
y 53.005247 54.091047 54.091047 54.0910477.4721232 6.8654765 6.8654765 6.8654765
N_pop 200,000 200,000 200,000 200,000
legend: b/se
I Reminder: µy is 60I Recall that g is not as strongly associated with y as f.
I Smaller change to the mean estimate.I Smaller change in the variance estimates.
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Stata Example
Raking-ratio using factor variables f and gsvyset su1 [pw=pw], strata(st1) ///
rake(bn.f bn.g, ///totals(1.f=45931 ///
2.f=54772 ///3.f=52677 ///4.f=46620 ///1.g=98757 ///2.g=101243))
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Stata Example
zero non-response sample, using f and g
Variable original rake regress
y 53.005247 64.435965 64.0793487.4721232 4.2315801 4.2355881
N_pop 200,000 200,000 200,000
legend: b/se
I Reminder: µy is 60I Distinct mean estimates.I Bigger reduction in the variance estimates.
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Stata Example
Raking-ratio using continuous variable a
I Using a without population totalsvyset su1 [pw=pw], strata(st1) ///
rake(a, totals(a=2000000))
I Using a with population totalsvyset su1 [pw=pw], strata(st1) ///
rake(a, totals(a=2000000 ///_cons=200000))
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Stata Example
zero non-response sample, using a
Variable orig rake_noc rake
y 53.005247 60.855469 64.0831797.4721232 3.6519173 3.6369672
N_pop 200,000 218,098 200,000
legend: b/se
I Reminder: µy is 60I Distinct mean estimates.I Big reduction in the variance estimates.
I Recall the strong association between y and a.
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Stata Example
zero non-response sample, using b
Variable orig rake_noc rake
y 53.005247 52.43749 52.3992757.4721232 6.4023137 6.4042111
N_pop 200,000 199,239 200,000
legend: b/se
I Reminder: µy is 60I Recall that b is not as strongly associated with y as a.
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Stata Example
CalibrationI Using a and bsvyset su1 [pw=pw], strata(st1) ///
rake(a b, totals(a=2000000 ///b=1000000 ///
_cons=200000))
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Stata Example
zero non-response sample, using a and b
Variable orig rake regress
y 53.005247 63.553724 63.6130317.4721232 1.5635263 1.5635551
N_pop 200,000 200,000 200,000
legend: b/se
I Reminder: µy is 60I Distinct mean estimates.I Biggest reduction in the variance estimates.
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Stata Example
Sample from the population, with non-responseStratified two-stage design:
1. select 20 PSUs within each stratum2. select 10 individuals within each sampled PSU
With 10% non-response, this sampling scheme yielded:I 361 sampled individualsI constant sampling weights
pw = 500
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Stata Example
Sample weighted cell totals for f. table f [pw=pw], c(freq min w4f) format(%9.0gc)
f Freq. min(w4f)
1 18,500 45,9312 66,500 54,7723 44,500 52,6774 51,000 46,620
I Over-represented: 2, 4I Under-represented: 1, 3
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Stata Example
10% non-response sample, using f
Variable orig post rake regress
y 68.335883 63.452068 63.452068 63.4520686.6819885 5.5113469 5.5113469 5.5113469
N_pop 180,500 200,000 200,000 200,000
legend: b/se
I Reminder: µy is 60I Weight adjustment changed the point estimate.I Smaller variance estimates, as we expected.
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Stata Example
10% non-response sample, using f and g
Variable orig rake regress
y 68.335883 59.974513 60.2344836.6819885 4.4071179 4.464893
N_pop 180,500 200,000 200,000
legend: b/se
I Reminder: µy is 60I Distinct mean estimates.I Bigger reduction in the variance estimates.
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Stata Example
10% non-response sample, using a
Variable orig rake regress
y 68.335883 58.572179 58.5956516.6819885 4.3092797 4.3223863
N_pop 180,500 200,000 200,000
legend: b/se
I Reminder: µy is 60I Distinct mean estimates.I Big reduction in the variance estimates.
I Recall the strong association between y and a.
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Stata Example
10% non-response sample, using a and b
Variable orig rake regress
y 68.335883 59.887132 59.8853566.6819885 1.1631547 1.1586559
N_pop 180,500 200,000 200,000
legend: b/se
I Reminder: µy is 60I Distinct mean estimates.I Biggest reduction in the variance estimates.
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Summary
I Calibration weight adjustments are determined by theoriginal sampling weights and auxiliary variables.
I Expect more efficient estimates for outcomes that have astrong association with the auxiliary variables.
I Use svyset option rake() or regress().I Use bn. operator for factor variables in varlist.I Use _cons to specify the population size in totals().
I Use svy: prefix.I All variance estimation methods support calibration.
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References
Deville, J.-C., and C.-E. Särndal. 1992. Calibration estimatorsin survey sampling. Journal of the American StatisticalAssociation 87: 376–382.
Deville, J.-C., C.-E. Särndal, and O. Sautory. 1993. Generalizedraking procedures in survey sampling. Journal of the AmericanStatistical Association 88: 1013–1020.
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