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| Survey weights account for the design of a survey sample and other biases/errors introduced by a survey instrument. | '''Survey weights''' account for the [[Statistics/SurveySampling|design of a survey sample]] and [[Statistics/SurveyInference#Non-sampling_Error|non-sampling error]]. |
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| == The Basic Process == | == Description == |
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| 1. Set survey dispositions 2. Calculate base weights 3. Apply non-response adjustments to base weights 4. Calibrate the weights See [[SurveyDisposition|here]] for details about survey dispositions. ---- |
The design weight, or base weight, reflects unequal [[Statistics/SurveySampling|probabilities of selection]]. Generally this is simply the inverse of the sampling probability: ''n,,k,,/N'' for all strata ''k''. |
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| == Calculating Weights == | === Non-Response Adjustments === |
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| The base weight is the inverse of the probability of being sampled. Think ''desired over actual''. As such, the sum of base weights should equal the population size. | All real surveys feature [[Statistics/SurveyInference#Non-sampling_Error|non-sampling error]], especially non-response. If non-response is uncorrelated with key metrics, it is negligible. There almost always is some observable [[Statistics/NonResponseBias|non-response bias]], i.e. an attribute that is known for the entire population and is correlated with both a key metric and responsivity. This bias can be corrected with a '''non-response adjustment''' to the survey weights. |
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| For a SRS design, this is calculated as a simple rate. Given a population of 20,000 and a sample size of 667, the propbability of being sampled is 20,000/667 = '''29.99'''. | It is also reasonable to expect that there is ''unobserved'' bias, i.e. an attribute that is not known. |
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| For a STSRS design, the same process is applied per stratum. | A non-response adjustment factor generally moves weight from non-respondents to comparable respondents. If there are no significant attributes that can be used to establish comparability, then the adjustment is a flat multiplier: the total of cases over the count of respondents. (Non-respondents have their weight set to 0.) |
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| ---- | If there are significant attributes, responsivity can be modeled. There are generally two approaches: * '''weighting class adjustment''': The population (or stratum subpopulation) is partitioned into N-tiles according to the predicted responsivity. Each N-tile then receives a separate flat multiplier as described above. * '''propensity score adjustment''': Every respondent's weight is multiplied by the inverse of the predicted responsivity, while non-respondents have their weight set to 0. General practice is then to re-normalize the weights such that they sum to the same total as before applying the adjustment. Modeling on insignificant or uncorrelated attributes does not introduce bias, but it does inflate variance. |
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| == Non-Response Adjustments == | === Post-Stratification === |
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| Survey weights can adjust for non-response bias. The core concept is to use auxiliary frame data (i.e. descriptives known for ''both'' respondents and non-respondents) that is correlated with key measures or responsivity. | Post-stratification is employed in survey weighting for several reasons: * There may be measurable [[Statistics/SurveyInference#Sampling_Error|sampling errors]], such as undercoverage, which can be corrected. * Incorporating auxiliary information, i.e. the known distribution of the population, into survey estimates should increase accuracy. * Post-stratified estimates are consistent. Estimates across surveys will match on e.g. the proportion of women in the population if they are all post-stratified according to the same targets. |
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| '''Weighting class adjustments''' divides the sample into weighting classes and applies a class-specific adjustment factor to every case. '''Propensity score adjustments''' calculates the inverse of the estimated probability to respond and applies that as a secondary weight. Adjustments are applied in phases. Cases with unknown eligibility often cannot be adjusted through these methods, and need to be removed. Ineligible cases often are undesirable in analysis datasets, so weights are further adjusted to account for their removal. ---- == Calibration Adjustments == Survey weights can be adjusted to ensure that known population descriptives are reflected in the estimates. Methods include: * post-stratification (i.e. ''desired over actual'') * raking * linear calibration (GREG) |
There are two approaches to this post-stratification: [[TheCalibrationApproachInSurveyTheoryAndPractice|GREG estimation and calibration estimation]]. Calibration is known under a variety of other names: '''raking''', '''iterative proportional fitting''', and '''RIM weighting'''. |
Survey Weights
Survey weights account for the design of a survey sample and non-sampling error.
Description
The design weight, or base weight, reflects unequal probabilities of selection. Generally this is simply the inverse of the sampling probability: nk/N for all strata k.
Non-Response Adjustments
All real surveys feature non-sampling error, especially non-response. If non-response is uncorrelated with key metrics, it is negligible. There almost always is some observable non-response bias, i.e. an attribute that is known for the entire population and is correlated with both a key metric and responsivity. This bias can be corrected with a non-response adjustment to the survey weights.
It is also reasonable to expect that there is unobserved bias, i.e. an attribute that is not known.
A non-response adjustment factor generally moves weight from non-respondents to comparable respondents. If there are no significant attributes that can be used to establish comparability, then the adjustment is a flat multiplier: the total of cases over the count of respondents. (Non-respondents have their weight set to 0.)
If there are significant attributes, responsivity can be modeled. There are generally two approaches:
weighting class adjustment: The population (or stratum subpopulation) is partitioned into N-tiles according to the predicted responsivity. Each N-tile then receives a separate flat multiplier as described above.
propensity score adjustment: Every respondent's weight is multiplied by the inverse of the predicted responsivity, while non-respondents have their weight set to 0. General practice is then to re-normalize the weights such that they sum to the same total as before applying the adjustment.
Modeling on insignificant or uncorrelated attributes does not introduce bias, but it does inflate variance.
Post-Stratification
Post-stratification is employed in survey weighting for several reasons:
There may be measurable sampling errors, such as undercoverage, which can be corrected.
- Incorporating auxiliary information, i.e. the known distribution of the population, into survey estimates should increase accuracy.
- Post-stratified estimates are consistent. Estimates across surveys will match on e.g. the proportion of women in the population if they are all post-stratified according to the same targets.
There are two approaches to this post-stratification: GREG estimation and calibration estimation. Calibration is known under a variety of other names: raking, iterative proportional fitting, and RIM weighting.