|
Size: 364
Comment:
|
Size: 4796
Comment: Link
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 3: | Line 3: |
| 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|survey design]], [[Statistics/SurveyInference#Sampling_Error|sampling error]], and [[Statistics/SurveyInference#Non-sampling_Error|non-sampling error]]. |
| Line 11: | Line 11: |
| == The Basic Process == | == Description == |
| Line 13: | Line 13: |
| 1. Set survey dispositions 2. Set base weights 3. Apply non-response adjustments to base weights 4. Calibrate the weights |
Survey data is collected through a mechanism which can be specified statistically. If it is not specified, bias can be introduced and [[Analysis/Estimation|estimates]] can be over-confident. [[Statistics/InverseVarianceWeights|Inverse variance weights]] are related, but not the same. Survey weights begin with [[Statistics/DesignWeights|design weights]] reflecting [[Statistics/SurveySampling|probability of selection]]. Generally this is simply the inverse of the sampling probability: ''n,,k,,/N'' for all strata ''k''. All real surveys feature [[Statistics/SurveyInference#Non-sampling_Error|non-sampling error]], especially [[Statistics/SurveyNonresponse|nonresponse]]. If nonresponse is uncorrelated with key metrics, it is negligible. Otherwise there is potential for [[Statistics/NonresponseBias|nonresponse bias]]. This bias can be corrected through survey weights in a few ways: * [[Statistics/InverseProbabilityWeights|inverse propensity adjustments]] * [[Statistics/WeightingClassAdjustment|weighting class adjustments]] Modeling on insignificant or uncorrelated attributes does not introduce bias, but it does inflate [[Statistics/Variance|variance]]. [[Statistics/Calibration|Calibration]] can be used to: * make estimates be consistent with known true population proportions * correct [[Statistics/SurveyInference#Sampling_Error|sampling error]] like undercoverage or overcoverage * further correct for non-sampling error like nonresponse bias The methods here include: * raking * iterative proportional fitting * RIM weighting * [[Statistics/GeneralizedRegressionEstimator|GREG estimators]] ---- == Weighted Estimators == Survey weights ''w'' are designed such that a population proportion ''μ'' can be calculated using the weighted estimator ''Σ(wx) / Σw''. In the case that all cases have equal weight, [[Statistics/Moments#Description|it is straightforward to show]] that the [[Statistics/Variance|variance]] of that estimator is ''w^2^σ^2^''. In any other case, the variance is given by ''Σ(w^2^σ^2^) / (Σw)^2^''. This ratio must then be linearized or simulated to arrive at an approximate variance. [[Calculus/TaylorSeries|Taylor expansion]] is a common strategy for linearization. ---- == Reading Notes == * [[TheEffectOfWeightTrimmingOnNonlinearSurveyEstimates|The Effect of Weight Trimming on Nonlinear Survey Estimates]], Frank J. Potter, 1993 * [[SamplingWeightsAndRegressionAnalysis|Sampling Weights and Regression Analysis]], Christopher Winship and Larry Radbill, 1994 * [[ImprovingOnProbabilityWeightingForHouseholdSize|Improving on Probability Weighting for Household Size]], Andrew Gelman and Thomas C. Little, 1998 * [[RandomEffectsModelsForSmoothingPoststratificationWeights|Random-effects Models for Smoothing PoststratiÆcation Weights]], Laura C. Lazzeroni and Roderick J.A. Little, 1998 * [[UsingCalibrationWeightingToAdjustForNonresponseAndCoverageErrors|Using Calibration Weighting to Adjust for Nonresponse and Coverage Errors]], Phillip S. Kott, 2006 * [[StrugglesWithSurveyWeightingAndRegressionModeling|Struggles with Survey Weighting and Regression Modeling]], Andrew Gelman, 2007 * [[TheCalibrationApproachInSurveyTheoryAndPractice|The calibration approach in survey theory and practice]], Carl-Erik Särndal, 2007 * [[ASingleFrameMultiplicityEstimatorForMultipleFrameSurveys|A single frame multiplicity estimator for multiple frame surveys]], Fulvia Mecatti, 2007 * [[PracticalConsiderationsInRakingSurveyData|Practical Considerations in Raking Survey Data]]; Michael P Battaglia, David C Hoaglin, and Martin R Frankel (and sometimes David Izrael); 2009 * [[StatisticalParadisesAndParadoxesInBigData|Statistical Paradises and Paradoxes in Big Data]], Xiao-Li Meng, 2018 * [[ANewParadigmForPolling|A New Paradigm for Polling]], Michael A. Bailey, 2023 * [[TheLawOfLargePopulationsDoesNotHeraldAParadigmShiftInSurveySampling|The “Law of Large Populations” Does Not Herald a Paradigm Shift in Survey Sampling]], Roderick J. Little, 2023 * [[SurveysOfConsumersTechnicalReport|Surveys of Consumers Technical Report: Technical Documentation for the 2024 Methodological Transition to Web Surveys]], 2024 * [[TheEffectOfOnlineInterviewsOnTheUniversityOfMichiganSurveyOfConsumerSentiment|The effect of online interviews on the University of Michigan Survey of Consumer Sentiment]], Ryan Cummings and Ernie Tedeschi, 2024 |
Survey Weights
Survey weights account for the survey design, sampling error, and non-sampling error.
Description
Survey data is collected through a mechanism which can be specified statistically. If it is not specified, bias can be introduced and estimates can be over-confident.
Inverse variance weights are related, but not the same.
Survey weights begin with design weights reflecting probability of selection. Generally this is simply the inverse of the sampling probability: nk/N for all strata k.
All real surveys feature non-sampling error, especially nonresponse. If nonresponse is uncorrelated with key metrics, it is negligible. Otherwise there is potential for nonresponse bias. This bias can be corrected through survey weights in a few ways:
Modeling on insignificant or uncorrelated attributes does not introduce bias, but it does inflate variance.
Calibration can be used to:
- make estimates be consistent with known true population proportions
correct sampling error like undercoverage or overcoverage
- further correct for non-sampling error like nonresponse bias
The methods here include:
- raking
- iterative proportional fitting
- RIM weighting
Weighted Estimators
Survey weights w are designed such that a population proportion μ can be calculated using the weighted estimator Σ(wx) / Σw.
In the case that all cases have equal weight, it is straightforward to show that the variance of that estimator is w2σ2.
In any other case, the variance is given by Σ(w2σ2) / (Σw)2. This ratio must then be linearized or simulated to arrive at an approximate variance. Taylor expansion is a common strategy for linearization.
Reading Notes
The Effect of Weight Trimming on Nonlinear Survey Estimates, Frank J. Potter, 1993
Sampling Weights and Regression Analysis, Christopher Winship and Larry Radbill, 1994
Improving on Probability Weighting for Household Size, Andrew Gelman and Thomas C. Little, 1998
Random-effects Models for Smoothing PoststratiÆcation Weights, Laura C. Lazzeroni and Roderick J.A. Little, 1998
Using Calibration Weighting to Adjust for Nonresponse and Coverage Errors, Phillip S. Kott, 2006
Struggles with Survey Weighting and Regression Modeling, Andrew Gelman, 2007
The calibration approach in survey theory and practice, Carl-Erik Särndal, 2007
A single frame multiplicity estimator for multiple frame surveys, Fulvia Mecatti, 2007
Practical Considerations in Raking Survey Data; Michael P Battaglia, David C Hoaglin, and Martin R Frankel (and sometimes David Izrael); 2009
Statistical Paradises and Paradoxes in Big Data, Xiao-Li Meng, 2018
A New Paradigm for Polling, Michael A. Bailey, 2023
The “Law of Large Populations” Does Not Herald a Paradigm Shift in Survey Sampling, Roderick J. Little, 2023
The effect of online interviews on the University of Michigan Survey of Consumer Sentiment, Ryan Cummings and Ernie Tedeschi, 2024