= Survey Weights = '''Survey weights''' account for the [[Statistics/SurveySampling|survey design]], [[Statistics/SurveyInference#Sampling_Error|sampling error]], and [[Statistics/SurveyInference#Non-sampling_Error|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 [[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 == * [[CalibrationEstimatorsInSurveySampling|Calibration estimators in survey sampling]], Jean-Claude Deville and Carl-Erik Särndal, 1992 * [[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 Poststratitication Weights]], Laura C. Lazzeroni and Roderick J.A. Little, 1998 * [[TheGeneralizedExponentialModelForSamplingWeightCalibrationForExtremeValuesNonresponseAndPostStratification|The generalized exponential model for sampling weight calibration for extreme values, nonresponse, and poststratification]], R.E. Folsom and A.C. Singh, 2000 * [[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 ---- CategoryRicottone