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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 |
Survey weights begin with the inverse of the [[Statistics/SurveySampling|sampling probability]]. This is known as the '''base weight'''. |
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| See [[SurveyDisposition|here]] for details about survey dispositions. | The weight of non-respondents, or more generally anyone who cannot be used for analysis, is reallocated to respondents. This is usually done in a manner that accounts for [[Statistics/SurveyInference#Non-sampling_Error|non-sampling error]], especially [[Statistics/NonResponseBias|measurable non-response bias]]. In the simplest case though, if there are no meaningful predictors of response propensity, the weights of non-respondents can be set to 0 and the weights of respondents can be scaled up by a corresponding flat adjustment factor. |
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| ---- == Calculating Weights == 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. 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'''. For a STSRS design, the same process is applied per stratum. |
The final step is [[Statistics/PostStratification|post-stratification]]. This can address [[Statistics/SurveyInference#Sampling_Error|sampling errors]] such as undercoverage. Typically, post-stratification is done by a large set of discrete dimensions such that the true population counts are not known. An algorithm called '''raking''' or '''calibration''' is used to approximate the adjustment. |
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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. | Non-response bias exists when non-response is correlated with a metric of interest, introducing bias into the population estimate. |
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| '''Weighting class adjustments''' divides the sample into weighting classes and applies a class-specific adjustment factor to every case. | If non-response is measurable, i.e. response propensity can be predicted using auxiliary information known about the entire sample, then it can also be corrected for. |
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| '''Propensity score adjustments''' calculates the inverse of the estimated probability to respond and applies that as a secondary weight. | A '''weighting class adjustment''' is calculated by using predicted propensity to segment the sample, leading to a response rate per class. Within each class, the inverse of the response rate is the non-response adjustment. Non-respondents have their weight set to 0, as it has been reallocated to respondents that are predicted to be similar in terms of response patterns. |
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| 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. | A '''propensity score adjustment''' is calculated as the inverse of predicted propensity. Inclusion of insignificant or uncorrelated predictors does not introduce bias in such an adjustment, but it does decrease precision because the variance is increased. As such, when utilizing a linear model for predictions, it is common to use stepwise removal of covariates. |
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| == Calibration Adjustments == | == Post-Stratification == |
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| Survey weights can be adjusted to ensure that known population descriptives are reflected in the estimates. | Post-stratification is applied because some characteristics of the true population are known, and furthermore are expected to correlate with the metric of interest. By forcing the survey weights to match the known distribution, they are more likely to correct for biases introduced by [[Statistics/SurveyInference#Sampling_Error|sampling errors]]. The population estimates are also more applicable to the true population. |
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| Methods include: | As a result, there are circumstances where post-stratified weights are not applicable. For example, when modeling non-response, the population of interest is in fact the sample, ''not'' the true population. |
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| * post-stratification (i.e. ''desired over actual'') * raking * linear calibration (GREG) |
Post-stratification is often done according to many complex dimensions. For example, the interactions of sex by age [[Statistics/Binning|bins]] (male and 18-24; male and 25-34; and so on). True population counts for the margins of these dimensions are usually available, not not necessarily the cells/intersections. Furthermore, some intersections are likely to have so few respondents that the weights would be inappropriately large. |
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| '''Iterative proportional fitting''', more generally known as '''raking''', is an algorithm for post-stratification in such a circumstance. It involves looping over the dimensions, post-stratifying the weights toward those marginal counts one at a time. This small loop is then repeated in a larger loop until a convergence criterion is achieved, or for a pre-determined number of iterations. '''RIM (random iterative method) weighting''' is essentially the same thing. | |
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| '''Calibration''', or '''GREG (generalized regression) estimation''', is a more generalized algorithm. It utilizes a linear regression model to re-weight towards marginal counts. | |
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| === Raking === Rakign, or RIM weighting, involves applying post-stratification by each dimension iteratively, until the weights converge. Convergence is defined as the root mean square (RMS) falling below a threshold, typically 0.000005. Raked weights generally should not be applied if their efficiency falls below 70%. |
In terms of automated convergence criteria, a common choice is to stop when the root mean square (RMS) of the weights themselves falls below a threshold like 0.000005. Another is to stop when the absolute change to the weights themselves falls below a threshold like 0.0001. |
Survey Weights
Survey weights account for the design of a survey sample and non-sampling error.
Description
Survey weights begin with the inverse of the sampling probability. This is known as the base weight.
The weight of non-respondents, or more generally anyone who cannot be used for analysis, is reallocated to respondents. This is usually done in a manner that accounts for non-sampling error, especially measurable non-response bias. In the simplest case though, if there are no meaningful predictors of response propensity, the weights of non-respondents can be set to 0 and the weights of respondents can be scaled up by a corresponding flat adjustment factor.
The final step is post-stratification. This can address sampling errors such as undercoverage. Typically, post-stratification is done by a large set of discrete dimensions such that the true population counts are not known. An algorithm called raking or calibration is used to approximate the adjustment.
Non-Response Adjustments
Non-response bias exists when non-response is correlated with a metric of interest, introducing bias into the population estimate.
If non-response is measurable, i.e. response propensity can be predicted using auxiliary information known about the entire sample, then it can also be corrected for.
A weighting class adjustment is calculated by using predicted propensity to segment the sample, leading to a response rate per class. Within each class, the inverse of the response rate is the non-response adjustment. Non-respondents have their weight set to 0, as it has been reallocated to respondents that are predicted to be similar in terms of response patterns.
A propensity score adjustment is calculated as the inverse of predicted propensity.
Inclusion of insignificant or uncorrelated predictors does not introduce bias in such an adjustment, but it does decrease precision because the variance is increased. As such, when utilizing a linear model for predictions, it is common to use stepwise removal of covariates.
Post-Stratification
Post-stratification is applied because some characteristics of the true population are known, and furthermore are expected to correlate with the metric of interest. By forcing the survey weights to match the known distribution, they are more likely to correct for biases introduced by sampling errors. The population estimates are also more applicable to the true population.
As a result, there are circumstances where post-stratified weights are not applicable. For example, when modeling non-response, the population of interest is in fact the sample, not the true population.
Post-stratification is often done according to many complex dimensions. For example, the interactions of sex by age bins (male and 18-24; male and 25-34; and so on). True population counts for the margins of these dimensions are usually available, not not necessarily the cells/intersections. Furthermore, some intersections are likely to have so few respondents that the weights would be inappropriately large.
Iterative proportional fitting, more generally known as raking, is an algorithm for post-stratification in such a circumstance. It involves looping over the dimensions, post-stratifying the weights toward those marginal counts one at a time. This small loop is then repeated in a larger loop until a convergence criterion is achieved, or for a pre-determined number of iterations. RIM (random iterative method) weighting is essentially the same thing.
Calibration, or GREG (generalized regression) estimation, is a more generalized algorithm. It utilizes a linear regression model to re-weight towards marginal counts.
In terms of automated convergence criteria, a common choice is to stop when the root mean square (RMS) of the weights themselves falls below a threshold like 0.000005. Another is to stop when the absolute change to the weights themselves falls below a threshold like 0.0001.