= Survey Weights =

Survey weights account for the design of a survey sample and other biases/errors introduced by a survey instrument.

<<TableOfContents>>

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== The Basic Process ==

 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.

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== Base Weights ==

'''Base weights''' incorporate effects from the [[SurveySamples#Sample_Type|sampling design]]. They are the inverse of the probability of being sampled. ''Think '''desired over actual'''.''

With a ''probability sample'', base survey weights account for...

 1. probability of selection
 2. probability of responding and providing enough information to confirm eligibility, given selection
 3. probability of being eligible, given selection and response

With a ''non-probability sample'', these probabilities are all unknown. Often this step is skipped altogether.



=== Examples ===

Some practical for different probability samples:

 * For a ''census'', all respondents have a weight of '''''1'''''.
 * 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.

Note that, in each, the sum of base weights should equal the population size.

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== Non-Response Adjustments ==

Collected measures should reflect the sample (and therefore the population), and incomplete data creates gaps. Therefore it is necessary to take non-response into account while weighting data.

There are two main methods for adjusting weights based on non-response:

 1. '''Weighting class adjustments''' involve dividing the sample into discrete classes and applying an adjustment factor by class.
 2. '''Propensity score adjustments''' involve calculating the inverse of the estimated probability to respond and applying that as a secondary weight.



=== Examples ===

A simple demonstration breaks the sample into weighting classes based on responsivity, and then reapportions the weight of non-respondents to respondents.

Consider a simple design without eligibility.

||'''Class'''   ||'''Count'''||
||Respondent    ||800        ||
||Non-respondent||200        ||

To re-apportion the weight of non-respondents, the respondents' weight factors would be adjusted by a factor of (800+200)/800 or 1.25. The non-respondents would then be dropped, or assigned weight factors of 0. ''This is, again, a calculation of '''desired over actual'''.''

The abstracted process in [[Stata]] looks like:

{{{
logistic respondent sampled
predict prop if respondent
generate double wt = 1/prop
}}}



=== Non-response Bias ===

Responsivity is commonly related to the key measures of a survey, and therefore introduces '''non-response bias'''. Weighting can account for this error. The core concept is to use auxiliary frame data (i.e. descriptives known for both respondents ''and'' non-respondents).

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.

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== Calibration ==

'''Calibration''' forces the measurements to reflect ''known'' descriptives of the population. If the population is ''known'' to be 50% female, then the final estimates of the population should not contradict that fact.

Calibration follows from the same basic ideas as above, but involves distinct methods. Weights are often calibrated by many dimensions, requiring a programmed calculation. Methods include:

 * post-stratification (i.e. ''desired over actual'')
 * raking
 * linear calibration (GREG)



=== Selection of Calibration Dimensions ===

Quota variables should be selected for calibration, ''especially'' when the quotas involved oversampling of some groups.

If key descriptives of the sample appear imbalanced when compared to a 'gold standard' data source (i.e. the census), then those should also be selected.

Lastly, any descriptives that predict key measures should be selected.



=== Raking ===

'''Raking''', 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%.



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