Survey Weights
Survey weights account for the design of a survey sample and other biases/errors introduced by a survey instrument.
Contents
The Basic Process
- Set survey dispositions
- Calculate base weights
- Apply non-response adjustments to base weights
- Calibrate the weights
See here for details about survey dispositions.
Calculating Weights
The base weight is the inverse of the probability of being sampled. Think desired over actual.
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.
Non-Response Adjustments
There are two main methods for adjusting weights:
Weighting class adjustments involve dividing the sample into discrete classes and applying an adjustment factor by class.
Propensity score adjustments involve calculating the inverse of the estimated probability to respond and applying that as a secondary weight.
Reapportioning Weight
The collected measures should reflect the sample (and therefore the population), but incomplete data complicates this. It is common to break the sample into weighting classes based on responsivity, and then reapportion 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.
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.
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)
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%.