survey weights are used when data are collected according to a probability sampling design with unequal probabilities of selection and/or response
Survey weights are used when data are collected according to a probability sampling design with unequal probabilities of selection and/or response.
In survey sampling, the inferential goal is to generalize from the sample to the finite population. The original motivation for survey weights comes from Horvitz-Thompson estimator of the population total: $$ t[y] = \sum_{i \in \mbox{units in sample}} \frac{y_i}{\pi_i} $$ where $\pi_i$ is the probability of selection. In this expression, $1/\pi_i$ can be interpreted as a weight attached to unit $i$, $w_i=\pi_i^{-1}$.
In practice, survey weights also include corrections for nonresponse, lack of population coverage, and other corrections for imbalance between the sample and the population.
References:
- Korn and Graubard (1995 JRSS-A)
- Korn and Graubard (1999 Wiley book)
- Heeringa, West and Berglund (2010 Chapman and Hall)
- Valliant, Dever and Kreuter (2013 Springer book)
- Kolenikov and Pitblado (2014 chapter in Wiley handbook)
- Pfeffermann (1996 SMMR)
- Lohr (2009 Cengage textbook)
- Lavallee and Beaumont (2015 invited article in SMIF)
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