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:

  1. Korn and Graubard (1995 JRSS-A)
  2. Korn and Graubard (1999 Wiley book)
  3. Heeringa, West and Berglund (2010 Chapman and Hall)
  4. Valliant, Dever and Kreuter (2013 Springer book)
  5. Kolenikov and Pitblado (2014 chapter in Wiley handbook)
  6. Pfeffermann (1996 SMMR)
  7. Lohr (2009 Cengage textbook)
  8. Lavallee and Beaumont (2015 invited article in SMIF)

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