Thomas Lumley (in his weblog Biased & Inefficient) and Andrew, Jennifer, and Aki (of their ebook Regression and Different Tales) write about 3 flavors of weights in statistics:
1. survey weights describe how the survey pattern could be scaled as much as the inhabitants. A technique to consider them is how many individuals within the inhabitants every individual within the pattern represents. These could also be extra sophisticated than 1/probability-of-being-sampled, as we’ll see under.
2. frequency weights describe what number of precise observations have a sure sample of variables (e.g. a weight of 12 on the women-age-37-from-New-York row says that there are 12 such ladies within the information).
3. precision weights describe the precision (1/variance) of the observations, making them fairly distinct from the primary 2 flavors.
For many level estimates, all 3 are handled the identical. What’s completely different is variance estimation. Go learn Thomas and Andrew et al. for heaps extra. We right here will deal with the primary taste and break it down into 3 subflavors (my spell examine says this isn’t a phrase) of survey weights:
A) inverse-response-probability weights are primarily based on a mannequin for response R (e.g. Logistic regression). The load is then W = 1/Ehat[R | X]. See Lumley 2010 Part 9.2.2:
B) equal weights are primarily based on a mannequin for consequence of curiosity Y. We calibrate to recognized inhabitants information about X: E[Ehat[Y | X, sample]]. Then the equal weights are the expressions in Gelman 2007, no less than for linear fashions of Y. Simplifying to classical linear fashions, that is the Generalized REGression (GREG) estimator, and is similar as our third subflavor:
C) calibrated weights are primarily based on discovering W such that the weighted estimates of X match their recognized totals. There is no such thing as a specific mannequin right here.
Särndal 2007 contrasts B and C:
Statisticians who work within the space are of two sorts: These devoted to “GREG considering” and people devoted to “calibration considering”….I’m not venturing to say that the latter considering is extra prevalent in nationwide statistical businesses and the previous extra prevalent within the tutorial circles, however maybe there may be such an inclination….The linear GREG estimator implies weights that occur to be calibrated…
Särndal acquired to be each kinds of statistician, as a researcher at Sweden’s nationwide statistical businesses and as a professor.
Which kind of statistician are you ? What’s your favourite taste of weights ?
