Sampling weight when using regression or descriptive statistics

Question

I came across sampling weight when I was looking into analyzing survey data.

I was wondering whether we need to take into consideration sampling weight when we are running linear/non-linear regression model or descriptive statistics.

Answer 1

Simple answer: Yes, we do

Complex answer: How we do this will depend on the nature of your sampling scheme. In SAS see the PROC SURVEY... procedures (there are several, all starting with "survey"). In R, see, e.g. the survey package. For texts, see, e.g.

Thompson, S.K. (2012). Sampling (3rd ed.), Wiley.

Answer 2

I am obviously seconding Peter Flom's answer, but would recommend somewhat different references (Thompson is just a sampling book, I don't recall him discussing the issue of modeling, although I could be wrong, I have not looked into that book for quite a while):

1. Binder and Roberts (2003, 2009) discuss comparisons between model-based inference (a plain i.i.d. regression model, simply speaking) and design-based inference (inference with the target of a finite population with an informative design)
2. Pfeffermann (2011) was an invited Waksberg lecture, the top distinction given by Statistics Canada to a survey statistician once a year. These lectures are always worth reading if you are in the survey statistics field.
3. Mary Thompson's book is a more theoretical material on modeling using complex surveys. She (together with Godambe) is the original developer of the framework of estimating equations as applied to survey data.

A condensed basic answer is: if you are absolutely sure that you have correctly specified your model, and you've included all the relevant design information (which in the case of nonlinear regression may imply interactions of every term with the strata indicators, and random effects for PSUs), then you might get accurate answers. Otherwise, you would want to proceed with straight design-based inference that is at least consistent for the population parameters of the census regression. If this paragraph did not make any sense, start looking up these references.