I have come across the sampling method called "Propensity Weighting Sampling/RIM", but I do not have a good idea of what these survey methods are all about.
What references in the literature cover this topic?
Solved – a propensity weighting sampling / RIM
samplingweighted-sampling
Related Solutions
I think if each dataset is already weighted to your satisfaction, then you have a couple of different options. Which one is the right one may vary based on your objectives and the particulars of your existing data collection and weighting.
- (#1) Union all of the datasets, along with their pre-calculated weights, and that's it.
This would be the right choice if each dataset was weighted towards a proper total count and didn't over-state the importance of any individual record relative to another dataset. If one dataset was weighted to reflect Total US Population, and another dataset was weighted in place to its own total count of respondents, then this would not be the right choice.
- (#2) Calculate a weight for each dataset to multiply by each record's existing weight
This would be the right choice if each of your datasets are of equal importance regardless of their size. Example below...
- (#3) Union all of the raw data and re-calculate the weights on the new, entire dataset
This would be the right choice if the reasons for non-response are similar across your different surveys - it results in the simplest data for you to work with, and it's the least likely to produce extreme weights.
Example for #2: each dataset is weighted to equal importance, with this "dataset weight" being multiplied by whatever weight has already been calculated within the dataset.
> Survey 1: 100 people weight: 2
> Survey 2: 200 people weight: 1
> Survey 3: 300 people weight: 2/3
> Survey 4: 150 people weight: 4/3
> Survey 5: 250 people weight: 4/5
Update: substituted downloadable reference
This can be done by calibration (Sarndal (2007). Tom Lumley's Survey Package in R has a calibrate function and John D'Souza has contributed a calibration module to Stata (ssc install calibrate). Here's your example analyzed by John's calibrate command. Setting the method to linear and the entry weight wt1 to 1 seemed to produce the most similar weights. If you have a sample weight variable then use that as the entry weight.
Reference: Sarndal, C.E. 2007. The calibration approach in survey theory and practice. Survey Methodology 33, no. 2: 99-119, available at http://www.statcan.gc.ca/pub/12-001-x/2007002/article/10488-eng.pdf.
clear
input id butter flour
1 1 2
2 3 3
3 3 1
end
/* Butter */
matrix M1 = [40]
gen wt1 = 1 /* arbitrary */
calibrate , ///
marginals(butter) poptot(M1) method(linear) ///
entrywt(wt1) exitwt(wt_but)
/* Flour */
matrix M2 = [50]
calibrate , ///
marginals(flour) poptot(M2) method(linear) ///
entrywt(wt1) exitwt(wt_flou)
/* The weights */
list id butter wt_but flour wt_flou
+-------------------------------------------+
| id butter wt_but flour wt_flou |
|-------------------------------------------|
1. | 1 1 2.736842 2 7.285714 |
2. | 2 3 6.210526 3 10.42857 |
3. | 3 3 6.210526 1 4.142857 |
+-------------------------------------------+
/* Calculate weighted totals to check */
gen xbut = wt_but*butter
gen xflou = wt_flou*flour
total xbut xflou
Total estimation Number of obs = 3
--------------------------------------------------------------
| Total Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
xbut | 40 15.89474 -28.38954 108.3895
xflou | 50 23.71558 -52.03989 152.0399
--------------------------------------------------------------
Best Answer
You may know that weighting generally aims at ensuring that a given sample is representative of its target population. If in your sample some attributes (e.g., gender, SES, type of medication) are less well represented than in the population from which the sample comes from, then we may adjust the weights of the incriminated statistical units to better reflect the hypothetical target population.
RIM weighting (or raking) means that we will equate the sample marginal distribution to the theoretical marginal distribution. It bears some idea with post-stratification, but allows to account for many covariates. I found a good overview in this handout about Weighting Methods, and here is an example of its use in a real study: Raking Fire Data.
Propensity weighting is used to compensate for unit non-response in a survey, for example, by increasing the sampling weights of the respondents in the sample using estimates of the probabilities that they responded to the survey. This is in spirit the same idea than the use of propensity scores to adjust for treatment selection bias in observational clinical studies: based on external information, we estimate the probability of patients being included in a given treatment group and compute weights based on factors hypothesized to influence treatment selection. Here are some pointers I found to go further:
As for a general reference, I would suggest