Dear Dr. Jay:
How do I know if my weighting matrix is good?
I’m excited you asked me this because it’s one of my favorite questions of all time.
First we need to talk about why we weight data in the first place. We weight data because our ending sample is not truly representative of the general population. This misrepresentation can occur because of non-response bias, poor sample source and even bad sample design. In my opinion, if you go into a research study knowing that you’ll end up weighting the data, there may be a better way to plan your sample frame.
Case in point, many researchers intentionally over-quota certain segments and plan to weight these groups down in the final sample. We do this because the incidence of some of these groups in the general population is small enough that if we rely on natural fallout we would not get a readable base without a very large sample. Why wouldn’t you just pull a rep sample and then augment these subgroups? The weight needed to add these augments into the rep sample is 0.
Arguments for including these augments with a very small weight include the treatment of outliers. For example, if we were conducting a study of investors and we wanted to include folks with more than $1,000,000 in assets, we might want to obtain insights from at least 100 of these folks. In a rep sample of 500, we might only have 25 of them. This means I need to augment this group by 75 respondents. If somehow I manage to get Warren Buffet in my rep sample of 25, he might skew the results of the sample. Weighting the full sample of 100 wealthier investors down to 25 will reduce the impact of any outlier.
A recent post by Nate Cohn in the New York Times suggested that weighting was significantly impacting analysts’ ability to predict the outcome of the 2016 presidential election. In the article, Mr. Cohn points out, “there is a 19-year-old black man in Illinois who has no idea of the role he is playing in this election.” This man carried a sample weight of 30. In a sample of 3000 respondents, he now accounts for 1% of the popular vote. In a close race, that might just be enough to tip the scale one way or the other. Clearly, he showed up on November 8th and cast the deciding ballot.
This real life example suggests that we might want to consider “capping” extreme weights so that we mitigate the potential for very small groups to influence overall results. But bear in mind that when we do this, our final sample profiles won’t be nationally representative because capping the weight understates the size of the segment being capped. It’s a trade-off between a truly balanced sample and making sure that the survey results aren’t biased. [Tweet this!]
Dr. Jay loves designing really big, complex choice models. With over 20 years of DCM experience, he’s never met a design challenge he couldn’t solve.
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