A web of correlations can help or hurt you. Be the spider, not the fly.

In recent posts, I’ve shown how confounding variables can flip your statistical analysis results on its head. And I’ve shown how random assignment in experiments can protect you from them in some cases. You might wonder:

• If you can’t randomize, is there another way to avoid the dangers of confounding variables?
• And, is there a way to use their power for good?

Fortunately, the answer to each question is “yes!”

What you need are proxy variables. A proxy variable is an easily measurable variable that is used in place of a variable that cannot be measured or is difficult to measure. The proxy variable can be something that is not of any great interest itself, but has a close correlation with the variable of interest.

Confounding variables and proxy variables are essentially the same thing: correlated predictor variables. But there's a huge difference between them:

• Confounding variables affect your results in undesirable ways by not being included in the model. They are primarily a danger when you aren’t aware of them during the analysis.
• Proxy variables benefit your analysis. You know about and intentionally include them in the model to improve your results.

Wise data analysts can find ways to avoid getting burned by confounding variables and instead use proxy variables to their advantage. Here's a case where knowledge truly is power: specifically, knowledge of your subject matter and the correlation structure amongst your variables allows you to use these correlations to your advantage.

Prediction

Imagine that you are mostly interested in predicting something and that you don’t care so much about identifying true cause-and-effect relationships. Fortunately, prediction doesn’t always require a causal relationship between predictor and response. Instead, a proxy variable that is simply correlated to the response, and is easier to obtain than a causally connected variable, might well do the job.

For example, my colleague, Kevin, does an excellent job using regression analysis to assist those who play fantasy football. Recently, he used a model that included one predictor variable -- each player’s fantasy football points from the prior season -- to predict his points for the subsequent season. Clearly, the points from one season are not causing the points for the next season. Rather, the points are a proxy variable for a host of other variables such as each player’s skills and capabilities, those of their team, the teams they play against, etc. It’s impossible to measure all of these, so a proxy variable is essential. His model for choosing quarterbacks has an r-squared of 73.68%. In this case, there is enough of a correlation from one year to the next that he can use the model for prediction, even though we don’t know or measure the exact causal variables.

Produce unbiased results

Now, imagine that you are working on a research project where some of the variables are difficult, if not impossible, to measure. Remember, if you don’t include the intended variable in any form, your results could be biased 180 degrees from what they should be. Including an imperfect proxy of a hard-to-measure variable is often better than not including an important variable at all. So, if you can’t include the intended variable, look for a proxy!

## Examples of proxy variables

Intended variable Proxy variable
Historical environmental conditions Widths of tree rings
Quality of life Per-capita GDP
True body fat percentage Body Mass Index (BMI)
Cognitive ability Years of education and/or GPA
Depth that light penetrates into the ocean over large areas Satellite images of ocean surface color
Hormone levels in blood Changes in height over a fixed time

Do you have examples of proxy variables that have helped you out in your analyses?