Proxy variables are easily measurable variables that analysts include in a model in place of a variable that cannot be measured or is difficult to measure. Proxy variables can be something that is not of any great interest itself, but has a close correlation with the variable of interest.
Imagine you have an important variable to include in your model but you can’t measure it. If you leave it out, it’s a confounding variable that can flip your statistical analysis results on its head thanks to omitted variable bias. Random assignment in experiments can protect you from confounders in some cases.
However, what do you do when you can’t randomize and you can’t measure the important variable to include it in your model? Are you stuck with omitted variable bias?
Fortunately, proxy variables are a potential solution.
Confounding variables and proxy variables are related concepts: 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. Statisticians also refer to them as lurking variables.
- 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 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, an analyst I know uses regression analysis for 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.
Related post: Using Regression to make Predictions
Produce unbiased results
Now, imagine 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, omitted variable bias can produce inaccurate results. 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!
Related posts: Confounding Variables and Omitted Variable Bias
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?
what proxy variables can be used for food security (availability, access and utilization)?
Great article – I download your intro to stat’s books to see if you cite the opening line but didn’t find it. Do you have a source or text book that can be referenced for using highly corelated proxy variables in a forecast model?
“Proxy variables are easily measurable variables that analysts include in a model in place of a variable that cannot be measured or is difficult to measure. Proxy variables can be something that is not of any great interest itself, but has a close correlation with the variable of interest.”
Hi Ron, I write about using proxy variables in my regression book. There is more detail in it than I include in this post.
Hi! Thanks for the great explanation. I was wondering if it possible to have two proxy confounders “between” the confounder and the outcome (or exposure)?
E.g. exposure proxy confounder -> proxy confounder -> outcome
Many thanks!
SW
Thank you so much for this wonder full explanation
You’re very welcome, Amanullah!
Another type of variable, the opposite of this in a way, is an “index” variable. It’s a combination of several measurements into one variable. For example, the Bureau of the Census has a lot of data it collects on census tracts: average people per household, percent of people earning over or under a certain amount, percent below the poverty level, etc… these can be combined with a formula into a “socioeconomic index” score for each census tract. You can make the formula any way you want — weight some variables more than others, for example; or include mostly economic characteristics. This is used in demographics and epidemiology, often as a proxy for socio-economic status. “Socio-economic Status” can be anything, there’s no strict definition of it, so it can’t be measured directly in the first place.
Thanks for sharing! That sounds like a great way to incorporate a variety of information in your model.
Very instrumental books indeed !
Thank you!