Andrey Kamenov, Ph.D. Probability and Statistics
In one of our previous posts, we presented you with a map showing how the average health levels (measured using our Health Index) differ between groups of respondents based on several factors, like income level or state of residence.
What we did not take into account (intentionally) was the correlation between these variables (or as a statistician would say, “regressors”). Can the difference in health index between the states be explained solely by looking at income levels (which affect ease of healthcare access as well as food choices)? In other words, are people in California indeed healthier than Texas residents with the same background? Let’s find out.
We are going to use quite a few control variables to minimize the effect they have on the respondents’ general health. These include age, Body Mass Index values, the average consumption of alcoholic beverages, smoking rates and others. Doing so will allow us to focus on our factor of choice.
Now, how do you measure the effect of a single factor? Let’s take the respondent’s sex, for example. After having controlled for all other correlated factors, we use the so-called average marginal effect, which shows us the average difference between the values (the probabilities, actually) predicted by our model for all respondents dependent on their sex. In fact, this single factor has a pretty significant effect — men are 5 percent more likely than women to assess their general health as “Very good” or even “Excellent.”
Next, let’s see how various chronic conditions affect respondents’ perception of their health. Again, the vertical axis shows how much the likelihood of having better-than-average health decreases with each condition alone.
The first point on the chart stands out — it appears as though skin cancer has virtually no effect on general health. Our guess is that there’s one more hidden variable: sun exposure. While commonly considered to have a positive impact on both physical and mental health, it has also been shown to positively correlate with skin cancer incidence rates. Unfortunately, the survey doesn’t contain any data on the amount of time spent outdoors, so we cannot offer a decisive conclusion.
All other chronic conditions (not surprisingly) have a statistically significant negative impact on respondents’ health. These range from an 8 percent decrease in the likelihood for people with asthma to have above-average health to a 22 percent decrease caused by diabetes.
Also, what about less obvious variables? We started the post discussing the location factor — let’s see if it does indeed matter for your health.
Here’s the thing to keep in mind: since we do not have any “reference” group to compare each state against, basically we are comparing them against the national average. This will lead us to have the data being centered — so that it reflects the relative effect the state of residence has after controlling for other variables.
Here you can see a somewhat less noisy picture, compared to the raw map we saw earlier. The southern states stand out; people living in Texas, Louisiana, Mississippi or Alabama are 4 percent more likely to rate their health as "Very good" or even "Excellent," given all other factors remain the same.
Source(s):
- Behavioral Risk Factor Surveillance System annual survey data, 2011-2014
About Andrey Kamenov
Andrey Kamenov, Ph.D. Probability and Statistics
Andrey Kamenov is a data scientist working for Advameg Inc. His background includes teaching statistics, stochastic processes and financial mathematics in Moscow State University and working for a hedge fund. His academic interests range from statistical data analysis to optimal stopping theory. Andrey also enjoys his hobbies of photography, reading and powerlifting.
Other posts by Andrey Kamenov: