What sort of identification do you get from panel data if effects are long-term? Air pollution and cognition example.

Don MacLeod writes:

Perhaps you know this study which is being taken at face value in all the secondary reports: “Air pollution causes ‘huge’ reduction in intelligence, study reveals.” It’s surely alarming, but the reported effect of air pollution seems implausibly large, so it’s hard to be convinced of it by a correlational study alone, when we can suspect instead that the smarter, more educated folks are more likely to be found in polluted conditions for other reasons. They did try to allow for the usual covariates, but there is the usual problem that you never know whether you’ve done enough of that.

Assuming equal statistical support, I suppose the larger an effect, the less likely it is to be due to uncontrolled covariates. But also the larger the effect, the more reasonable it is to demand strongly convincing evidence before accepting it.

From the above-linked news article:

“Polluted air can cause everyone to reduce their level of education by one year, which is huge,” said Xi Chen at Yale School of Public Health in the US, a member of the research team. . . .

The new work, published in the journal Proceedings of the National Academy of Sciences, analysed language and arithmetic tests conducted as part of the China Family Panel Studies on 20,000 people across the nation between 2010 and 2014. The scientists compared the test results with records of nitrogen dioxide and sulphur dioxide pollution.

They found the longer people were exposed to dirty air, the bigger the damage to intelligence, with language ability more harmed than mathematical ability and men more harmed than women. The researchers said this may result from differences in how male and female brains work.

The above claims are indeed bold, but the researchers seem pretty careful:

The study followed the same individuals as air pollution varied from one year to the next, meaning that many other possible causal factors such as genetic differences are automatically accounted for.

The scientists also accounted for the gradual decline in cognition seen as people age and ruled out people being more impatient or uncooperative during tests when pollution was high.

Following the same individuals through the study: that makes a lot of sense.

I hadn’t heard of this study when it came out so I followed the link and read it now.

You can model the effects of air pollution as short-term or long-term. An example of a short-term effect is that air pollution makes it harder to breathe, you get less oxygen in your brain, etc., or maybe you’re just distracted by the discomfort and can’t think so well. An example of a long-term effect is that air pollution damages your brain or other parts of your body in various ways that impact your cognition.

The model includes air pollution levels on the day of measurement and on the past few days or months or years, and also a quadratic monthly time trend from Jan 2010 to Dec 2014. A quadratic time trend, that seems weird, kinda worrying. Are people’s test scores going up and down in that way?

In any case, their regression finds that air pollution levels from the past months or years are a strong predictor of the cognitive test outcome, and today’s air pollution doesn’t add much predictive power after including the historical pollution level.

Some minor things:

Measurement of cognitive performance:

The waves 2010 and 2014 contain the same cognitive ability module, that is, 24 standardized mathematics questions and 34 word-recognition questions. All of these questions are sorted in ascending order of difficulty, and the final test score is defined as the rank of the hardest question that a respondent is able to answer correctly.

Huh? Are you serious? Wouldn’t it be better to use the number of questions answered correctly? Even better would be to fit a simple item-response model, but I’d guess that #correct would capture almost all the relevant information in the data. But to just use the rank of the hardest question answered correctly: that seems inefficient, no?

Comparison between the sexes:

The authors claim that air pollution has a larger effect on men than on women (see above quote from the news article). But I suspect this is yet another example of The difference between “significant” and “not significant” is not itself statistically significant. It’s hard to tell. For example, there’s this graph:

The plot on the left shows a lot of consistency across age groups. Too much consistency, I think. I’m guessing that there’s something in the model keeping these estimates similar to each other, i.e. I don’t think they’re five independent results.

The authors write:

People may become more impatient or uncooperative when exposed to more polluted air. Therefore, it is possible that the observed negative effect on cognitive performance is due to behavioral change rather than impaired cognition. . . . Changes in the brain chemistry or composition are likely more plausible channels between air pollution and cognition.

I think they’re missing the point here and engaging in a bit of “scientism” or “mind-body dualism” in the following way: Suppose that air pollution irritates people, making it hard for people to concentrate on cognitive tasks. That is a form of impaired cognition. Just cos it’s “behavioral,” doesn’t make it not real.

In any case, putting this all together, what can we say? This seems like a serious analysis, and to start with the authors should make all their data and code available so that others can try fitting their own models. This is an important problem, so it’s good to have as many eyes on the data as possible.

In this particular example, it seems that the key information is coming from:

– People who moved from one place to another, either moving from a high-pollution to a low-pollution area or vice-versa, and then you can see if their test scores went correspondingly up or down. After adjusting for expected cognitive decline by age during this period.

– People who lived in the same place but where there was a negative or positive trend in pollution. Again you can see if these people’s test scores went up or down. Again, after adjusting for expected cognitive decline by age during this period.

– People who didn’t move, comparing these people who lived all along in high- or low-pollution areas, and seeing who had higher test scores. After adjusting for demographic differences between people living in these different cities.

This leaves me with two thoughts:

First, I’d like to see the analyses in these three different groups. One big regression is fine, but in this sort of problem I think it’s important to understand the path from data to conclusions. This is especially an issue given that we might see different results from the three different comparisons listed above.

Second, I am concerned with some incoherence regarding how the effect works. The story in the paper, supported by the regression analysis, seems to be that what matters is long-term exposure. But, if so, I don’t see how the short-term longitudinal analysis in this paper is getting us to that. If effects of air pollution on cognition are long-term, then really this is all a big cross-sectional analysis, which brings up the usual issues of unobserved confounders, selection bias, etc., and the multiple measurements on each person is not really giving us identification at all.