I am in the midst of revising a paper that uses a very specific question from the Fragile Families Data set about reading to children. When I began writing the paper, I started looking for evidence with time-use surveys, such as the American Time Use Suvey (ATUS) which asks participants to record everything they do and for how many minutes on two given days (a weekday and a weekend, usually). I noticed, particularly at the PAA meetings this Spring, that there was a lot of controversy about these surveys. What, exactly, can they tell us about general effects, when we are looking at such a small sample of time for any given individual? More specifically, if we want to examine the effects of a particular policy, how does looking at one individual’s day give us a causal effect of a policy? Time use surveys are incredibly useful for seeing exactly how individual spends his time on any given day, and the possibilities for understanding the dynamics of child-rearing and marriage are far-reaching. The trade-off is that you have no way of knowing whether this is a typical day or not. On average, for the population, if we have a random sample of individuals and days are sufficiently randomly assigned, we should get an idea of what the population does, on average. But asking if a particular impetus leads to a specific behavioral change (for instance, does an increase in income mean you invest more in child’s education) is a little more problematic. The alternative is to ask questions in a survey setting about time-use behaviors without specifying the time. That’s what the Fragile Families does, and the question about how many days per week you read with your child has its own problems. I have long argued that when individuals answer the question, they must do some averaging over time. The question is not “how many days did you read with your child last week” as might be preferred or indicated by the literature on work (did you work last week?), but rather a sort of what do you usually do? I’ve been surprised at how much pushback I’ve received on this matter from discussants and reviewers. Most say the natural model to use is a count model, like negative binomial or Poisson, but I think it makes more sense to use an ordered probit, which allows for 4 to be more than 2, but not necessarily twice as much as 2. I don’t think the reading days answer is as firmly countable and identifiable as something like parking tickets, where a count model is the readily apparent model. I imagine the question is a lot like exercise. Over the weekend, I helped a friend with her match.com profile and one of the questions is how many days a week do you exercise? For some, the answer is absolutely 7, every single day. For others, zero, not lifting a finger. For most, though, I’d guess it varies from week to week. One week, you go every day, the next week is busy at work, so you go less often. Perhaps you go on a whole-day hike and tell me two days instead of one because you don’t want to seem lazy. Thus, when I ask you the question of how many days a week you exercise, you’re not really giving me a straight answer, through no fault of your own. You’re averaging over the last couple of weeks, you’re perhaps adjusting your answer to reflect what you think the surveyor is looking for, and you’re partially giving an impression of how much you value exercise. I’m having a hard time making this same argument regarding time spent with children to discussants and reviewers, and I’m not sure what I’m missing in my explanation to make it more convincing.
There’s a strong tendency in human nature to draw distinctions along dichotomous lines. Good and evil, black and white, ugly and pretty. We all know that these distinctions only really work in children’s fiction, and even then tend to fall flat, but we try anyway. In teaching, particularly a new subject, those dichotomies are both useful and can lead to the downfall of a lesson.
In that vein, the instructor in my spatial econometrics workshop last week presented two significant data issues that a researcher might encounter in using spatial data: spatial heterogeneity and spatial dependence.
By way of definition: spatial heterogeneity is simply that there is something about an area or a piece of space that is different than the spaces around it. My dichotomizing, learning mind went immediately to the idea of observables. Clearly, if we are trying to include spatial information–location–in a regression, we know that the area has certain characteristics. As long as we explicitly control for these in our regression (and believe they are accurately measured), it doesn’t present much of a problem.
However, this is not always the case due to the level of analysis problem. In a general econometric specification, we control for the unit of spatial analysis that is relevant–county, Metropolitan Statistical Area (MSA), state, whatever it may be. By choosing the level and assigning a dummy variable, perhaps, we assume that all those characteristics are captured uniquely, but also that they are assigned independently to the spatial unit. Take for instance the distribution of the African-American population in the United States. Regression analysis that uses that variable as a covariate assumes that the number of African-Americans in Georgia is independent from the number of African-Americans in South Carolina, which makes little intuitive sense. Both were states with large plantation economies that employed Black slaves from Africa in production of goods. It makes sense that these two states, spatially proximate, would also have similar factors leading to their demographic makeup. Thus, spatial heterogeneity: areas in the South have higher Black populations than in the North.
The corollary to spatial heterogeneity is spatial dependence. Like spatial heterogeneity, we see patterns occur in certain variables, but rather than an outside, perhaps observable and easily measurable factor that accounts for the clustering, there’s something inherent about the place itself that causes proximate areas to change their realization of some variable. Think of housing prices. Housing prices are higher in places with certain amenities (close to transportation, mountains, whatever), but housing prices are also higher in areas with higher housing prices. Perhaps homeowners see their neighbors selling their houses for more and thus put them on the market for more. Or buyers see houses in the area with higher values and thus are willing to spend more. This spills over county and other lines, too.
Both of these problems, regardless of how strict that line is between the two, manifest in spatial auto-correlation. The variation we see in each variable for two spatially proximate observations is less than the variation for two independently observations because the information comes from the same place. Some of this we can control for, some of it we can’t, and some of it we can try to control for with the tools I’ll discuss in coming days.
Regardless, it’s important to remember that the realization of spatial heterogeneity and spatial dependence is the same mathematically. Statistically, we cannot differentiate between whether some unobservable variable caused everything to be higher, or whether each observation is exerting an effect on its neighbors (a butterfly flaps its wings…). So, even with acknowledgement of these problems, we have not established causation.
A familiar refrain is, thus, minimally modified: spatial auto-correlation is not causation.
A note on correlation and causation: (see Marc Bellemare’s primer for a more detailed explanation)
Anyone who has ever taken a statistics course is familiar with the refrain that correlation is not causation. It’s a common refrain because it’s something that is often ignored when statistics are cited in news articles and personal anecdotes. My favorite example of this is that ice cream sales and murder rates are highly correlated. Only the biggest of scrooges would believe that ice cream sales caused murder rates to increase. In the abridged words of Elle Woods, happy people don’t kill people. And in my words, ice cream makes people happy.
They do move together, though, which is essentially the definition of correlation. When ice cream sales go up, murder rates go up; when murder rates go down, ice cream sales go down. Not because one causes the other, but rather because of the seasonality of both variables. More homicides occur in the summertime, and more ice cream is sold in the summertime.
Last week, I spent three days in a workshop (or short course) on spatial econometrics at the University of Colorado‘s interdisciplinary population center, the Institute for Behavioral Science. At the beginning of last semester, many of my methods students expressed interest in doing their research papers on a topic with a significant spatial component. I would have loved for them to incorporate spatial analysis, but it was a topic I had touched only tangentially and didn’t feel qualified to learn it at the same time as teaching that (incredibly demanding) course for the first(ish) time. In addition, having just attended the PAA meetings in San Francisco, I’ve been looking for ways to expand my econometric skills and incorporate spatial data into my work. It was really fantastic. I don’t know whether they’ll be hosting the event again next summer, but do keep a lookout if you’re interested. I thought it was extremely helpful. And fun (see nerdy tweets from last week about loving matrix algebra). Paul Voss, of the University of North Carolina’s Population Center, Elisabeth Root, and Seth Spielman were all great.
I posted a short introduction to spatial econometrics last week based on my readings for the first class and am now excited to share some of the things I learned, so over the next few weeks, I’ll post some of my thoughts in a mini-series on spatial econometrics. This post will be updated with a list of posts in the series, so do follow along.
Experts, please keep me honest! This stuff is very cool, but I’m still a newbie.
Preliminary outline (subject to change):