More on modeling uncertainty and approaching model results

People around the world want answers about the spread of COVID-19. Models offer data-driven certainties, right?

The only problem with this bit of relatively good news? It’s almost certainly wrong. All models are wrong. Some are just less wrong than others — and those are the ones that public health officials rely on…

The latest calculations are based on better data on how the virus acts, more information on how people act and more cities as examples. For example, new data from Italy and Spain suggest social distancing is working even better than expected to stop the spread of the virus…

Squeeze all those thousands of data points into incredibly complex mathematical equations and voila, here’s what’s going to happen next with the pandemic. Except, remember, there’s a huge margin of error: For the prediction of U.S. deaths, the range is larger than the population of Wilmington, Delaware.

“No model is perfect, but most models are somewhat useful,” said John Allen Paulos, a professor of math at Temple University and author of several books about math and everyday life. “But we can’t confuse the model with reality.”…

Because of the large fudge factor, it’s smart not to look at one single number — the minimum number of deaths, or the maximum for that matter — but instead at the range of confidence, where there’s a 95% chance reality will fall, mathematician Paulos said. For the University of Washington model, that’s from 50,000 to 136,000 deaths.

Models depend on the data available, the assumptions made by researchers, the equations utilized, and then there is a social component where people (ranging from academics to residents to leaders to the media) interact with the results of the model.

This reminds me of sociologist Joel Best’s argument regarding how people should view statistics and data. One option is to be cynical about all data. The models are rarely right on so why trust any numbers? Better to go with other kinds of evidence. Another option is to naively accept models and numbers. They have the weight of math, science, and research. They are complicated and should simply be trusted. Best proposes a third option between these two extremes: a critical approach. Armed with some good questions (what data are the researchers working with? what assumptions did they make? what do the statistics/model actually say?), a reader of models and data analysis can start to evaluate the results. Models cannot do everything – but they can do something.

(Also see a post last week about models and what they can offer during a pandemic.)

Models are models, not perfect predictions

One academic summarizes how we should read and interpret COVID-19 models:

Every time the White House releases a COVID-19 model, we will be tempted to drown ourselves in endless discussions about the error bars, the clarity around the parameters, the wide range of outcomes, and the applicability of the underlying data. And the media might be tempted to cover those discussions, as this fits their horse-race, he-said-she-said scripts. Let’s not. We should instead look at the calamitous branches of our decision tree and chop them all off, and then chop them off again.

Sometimes, when we succeed in chopping off the end of the pessimistic tail, it looks like we overreacted. A near miss can make a model look false. But that’s not always what happened. It just means we won. And that’s why we model.

Five quick thoughts in response:

  1. I would be tempted to say that the perilous times of COVID-19 lead more people to see models as certainty but I have seen this issue plenty of times in more “normal” periods.
  2. It would help if the media had less innumeracy and more knowledge of how science, natural and social, works. I know the media leans towards answers and sure headlines but science is often messier and takes time to reach consensus.
  3. Making models that include social behavior is difficult. This particular phenomena has both a physical and social component. Viruses act in certain ways. Humans act in somewhat predictable ways. Both can change.
  4. Models involve data and assumptions. Sometimes, the model might fit reality. At other times, models do not fit. Either way, researchers are looking to refine their models so that we better understand how the world works. In this case, perhaps models can become better on the fly as more data comes in and/or certain patterns are established.
  5. Predictions or proof can be difficult to come by with models. The language of “proof” is one we often use in regular conversation but is unrealistic in numerous academic settings. Instead, we might talk about higher or lower likelihoods or provide the best possible estimate and the margins of error.

Countering gerrymandering in Pennsylvania with numerical models

Wired highlights a few academics who argued against gerrymandered political districts in Pennsylvania with models showing the low probability that the map is nonpartisan:

Then, Pegden analyzed the partisan slant of each new map compared to the original, using a well-known metric called the median versus mean test. In this case, Pegden compared the Republican vote share in each of Pennsylvania’s 18 districts. For each map, he calculated the difference between the median vote share across all the districts and the mean vote share across all of the districts. The bigger the difference, the more of an advantage the Republicans had in that map.

After conducting his trillion simulations, Pegden found that the 2011 Pennsylvania map exhibited more partisan bias than 99.999999 percent of maps he tested. In other words, making even the tiniest changes in almost any direction to the existing map chiseled away at the Republican advantage…

Like Pegden, Chen uses computer programs to simulate alternative maps. But instead of starting with the original map and making small changes, Chen’s program develops entirely new maps, based on a series of geographic constraints. The maps should be compact in shape, preserve county and municipal boundaries, and have equal populations. They’re drawn, in other words, in some magical world where partisanship doesn’t exist. The only goal, says Chen, is that these maps be “geographically normal.”

Chen generated 500 such maps for Pennsylvania, and analyzed each of them based on how many Republican seats they would yield. He also looked at how many counties and municipalities were split across districts, a practice the Pennsylvania constitution forbids “unless absolutely necessary.” Keeping counties and municipalities together, the thinking goes, keeps communities together. He compared those figures to the disputed map, and presented the results to the court…

Most of the maps gave Republicans nine seats. Just two percent gave them 10 seats. None even came close to the disputed map, which gives Republicans a whopping 13 seats.

It takes a lot of work to develop these models and they are based on particular assumptions as well as methods for calculations. Still, could a political side present a reasonable statistical counterargument?

Given both the innumeracy of the American population and some resistance to experts, I wonder how the public would view such models. On one hand, gerrymandering can be countered by simple arguments: the shapes drawn on the map are pretty strange and can’t truly represent any meaningful community. On the other hand, the models reinforce how unlikely these particular maps are. It isn’t just that the shapes are unusual; they are highly unlikely given various inputs that go into creating meaningful districts. Perhaps any of these argument are meaningless if your side is winning through the maps.

“Using a Real Life SimCity to Design a Massive Development”

As a massive SimCity fan, I find this use of predictive urban models intriguing:

596 acres, 50,000 residents, $4 billion dollars and even a 1,500-boat marina: Everything about the proposed Chicago Lakeside Development, developer Dan McCaffery’s massive micro-city being built at the former site of the U.S. Steel Southworks Plant, is on a different scale. It follows that the design process for this mixed-use project requires a different set of tools, in this case, LakeSim, an advanced computer modeling program. Developed as part of a collaboration between the University of Chicago, Argonne National Laboratory, Skidmore, Owings & Merrill and McCaffery Interests, this program functions like a customized SimCity, analyzing and simulating weather, traffic patterns and energy usage to help architects and designers plan for a site that may eventually contain more than 500 buildings.

“A lot of the Big Data approaches tend to be statistical in nature, looking at past data,” says Argonne scientist Jonathan Ozik. “We’re modeling a complex system of interactive components, running the data forward, so what we end up having is your SimCity analogy, energy systems interacting, vehicles and people moving. What we’re doing here is using a complex systems approach to tackle the problem.”…

The challenge for planners is predicting how so many different systems and variables will interact. LakeSim gives them a framework to analyze these systems over long timelines and run millions of scenarios much quicker than past models — hours as opposed to days — asking “hundreds of questions at once,” according to Ozik. The program is a step forward from similar modeling software, especially valuable at a site that in most respects is being built from scratch.

This seems quite useful at this point but it will be necessary to look at this down the road once the site is developed. How much time did the model save? How accurate was the model? Did relying on such a model lead to negative outcomes? If this is a predictive model, it may be only as good as the outcome.

Interesting to note that the commenters at the bottom are wondering where all the people to live in this development are going to come from. I assume that demand is appropriately accounted for in the model?

The Chicago School model of urban growth doesn’t quite fit…but neither do other models

Sociologist Andy Beveridge adds to the ongoing debate within urban sociology over the applicability of the Chicago School’s model of growth:

Ultimately, Beveridge’s interesting analysis found that the basic Chicago School pattern held for the early part of the 20th century and even into the heyday of American post-war suburbanization. But more recently, the process and pattern of urban development has diverged in ways that confound this classic model…

The pattern of urban growth and decline has become more complicated in the past couple of decades as urban centers, including Chicago, have come back. “When one looks at the actual spatial patterning of growth,” Beveridge notes, “one can find evidence that supports exponents of the Chicago, Los Angeles and New York schools of urban studies in various ways.” Many cities have vigorously growing downtowns, as the New York model would suggest, but outlying areas that are developing without any obvious pattern, as in the Los Angeles model.

The second set of maps (below) get at this, comparing Chicago in the decades 1910-20 and 1990-2000. In the first part of the twentieth century, decline was correlated with decline in adjacent downtown areas, shown here in grey. Similarly, growth was correlated with growth in more outlying suburbs, shown here in black. In the earlier period growth radiated outwards — a close approximate of the Chicago school concentric zone model. But in the more recent map, growth and decline followed less clear patterns. Some growth concentrated downtown, while other areas outside the city continued to boom, in ways predicted more accurately by the New York and Los Angeles models. The islands of grey and black–which indicate geographic correlations of decline and growth, respectively–are far less systematic. As Beveridge writes, the 1990-2000 map shows very little patterning. There were “areas of clustered high growth (both within the city and in the suburbs), as well as decline near growth, growth near decline, and decline near decline.”

Interesting research. It sounds like the issue is not necessarily the models of growth but how widely they are applied within a metropolitan region. Assuming the same processes are taking place over several hundred square miles is making too much of a leap. We might then need to look at smaller areas or types of areas as well as micro processes.

This reminds me that when teaching urban sociology this past spring and reading as a class about the Chicago School, New York School, and Los Angeles School, students wanted to discuss why sociologists seem to want one theory to explain all cities. This isn’t necessarily the case; we know cities are different, particularly when you get outside of an American or Western context. At the same time, we are interested in trying to better understand the underlying processes surrounding city change. Plus, Chicago, New York, and LA have had organized (sometimes more strongly, sometimes more loosely) groups based in important schools pushing theories (and we don’t have such schools in places like Miami, Atlanta, Dallas, Portland, etc.).

Viewing cities as crosses between stars and social networks

A new paper from a physicist suggests cities are “social reactors,” somewhere between social networks and stars:

Others have suggested that cities look and operate like biological organisms, but that is not the case, says Bettencourt. “A city is a bunch of people, but more importantly, it’s a bunch of people interacting, so hence the social network,” he explains. “What’s important are the properties of this social network: the scaling was giving us clues. But then when you think of this superlinearity, which means the socioeconomic outputs are the result of those interactions, are expressed as growing superlinear functions of populations, the only system that I could think of in nature is a star. A star does have this property – it’s essentially a nuclear reactor sustained by gravity and shines brighter (has greater luminosity) the larger its mass. So there’s a sense that this behavior that is sustained by and created by attractive interactions and whose output is proportional to rate of interactions, is what a city is and a star is, and so in that sense they are analogous.”…

The result is this “special social reactor” that adheres to four main assumptions about city dynamics and scaling:

1) There are “mixing populations”: basically, cities have attractive interactions and social outputs are the results of those, which leads to more social interactions.

2) There is “incremental network growth”: notably, the networks themselves and the supporting infrastructure develop gradually as the city grows. The infrastructure is decentralized as are the networks themselves. This is very different from an organism, says Bettencourt, whose internal “infrastructure” (analogous to a vascular system for example) develops basically all at once and has a centralized node.

3) “Human effort is bounded”: as he writes in his paper, “The increasing mental and physical demand from their inhabitants has been a pervasive concern to social scientists. Thus this assumption is necessary to lift an important objection to any conceptualization of cities as scale-invariant systems.” In other words, “The costs imposed on people by living in the city do not scale up,” he says, because as the number of social interactions increase, one doesn’t have to necessarily travel more to get to these interactions. “The city comes to you as it becomes denser,” he notes.

4) “Socioeconomic outputs are proportional to local social interactions”: this gives us an interesting snapshot of exactly what a city is – not just a conglomeration of individuals, but rather a concentration of social interactions.

Sounds interesting. Cities are both agglomerations of social interactions as well as have unique infrastructures (physical and social) that gives shape to and is shaped by these interactions.