As a followup to my previous post about the TTI’s new congestion report, I finally did a multivariate regression analysis, with the dependent variable being cost and the independent variables being size and freeway lane-miles per capita. Such an analysis reduces the regression coefficient between freeways and congestion even more, to -42.5 from the uncontrolled -233. More interestingly, if we log all numbers (population, congestion cost, and freeways), the regression coefficient becomes a positive 0.02 – that is, adding freeways is correlated with making congestion a little worse.

Of course, it’s not literally true that adding freeways makes congestion worse. There’s a correlation if we look at the variables in some way, but it’s not going to have any statistical significance. Therefore tweaking variables slightly can make a correlation go from weakly positive to weakly negative.

In univariate regression, we can think about the square of the correlation as the percentage of the variance that is explained by the regression line. Freeway lane-miles per capita explain 3.8% of the variance in congestion (and logging either variable makes this number smaller); with 101 urban areas surveyed, it’s statistically significant, but barely so. But after controlling for population, this proportion drops to 0.7%. Thus, any sentence of the form “adding one freeway lane-mile per thousand people only cuts $42.5 from the annual congestion cost per capita” is inherently misleading: the correlation is so weak that some cities can reduce congestion without building the requisite amount of roads, or building any roads at all (for example, nearly all American cities in the last five years, congestion having crashed in the oil price boom and the recession), while others can keep building but see congestion increase (for example, Houston since the 1980s, and even today).

It goes without saying that such analysis is not going to appear in the TTI report itself. The TTI gets funding from APTA and the American Road and Transportation Builders Association. It pays lip service to congestion pricing as a solution to congestion, and instead talks a lot about building public transportation and even more about building freeways to keep up with demand. American cities may be building freeways faster than their population growth, but cities that enact no traffic restraint and just pour concrete can expect demand to grow faster than population as people become more hypermobile.

The Texas Transportation Institute has just released the latest version of its much-criticized Urban Mobility Report. Although the conclusions and recommendations made by the TTI tend to reflect its funding sources (APTA, American Road and Transportation Builders Association), the underlying data seems sound, and suggests conclusions orthogonal to those made by the report. In addition, looking at the correlations more closely suggests obvious hazards coming from any simplistic analysis of linear regression. It even showcases how we could use data dishonestly and lie with statistics. So let’s take the data that’s relevant right now and see what we can conclude ourselves.

First, the size of an urban area is a very strong correlate of its level of congestion. The linear correlation between size and per capita congestion cost is 0.71. The correlation increases to 0.8 if we take the log of population and the log of congestion, or if we consider congestion in the absence of public transportation; in both cases, it comes from the fact that New York is far below the population-congestion regression line.

Now, more freeways do not really lead to congestion reduction. There’s some correlation between freeway miles per capita and congestion per capita, going in the expected direction, but it’s weak, -0.2, and while it’s statistically significant, the p-value is an uninspiring one-tailed 0.025. Looking at a scattergram doesn’t make any nonlinear relationship obvious.

Moreover, size is a correlate of both congestion (0.71 as above) and freeways (-0.23). This is fully expected: literature on cities’ economies of scale (here is a story of one controversial example) suggests that congestion and the economic activity causing it grow faster than linearly in city size while the amount of required energy and infrastructure grows slower than linearly. I open the floor to anyone with more powerful tools than OpenOffice Calc to do multiple regression; again, the sanitized data is here.

Even without controlling for population, freeways are not a very strong correlate. The regression coefficient is -233: increasing the number of freeway miles per thousand people by 1 (the range is 0.13-1.4, with few large metros above 1 or below 0.35) reduces the congestion cost per capita by $233 per year, also uninspiring.

The regression number alone can be used as a dishonest trick when arguing on the Internet. If we overinterpret weak correlations, we can declare that the only way to decrease congestion is to build an unrealistic number of freeways, and thus declare the problem unsolvable. Of course, for most cities we can find other cities of comparable size with much less congestion and without enormous amounts of asphalt – this is why the correlation is so weak. But a good hack should not bother himself with such caveats to talking points.

So if making an urban area larger makes it more congested, independently of and much more strongly than all else, should we give up on cities? Well, no. Assuming no change in traffic policy, congestion results from more economic activity. It then becomes straightforward to institute congestion pricing. It’s no different from how big cities can use their resources to hire more cops to deal with the crime that could result from extra interactions between people. On top of this, in very large cities, mass transit becomes a serious option: this not only reduces the amount of congestion per capita, but also removes many people from the highways to the point that congestion becomes irrelevant to their daily lives, except perhaps through higher transportation prices, which they can fully afford given the extra wealth.

Another thing to consider is that most American cities have added more freeways than people since 1982, the first year for which TTI data is available, while also becoming much more congested. If a simple relationship between freeway miles per capita and congestion held, it would be robust to these changes over time. Of course, traffic has grown even faster, leading the main report to showcase on PDF-page 21 how congestion increased the fastest in regions where road demand outgrew supply the most. But this raises the question of whether the main issue is one of demand, rather than one of supply. This is not just an issue of size: the log-log regression coefficients with cost and time is 0.42, i.e. doubling an urban area’s population will raise its per-driver congestion cost and travel delay by a factor of 2^0.42; since 1982, the average urban area on the list has seen its population grow by a factor of 1.46 and its travel delay per driver grow by a factor of 2.85 = 1.46^2.77. Cost has grown even faster, because of higher value of time.

That said, quantity of freeways does not equal quality (from the drivers’ perspective, of course, rather than the city’s). On paper, Greater New York has added freeway lanes about 9% faster than people over the last thirty years. In practice, none has addressed the major chokepoints within and into the city itself, where traffic is worst. Of course, commutes involving Manhattan are overwhelmingly likely to be done on public transportation, but diagonal commutes within the city are more likely to be done by car than on transit.

On a parenthetical note, the units of comparison here are TTI-defined urban areas. TTI’s belief about urban area population growth trends is sometimes at odds with that of the Census Bureau, but the raw population numbers are close enough. More important is the question of what to do about urban areas that are really exurbs of larger areas, such as Poughkeepsie-Newburgh and the Inland Empire. My first instinct was to lump them in with their core metro areas, but their congestion level per capita is not high. Their commutes are long, but not very congested for their size. Finally, although most correlations here are with congestion cost, the correlation numbers with travel delay and excess fuel consumptions are very similar; the one exception I’ve checked, for which I have no explanation, is log-log congestion-fuel correlation (0.84, with regression coefficient 0.73).

A few months ago, in response to the Raquel Nelson case, author Tom Vanderbilt found an FHWA study from 2005 that finds that on wide, busy roads, pedestrian death rates are higher on marked crosswalks than on unmarked ones. The study itself is worth reading; its explanation of the finding is that,

These results may be somewhat expected. Wide, multilane streets are difficult for many pedestrians to cross, particularly if there is an insufficient number of adequate gaps in traffic due to heavy traffic volume and high vehicle speed. Furthermore, while marked crosswalks in themselves may not increase measurable unsafe pedestrian or motorist behavior (based on the Knoblauch et al. and Knoblauch and Raymond studies) one possible explanation is that installing a marked crosswalk may increase the number of at-risk pedestrians (particularly children and older adults) who choose to cross at the uncontrolled location instead of at the nearest traffic signal.

An even greater percentage of older adults (81.3 percent) and young children (76.0 percent) chose to cross in marked crosswalks on multilane roads compared to two-lane roads. Thus, installing a marked crosswalk at an already undesirable crossing location (e.g., wide, high-volume street) may increase the chance of a pedestrian crash occurring at such a site if a few at-risk pedestrians are encouraged to cross where other adequate crossing facilities are not provided. This explanation might be evidenced by the many calls to traffic engineers from citizens who state, “Please install a marked crosswalk so that we can cross the dangerous street near our house.” Unfortunately, simply installing a marked crosswalk without other more substantial crossing facilities often does not result in the majority of motorists stopping and yielding to pedestrians, contrary to the expectations of many pedestrians.

This is a rather standard application of Smeed’s law and similar rules governing traffic, whose one-line form is that traffic fatalities are determined primarily by psychology. This is not a problem; the problem is why such issues are only ever brought up in case of pedestrian fatalities.

In 1949, R. J. Smeed found a simple explanation for traffic fatalities: they depend less-than-linearly on the number of cars on the road. In the 1980s John Adams revised this to a more accurate rule based on VMT rather than the number of cars, and based on a constant decline in per-VMT accidents over time. Safety improvements do not bend or break the general trend. Quoting Adams again, the introduction of seat belts caused no reduction in traffic fatalities, and on the contrary caused pedestrian fatalities to temporarily inch up, as drivers felt safer and drove more recklessly. The only way to reduce the number of car accident victims is to reduce traffic.

And yet, government reaction is consistently on the side of accepting Smeed’s law when it implies there’s no need to improve pedestrian facilities, and rejecting it when its implication is bad for cars or good for pedestrians and cyclists. Local governments in the US routinely argue that safety is at stake when they want to upgrade a road with grade crossings into a full freeway. The FHWA helpfully adds that intersections are responsible to half of all car crashes and “FHWA will identify the most common and severe problems and compile information on the applications and design of innovative infrastructure configurations and treatments.”

In reality, all building freeways does is create more traffic, and cause more people to die in crashes. The average per-VMT death rate in the US has declined by 3.3% per year, but in the years following the Interstate Highway Act, it was practically flat – in other words, building freeways did nothing to accelerate the trend for reduction in per-VMT accident deaths. Although an individual freeway is undoubtedly safer than an individual road with intersections, the road network has to be viewed as a system: increase safety in one area and people will drive more recklessly elsewhere.

This systemwide view is clearly present in the case of pedestrians: the FHWA isn’t claiming that crosswalks are inherently unsafe, only that they cause more at-risk pedestrians to cross. In other words, the problem is that they cause too many of the wrong kind of pedestrians to cross. The implication is never used for roads. Traffic is never treated as variable, and if people shoot down freeway upgrades on the grounds that they’ll induce more traffic, it’s always on environmental or community grounds rather than on safety grounds.