Chapter 4 Spatial Scales

Due to the various data sources or research interests, built environment-travel studies divide into two groups. One group uses aggregated travel and built-environment variables at the city, county, or metropolitan level. At the same time, the other group uses trip data at the individual or household level.

Research also find that the models at different scales would give different result. This phenomenon is called Modifiable areal unit problem (MAUP). Previous studies found that the density variables evaluated at different spatial scales have different impact on travel (Boarnet and Crane 2001; Buchanan et al. 2006; Sultana and Weber 2007). It is not reasonable to neglect the scale issues in built environment-travel studies.

4.1 Urban/Region Scale

Tradition of aggregate analysis treat a city or metropolitan as an observation. Both dependent and independent variables are aggregated at macro level. Here the land use factors only reflect the density, pattern and structure at the whole city.

Coevering and Schwanen (2006) carry on Newman and Kenworthy’s work and consider four sets of potential explanatory variables: ten of urban form, six of transport service, five of housing and development history, and thirteen of socio-economic situations. They fit some linear regression models (all the variables keep the initial magnitude without taking logarithm or other transformation) and all of their adjusted \(R^2\) are higher than 0.7. Their models also show that the cities with higher population density drive less. They found the land use characteristics of the inner area are more important than metropolitan-wide population density. Similarly, a recent city-level study (Gim 2021) fit multiple regression models based on the data from 65 global cities. The population density becomes not significant in this model. Their results show that fuel price, household size, and congestion level have strong effects on travel time. Using structural equation modeling, they also find the population density of the high-density built-up areas has a larger effect on travel than overall city density.

The aggregate models confound the individual level’s variance. Urban form factors usually show significant effect.

4.2 Neighborhood Scale

In disaggregate analysis, the travel records by individual or household are the basic unit of dependent variables. traveler’s socio-demographic characteristics also keep this resolution such as income and vehicle ownership. However, built environment factors technically have a minimum geographic unit as the measure scope. Census tract and block group are the most common unit in disaggregate analysis.

Scholars who choose disaggregate analysis believe that the internal difference of urban characteristics be neglected at region level. They are interested in the impact of meso-level built-environment factors like the population and employment distribution of intra-urban.

Using disaggregate data can disclose the neighborhood-level differences and eliminate aggregation bias. Using logarithms of VMTs per vehicle from National Personal Travel Survey (NPTS) data with 114 urban areas, Bento et al. (2005) fit the linear model with 19 variables. They found that, instead of population density, population centrality has a significant effect on VMT. The elasticity of annual VMT with respect to population centrality is 1.5.13

The results of travel models at different scales are often inconsistent. Using the same data source, Reid Ewing et al. (2018) found that the elasticities of VMT with respect to population density is -0.164 in the aggregate models, which is a much higher value than disaggregate studies (-0.04 in the meta-analysis of Reid Ewing and Cervero (2010)). They suspect that this phenomenon is aggregation bias or ecological fallacy. They further explain that the two scales represent two different questions: The metropolitan-level density, which strongly affects the VMT, is not equivalent to the neighborhood density, which has much weaker effects on VMT.

4.3 Multi-scale Studies

Schwanen, Dieleman, and Dijst (2004) explains that many urban form dimensions are tied to specific geographical scales. Recently, more studies import the spatial scales as an explanatory variable. In a report of travel and polycentic development, Reid Ewing et al. (2020) identify 589 centers in 28 U.S. regions. Then a categorical variable, ‘within/outside a center’ is added into the model. The results show that the household living within a center have more walk trips and fewer VMT than who living outside a center.

S. Lee and Lee (2020) also conduct a study involving factors at three level: household, census tract, and urbanized area. They find that density and centrality affect VMT at urban level as well as the meso-scale jobs-housing mix. After controlling for factors, the effect of local factors the urban-level spatial structure moderates the effects size of local built environment on travel.

4.4 Modifiable areal unit problem (MAUP)

Early in 1930, scholars noticed that, when a set of smaller areal units was aggregated into larger areal units, the variance structure will be changed and the estimated coefficients will be larger (Gehlke and Biehl 1934). This inconsistency/sensitivity of analysis results is called modifiable areal unit problem (MAUP) and ecological fallacy (Openshaw 1984).

In aggregated analysis, two kinds of MAUP often happen simultaneously (Wong 2004). The first one called ‘scale effect’ means that the correlation among variables depends on the size of areal units. Larger units usually lead to larger estimations. The second one, zone effect describe the various results of correlation by choosing different areal shape or subset at the same scale.

Fotheringham and Wong (1991) found that multivariate analysis is unreliable when using the data from areal units. Both value and direction of estimated coefficients may change for different spatial configurations (G. Lee, Cho, and Kim 2016; Xu, Huang, and Dong 2018).

Meanwhile, some aggregate studies shows that, using the simple averages of individual data, the estimations of coefficients in linear model are unbiased (Prais and Aitchison 1954). A condition is that the regression model must fix the omission error using proper specification (Amrhein 1995; Ye and Rogerson 2021). The check of unit consistency may help to examine the biases by MAUP on the estimations.

4.5 Discussion

The factors measured at a specific scale could only explain the variation generated at or above that level. Even some factors such as density has cross scales. Their distributions in different units and scales are not identical. It is reasonable for them to have various meanings and influences on travel. A systematic comparison should be conducted among multi-scale studies. The inconsistent might not be about correct or wrong. As Reid Ewing et al. (2018) commented, the aggregate and disaggregate studies are asking the apples and oranges questions.

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  1. “population centrality measure is computed by averaging the difference between the cumulative population in annulus n (expressed as a percentage of total population) and the cumulative distance-weighted population in annulus n (expressed as a percentage of total distance-weighted population).”↩︎