Urban form in Canada at a small-area level: Quantifying “compactness” and “sprawl” with bayesian multivariate spatial factor analysis

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Quantifying urban forms to explore urban compactness or sprawl has become increasingly popular in multiple fields in the past decades. However, previous studies predominantly analyze the multidimensional phenomenon at large-area levels such as metropolitan areas, concealing variations that probably occur at small-area levels. Canadian studies measuring urban forms are usually conducted at the regional level with inconsistent indicators and approaches, hindering meaningful comparisons of compactness or sprawling between different regions. This study bridges a previous gap by applying Bayesian multivariate spatial factor analysis to construct a new composite urban compactness index for all Census Tracts (CT) in Canada. Nine urban form indictors representing four dimensions, density, centering, land use, and street connectivity are used in developing the index. Posterior probability is used to detect CTs that are most compact or sprawling. Results indicate that gross population and employment densities best characterize urban compactness at the CT level while land-use mix is the least central indictor to define the multi-faceted concept. Notable differences of urban compactness are detected across Canada and among different Census Metropolitan Areas (CMA). The most compact CTs usually locate in downtown or city center areas of a CMA. Larger and more populous CMAs, which also capture a larger extent of periphery areas, are not necessarily more compact and vice versa, suggesting the need to measure local variations of urban compactness. The constructed composite index allows direct urban compactness comparisons across different Canadian regions. Findings from this study can be used to guide smart and sustainable urban development in Canada.