We can analyze the aggregate data using statistical techniques (while being mindful of arbitrary boundary and unit problems, as well as dependences in the data). The space-time units can show diurnal patterns in the social geography of the city as well as interactions between activities, social settings, and urban form. They allow measurement and prediction of the impact of changes in demographics, socioeconomic structures, and activity patterns within the urban environment as well as time-varying demands for transportation infrastructure. Longitudinal studies can allow assessment of the effect of long-term changes on livability; for example, the effects of changing demographics, continuing intensive use of the automobile, the growth of multi-income households and participation of women in the labor force, and the wider use of telecommunication technologies (Goodchild and Janelle, 1984; Janelle et al., 1998).

Incompatible Data Units

Livability and sustainability are complex phenomena measured across multiple dimensions. Geographical data are often collected using different, sometimes arbitrary, spatial units. For example, data available from a census, based on census tracts or other secondary sources, may not match the traffic analysis zones used by transportation planners in a transportation department or a metropolitan planning organization (MPO). Integrating these data means resolving different spatial recording systems. Spatial basis transfer is the term used to describe the conversion of data from one spatial system to another. If spatial basis transfer is not conducted properly, the resulting place-based measurements can be arbitrary, and even misleading, since the geographic framework for the measure is distorted.

Sometimes there is a need to transfer data from one area (the source zone) and apply them to another (the target zone). If the target zones nest perfectly within the source zones, this process is straightforward. If the nesting is not perfect, then areal interpolation is required (Goodchild and Lam, 1980). The appropriate method for interpolating data from source zones to target units depends on beliefs or assumptions about the spatial variation of the data within these zones (Goodchild et al., 1993). If both the source and the target zones are relatively homogeneous, the method of areal weighting can be used. This method distributes the data in the source zones to the target zones based on the share of the source zone within each target zone (see Goodchild and Lam, 1980). If the source zones are not homogeneous and there are other data that say something about the distribution of the variable within each zone (e.g., housing value as a surrogate for household income), statistical techniques such as the expectation-maximization algorithm can be used (see Flowerdew et al.,

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