neity in the model to account for the missing or incorrectly specified effects.

Multivariate statistical techniques such as regression analysis are often used to test causal relationships between livability indicators and fiscal, social, economic, and environmental variables. These methods can be used to determine how much of the variability is attributable to specific factors. Standard multivariate statistical methods make the assumption that all observations are independent of one another, that is, they do not vary one with another. With geographic data, independence cannot always be assumed because of spatial dependence, whereby factors do vary in relation to one another. Spatial dependence in the observations means that parameter estimates and significance tests are unreliable (Anselin and Griffith, 1998). It does not necessarily affect the model’s predictive accuracy but does seriously undermine the ability to use calibrated parameters to explain the relative causal effects of the independent variables.

There are many different methods for dealing with the challenges of measuring spatial dependence and spatial heterogeneity (see Getis and Ord, 1992; Anselin, 1995; Ord and Getis, 1995). Problems associated with spatial dependence among observations in multivariate regression and related techniques can be resolved by including spatial autocorrelation in the dependent variable, independent variables, error terms, or some combination (Anselin, 1988, 1993). Spatial dependence and spatial heterogeneity can be captured simultaneously using geographically weighted regression. Geographically weighted regression generates disaggregate, location-based regression parameters that show spatial variations in the relationships between the independent variables and the dependent variable (see Brunsdon et al., 1996). Geographically weighted regression results are easily mapped, creating powerful geographic visualizations to highlight spatial trends and spatial variations, and to identify local exceptions to these relationships (Fotheringham, 2000).

MEASURING ACCESSIBILITY

Accessibility is a key component of livability that implicitly or explicitly underlies many measures and analyses of livability. Accessibility is also closely intertwined with policies that intentionally or unintentionally influence livability.

Many livability measures assume that the resources and opportunities at a place are perfectly available to individuals who are “proximal” to that location. New policies that attempt to influence livability also make this assumption. However, factors other than propinquity can affect the ability of individuals to obtain resources and opportunities. This result means that measures can overestimate livability and the effectiveness of



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