The Effectiveness of Spline Urban Density Functions: An Empirical Investigation

Abstract

Recent studies of population distribution in urban settings suggest that cubic-spline functions may be preferable to the conventional exponential form. It is contemplated that this specification is more suitable for untangling, discovering and depicting the complex density patterns of today's relatively dispersed urban areas. This paper examines the usefulness as well as the amenability of the cubic-spline function for describing and testing hypotheses on the processes underlying the determination of population densities in Tel Aviv-Yafo. The principal findings of the analysis are threefold. First, from the theoretical and empirical points of view the cubic-spline function is unlikely to be useful for testing hypotheses. Multicollinearity among distance variables renders the cubic-spline function without much practical merit for this purpose. Secondly, an exponential spline form which does not utilise high-order terms of distance is better suited for this purpose and should therefore be preferred to the cubic-spline. Thirdly, an alternative approach which employs an improved exponential form obtained by incorporating pertinent information on actual patterns of land-use development into the theoretically derived exponential form was highly supported by the data. Utilisation of the latter approach led to an increase in the explanatory power of the model from a mere 0.24 to a respectable 0.83. Indeed, the general lesson to be learned from the analysis is that utilisation of general functional forms cannot by itself correct for possible biases in sample selection, model specification or, for that matter, replace thorough understanding of the processes one is trying to model.