Heteroscedasticity and the Gravity Model
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The study of human interaction over space forms a central part of one of the four traditions in geography [8, pp. 211-16; 10, pp. 1-16]. Perhaps the most fundamental regularities observed in such interactions are the direct influence of the attraction mass, usually a population size measure, and the inverse impact of distance or its surrogate. These relationships are commonly formulated as the “gravity model” of spatial interaction and the model’s parameters are often estimated using multiple linear regression [I, pp. 221301.
Application of regression to the problem of estimating the parameters of the gravity model requires that certain assumptions be met [12, pp. 106-7. This paper presents a case where one of the assumptions of ordinary least-squares (OLS) regression, namely homoscedastic disturbances, is not fulfilled so that best estimates of the gravity model will not be obtained in the usual way. Since the major justification for using the gravity model is empirical realism, it is impossible to generalize the results presented here to all cases. What can be said, however, is that geographers need to be aware of the possible existence of heteroscedasticity when using the gravity model. Thus, a test for the presence of heteroscedasticity should be undertaken when comparisons of alternative specifications of the model are being made. In cases where all specifications fit the data very well, but heteroscedasticity is present, an analysis of its nature may be very useful in selecting the best alternative.
Stronge, William, "Heteroscedasticity and the Gravity Model" (1978). HCBE Faculty Articles. 819.