Chorological matrices and gravity models in human geography

Abstract

The aim of this paper is to determine the significance of the chorological matrices used in area analyses and, in particular, to decide how important a role is played by the size of the area units used when studying human fields of gravity.

Attention has been focussed on the b‑parameters of Pareto‑type models and the parameters of quadratic gravity models when using distance zones 1‑10 km broad. A comparison of three different chorological matrices is carried out. The first matrix is made up of the 1/4 square kilometre coordinate grid of the Basic Map of Finland; the second a grid of 134 squares arrived at by combining squares from the first matrix which were comparable from the point of view of in‑commuter traffic to Turku; and the third matrix, made up of administrative units, comprised the 51 communes in the area studied.

It was found that increasing the zone breadths and reducing the cross­-sections of the centres studied causes an observable systematic increase in the size of the b‑parameters. Furthermore, the values of the b‑parameters were considerably affected by irregularities in the empirical field of study. Of these it was variations in population density that exerted the greatest influence.

The quadratic gravity model proved to be somewhat better than the Pareto‑type model in predicting the gradient of the attraction field of com­muter traffic. Using regression analysis to minimize gravity functions cannot be regarded as entirely satisfactory as logarithm transformation does not cause the true observed results to fall into a linear pattern.

A stochastic method, not hitherto used in geography, for minimizing the functions is therefore introduced. Gravity models arrived at by this method give function values which correlate much better with the true observed values than is the case with models based on old deterministic principles. This stochastic method can be recommended for wide use in geography to minimize functions of varying types.