Environment and Planning A: Economy and Space

This paper is concerned with an inquiry into the way in which the organisation of a spatial data set affects the interpretation of the spatial phenomena which it records, in terms of its underlying pattern or density. It is argued that the number and configuration of zones affects the level of information which is imparted to the spatial analyst, and thus the quest becomes one in which the data set is to be reorganised spatially to impart maximum information. The paper sets out to define an appropriate measure of information and an algorithm designed to optimise its value. The information measure developed is in essence a modified Shannon entropy, modified to account for uneven zonal configurations and converging to Shannon entropy when the zoning system is equal-area and the distribution the best approximation to the density. The measure has some well-known aggregation properties which are presented and several interpretations of its form in spatial terms are made. Empirical measurements of this information measure on the distribution of population in seven metropolitan areas indicate that by aggregation of zones to equal areas, increases in information might be possible and a clearer picture of the underlying density perceived. Accordingly a simple algorithm embodying an heuristic to optimise towards the equal-area norm is developed and applied to the Los Angeles region. The results, in fact, indicate that information cannot be improved in this case, and this leads to a reexamination of the nature of the problem and to suggestions for further research.

The results obtained from studies of spatially aggregated data are not independent of the choice of zoning system. The paper investigates the effects of different zone-design criteria on a linear-regression model. It is concluded that there is unlikely to be either a simple or general-purpose solution to the problem.

This paper investigates the usefulness of parameter disaggregation within a logistic modal-split model. Changes in parameter values caused by different origin-location and household characteristics are compared with parameter changes due to slight alterations to the model's structure. This spatial and sectoral parameter disaggregation scheme is used to link a modal-split model with a previously developed trip-distribution model at the same level of resolution. The disaggregations are seen as offering useful insights into intraregional variations in modal choice.

The transportation problem and a doubly constrained gravity model with a power deterrence function are used to find predictions of a number of 134 × 134 freight matrices detailing tonnages moved in Great Britain in 1972. The matrices detail movements by thirty commodity groups, and predictions are obtained for movements by road for all but one of the commodities and for the principal items carried by rail. These predicted matrices are used to examine a number of questions. The relationships between some alternative goodness-of-fit statistics are examined to establish which commodities are best modelled by each technique and to point out empirically which statistics give unreliable rankings. Various summary measures of the actual matrices are examined to see if it is possible to predict which matrices will be best modelled by each technique. The modelling techniques are compared to indicate which provides the best predictions for each matrix, and some conclusions are offered on the absolute efficiency of the best models.

Part 1 of this paper discusses the treatment of zero observations in growth-factor methods; part 2 discusses the calibration of gravity models when the data are of different sampling variability. The problem discussed in part 1 is that zero observations are preserved at zero value in the forecast year, no matter how much growth takes place. Since the probability of making a trip is not zero but very small for those matrix cells that are empty by chance, it is shown how to estimate nonzero values for these cells by use of a method of smoothing reported in the statistical literature. It is argued in part 2 that the usual practice of calibrating against ‘grossed-up’ data is incorrect. If the survey method is the same for all trips, but the sampling fraction varies from one cell to another, it is shown, by use of maximum-likelihood methods, that it is the raw sample data against which the model should be calibrated. If the matrix is made up of data from different surveys, it is shown, by use of least-squares methods, that the raw sample data should be modified before estimating the parameters, leading to a minimum χ² fitting criterion.

This paper presents the results of a time-series analysis of short-term changes in the conditions prevailing in regional labour markets. A set of alternative indicators of changes in these conditions are evaluated for each of the standard regions by use of quarterly data for a period that includes the rapid changes in the economy associated with the ‘Barber Boom’. Leading indicators of changes in labour demand are contrasted with lagging indicators and the findings for different regions compared. The results of the analysis show that in general the numbers of vacant jobs and the rates at which the jobs are being filled provide leading indicators of changes in the region's level of unemployment and of changes in the duration of unemployment in the region, and that there is no feedback from unemployment to change the demand for labour in the region. In consequence it would be justified to claim that changes in regional unemployment and its duration are caused by changes in the demand for labour in the region.