Year

2001

Degree Name

Doctor of Philosophy

Department

School of Mathematics and Applied Statistics

Abstract

There is an increasing tendency to take a spatial perspective in analysing census or sample data. This thesis contributes to the development of spatial analysis and concentrates on methods for analysing data on social characteristics. The important case of aggregated census data will be considered.

If we are interested in spatial relationships, then we must consider how to analyse social data that have been obtained by methods of sampling or aggregation. There may not be a direct interest in spatial relationships, but the presence of spatial interdependence may still need to be taken into account in the analysis. There may be spatial trends in means and variances, and the correlation between the characteristics of different individuals that depend on their relative locations.

The main outputs of the thesis have contributed in the development of the analysis of aggregate social data from a spatial perspective, in particular using semivariogram analysis. Some outputs are outlined The role of the semivariogram and cross-semivariogram of the aggregate data is to explore and explain covariance structure and spatial dependency in the population. This includes the relationship between spatial autocorrelation and the variogram. The connection between the variogram of the aggregated data and the variogram of the unit level data, which leads to the development of a non-linear model of the group level semivariogram to provide estimates of the individual level semivariogram model parameters. The extension into the bivariate case involving cross-semivariogram analysis is discussed. The MAUP as an analysis tool to explore spatial dependence of aggregate social data is discussed. Simulation results empirical analysis of actual aggregate data are implemented to confirm the methods. The empirical work is based on analysis of the 1991 Australian Census of Population and Housing.

The thesis shows the role of semivariogram analysis (univariate case) and cross-semivariogram analysis (bivariate case) in understanding the aggregation effect for social data. The aggregation effect, which includes the two main aspects of the scaling effect and zoning effect, is mainly determined by the presence of dependency within the data. Another factor is existence of the relationship between group size and within group variation.

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