Doctor of Philosophy
School of Mathematics and Applied Statistics, Faculty of Informatics
Familar, Russell R, Scale effects in multilevel modeling, PhD thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2008. http://ro.uow.edu.au/theses/566
In many instances data are available as aggregated measurements for a set of areal units that are arbitrarily defined in terms of number and boundaries. Analysis using spatial data is a multi-disciplinary subject attracting the attention of statisticians, geographers, physical and social scientists. The Modifiable Areal Unit Problem (MAUP) is the sensitivity of results of statistical analysis to the definition of areal units for which the data are available. The results vary with the level of aggregation and the configuration of the zoning system. Multilevel models offer an approach to the MAUP. Multilevel modeling is potentially subject to the MAUP, since different estimates of the variance components can be obtained if boundaries are changed or a different scale is used.
This thesis presents results of experiments conducted to look into the scale effects of statistics calculated directly from aggregated data and statistics derived from a simple multilevel under different initial conditions. The analysis of spatial data is usually affected by the complex relationships between variables and the existence of spatial autocorrelation. A reason for multilevel models being subject to the MAUP is that, while the data available may be hierarchical, the population structure may be more complex. Theoretical and empirical investigations to link a simple multilevel model and spatial autocorrelation and the implications for the MAUP are conducted.
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