Measuring and Analyzing the Within Group Homogeneity of Multi-category Variables
Many variables have within group homogeneity (similarity of values for the individual units that comprise the groups). Measures of within group homogeneity are useful for the sample design and statistical analysis of datasets for populations that contain groups, such as individuals in geographical areas. Homogeneity measures can easily be defined for continuous or dichotomous variables. Here, we propose a homogeneity measure for a multi-category variable, and show how this measure can be calculated without access to individual level data. We apply the measure to data from the UK census, and show how this measure can be related to the homogeneity of particular linear combinations of the categories, called Canonical Grouping Variables (CGVs), and explain how these are interpreted.
AMS Subject Classification91G70
Key-wordsGroups Clustering Homogeneity Intra-class correlation Categorical variables Canonical grouping variables Aggregate data Census area data
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- Goldstein, H., 2003. Multilevel Statistical Models, Third edition. Edward Arnold.Google Scholar
- Holt, D., Steel, D.G., Tranmer, M., 1996. Area homogeneity and the modifiable areal unit problem. Geographical Systems, 3, 181–200.Google Scholar
- Martin, D., 2000. Towards the Geographies of the 2001 UK Census of Population. Transactions of the Institute of British Geographers, 25, 321–332.Google Scholar
- Openshaw, S., Taylor, P., 1983. The Modifiable Areal Unit Problem. Geo Books, Norwich.Google Scholar
- Skinner, C.J., 1989. Introduction to Part A. Wiley, Chichester.Google Scholar
- Steel, D.G., 1985. Statistical Analysis of Populations with Group Structure. Ph.D. thesis, University of Southampton.Google Scholar
- Steel, D.G., Holt, D., Tranmer, M., 1996. Making Unit-Level Inferences from Aggregated Data. Survey Methodology, 22, 3–15.Google Scholar