Steel, David Geoffrey (1985) Statistical analysis of populations with group structure. University of Southampton, Doctoral Thesis.
Abstract
This thesis is concerned with the analysis of data obtained from a population of individual units divided into groups in which the method of obtaining or producing the data involves the groups, either through the use of sampling, or aggregation of data to group level. It is assumed that the objective of the statistical analysis is the estimation of parameters or relationships at the unit level. It is argued that the resolution of the problems associated with the analysis of such data requires the inclusion of the groups and their effects in the statistical model on which the analysis is based. The models and methods currently available are reviewed and three classes of models identified. A formal framework for statistical inference in grouped populations is developed which enables the examination of the fundamental issues of when the sampling and grouping can be ignored for the analysis of unit level data, and the groups treated as fixed for the analysis of group level data. A particular model is developed in which it is supposed that the expectations of the variables of interest are independent of the groups. The consequences of this model are investigated for some standard statistical analysis techniques. Alternative estimators are also considered. The central role of the Canonical Grouping Variables is shown and a strategy suggested for the analysis of group effects.
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