ABSTRACT
Chapter 7 introduces three multivariate statistical methods, principal components analysis (PCA), factor analysis (FA), and cluster analysis (CA). PCA and FA can be considered as data reduction methods to reduce the dimensions (columns) of data by structuring many correlated variables into a smaller number of independent components (factors). CA may be regarded as a data consolidation method to reduce the observations (rows) of data by grouping numerous similar data points into fewer clusters. The methods all simplify and organize data in a way for better understanding. Social area analysis uses the PCA or FA to consolidate many socio-demographic variables collected from census or field surveys into a few factors (constructs), and then employs the CA to group small analysis areas measured in the constructs into larger social areas. When the results of social areas are mapped, these constructs exhibit distinctive spatial patterns that can be characterized by the concentric (zonal) model, the sector model, or the multi-nuclei model. In a case study, a regression model with dummy variables is designed to test whether a factor conforms to a concentric or a sector model with statistical significance.
