Dimensional Variation Estimation: A Methodological Comparison

Estimation of the dimensional variation of points from data on the distances between pairs of points is a task common to several disciplines, disciplines which include behavioral geography, surveying, and cartography. Three methods for estimating dimensional variation are described and compared using an experiment involving simulated data and using empirical data from two studies, one based on distance judgments and the other based on direct coordinate judgments. The methods are shown to have different mathematical properties and to result in very different estimates.