BiDimRegression: Bidimensional Regression Modeling Using R - Carbon, Claus-Christian (Journal of Statistical Software, Code Snippets, 2013)
Tobler (1965) introduced bidimensional regression to the research field of geography in 1965 to provide a method for estimating mapping relations between two planes on the basis of regression modeling. The bidimensional regression method has been widely used within geographical research. However, the applicability in assessing the degree of similarity of two-dimensional patterns has not much explored in the area of psychological research, particularly in the domains of cognitive maps, face research and comparison of 2D-data patterns. Describing Tobler's method in detail, Friedman and Kohler (2003) made an attempt to bridge the gulf between geographical methodological knowledge and psychological research practice. Still, the method has not been incorporated into psychologists' standard methodical repertoire to date. The present paper aims to make bidimensional regression applicable also for researchers and users unfamiliar with its theoretical basis. The BiDimRegression function provides a manageable computing option for bidimensional regression models with affine and Euclidean transformation, which makes it easy to assess the similarity of any planar configuration of points. Typical applications are, for instance, assessments of the similarity of facial images defined by discrete features or of (cognitive) maps characterized by landmarks. BiDimRegression can be a valuable tool since it provides estimation, statistical inference, and goodness-of-fit measures for bidimensional regression.