Abstract

Bidimensional regression is a method for comparing the degree of resemblance between 2 planar configurations of points and, more generally, for assessing the nature of the geometry (Euclidean and non-Euclidean) between 2-dimensional independent and dependent variables. For example, it can assess the similarity between location estimates from different tasks or participant groups, measure the fidelity between cognitive maps and actual locations, and provide parameters for psychological process models. The authors detail the formal similarity between uniand bidimensional regression, provide computational methods and a new index of spatial distortion, outline the advantages of bidimensional regression over other techniques, and provide guidelines for its use. The authors conclude by describing substantive areas in psychology for which the method would be appropriate and uniquely illuminating. Ever since One of the main tools for assessing the configural relations between cognitive and actual maps is the bidimensional regression methodology introduced to the geography literature by Psychological Methods Copyright 2003 by the American Psychological Association, Inc. 2003, Vol. 8, No. 4, 468-491 1082-989X/03/$12.00 DOI: 10.1037/1082-989X.8.4.468 468 shi Because of the potential utility, but relative obscurity, of bidimensional regression in the psychological literature, our main intent in the present article is to introduce its concepts and computational methods and to demonstrate when and why it is to be preferred over several other analytical techniques. In addition, because an important feature of human cognitive maps is that they are often systematically distorted (e.g., To accomplish these goals, we first briefly review the background of bidimensional regression and the index of distortion that was developed from it. Second, we provide for the first time, the detailed, formal correspondence between uni-and bidimensional regression. Doing so serves to make explicit the two fundamentally different ways in which bidimensional regression and indices of distortion in cognitive maps can be implemented. Third, we discuss the advantages of bidimensional regression compared with other methods. Fourth, we describe and critique Waterman and Gordon's (1984) distortion index (DI ) and offer our alternative. Fifth, we demonstrate the two implementations of bidimensional regression with both a "toy world" and a real-world example, to illustrate how each implementation provides different information that may alter the interpretation of data. Finally, we provide some methodological guidelines and examples of substantive areas in psychology-both within and outside of cognitive mapping-in which bidimensional regression should provide unique and useful information.