Bidimensional regression: assessing the configural similarity and accuracy of cognitive maps and other two-dimensional data sets.

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 uni- and 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.

[1]  Rob Kitchin,et al.  Methodological convergence in cognitive mapping research: investigating configurational knowledge , 1996 .

[2]  Barbara P. Buttenfield,et al.  COMPARING DISTORTION ON SKETCH MAPS AND MDS CONFIGURATIONS , 1986 .

[3]  Ray Hyman,et al.  Perceptual separability and spatial models , 1968 .

[4]  A. Siegel,et al.  The development of cognitive mapping of the large-scale environment , 1978 .

[5]  S. Shettleworth,et al.  Hippocampal lesions impair memory for location but not color in passerine birds. , 1996, Behavioral neuroscience.

[6]  Earl Hunt,et al.  Spatial Representations of Virtual Mazes: The Role of Visual Fidelity and Individual Differences , 2001, Hum. Factors.

[7]  Robert Lloyd,et al.  Cognitive Maps: Encoding and Decoding Information , 1989 .

[8]  J. Huttenlocher,et al.  The Coding of Spatial Location in Young Children , 1994, Cognitive Psychology.

[9]  N. Newcombe,et al.  Barrier effects in the cognitive maps of children and adults. , 1982, Journal of experimental child psychology.

[10]  Marc Bélisle,et al.  Conservation Ecology: Cumulative effects of barriers on the movements of forest birds , 2001 .

[11]  J. Hudson.  A DIAMOND ANNIVERSARY , 1979 .

[12]  A Friedman,et al.  Reasoning about geography. , 2000, Journal of experimental psychology. General.

[13]  R. Kitchin,et al.  Cognitive mapping , 2018, Cognitive Mapping.

[14]  T. McNamara,et al.  Symmetry and Asymmetry of Human Spatial Memory , 1997, Cognitive Psychology.

[15]  Dan Gordon,et al.  A QUANTITATIVE-COMPARATIVE APPROACH TO ANALYSIS OF DISTORTION IN MENTAL MAPS , 1984 .

[16]  W. R. Garner.  The Processing of Information and Structure , 1974 .

[17]  Nora S. Newcombe,et al.  THE DEVELOPMENT OF SPATIAL LOCATION CODING: PLACE LEARNING AND DEAD RECKONING IN THE SECOND AND THIRD YEARS , 1998 .

[18]  S. Imai,et al.  The free classification of analyzable and unanalyzable stimuli , 1972 .

[19]  Ken Cheng,et al.  How honeybees find a place: Lessons from a simple mind , 2000 .

[20]  Robert Lloyd,et al.  Systematic Distortions in Urban Cognitive Maps , 1987 .

[21]  M. Blades,et al.  The Cognition of Geographic Space , 2002 .

[22]  David Waller,et al.  Scaling techniques for modeling directional knowledge , 2003, Behavior research methods, instruments, & computers : a journal of the Psychonomic Society, Inc.

[23]  Joseph Glicksohn,et al.  Rotation, orientation, and cognitive mapping , 1994 .

[24]  Wesley A. Mah,et al.  Cognitive reference points in judgments of symbolic magnitude , 1982, Cognitive Psychology.

[25]  S. Shettleworth,et al.  Hippocampus and memory in a food-storing and in a nonstoring bird species. , 1996, Behavioral neuroscience.

[26]  I. Mclean,et al.  FIDELITY TO NEST SITE AND MATE IN FIORDLAND CRESTED PENGUINS EUDYPTES PACHYRHYNCHUS , 1999 .

[27]  J. Huttenlocher,et al.  Making Space: The Development of Spatial Representation and Reasoning , 2000 .

[28]  Lance J. Rips,et al.  Semantic distance and the verification of semantic relations , 1973 .

[29]  B. Tabachnick,et al.  Using Multivariate Statistics , 1983 .

[30]  B. Tversky.  Distortions in memory for maps , 1981, Cognitive Psychology.

[31]  A. Friedman,et al.  Updating geographical knowledge: principles of coherence and inertia. , 2000, Journal of experimental psychology. Learning, memory, and cognition.

[32]  K. Cheng.  Landmark-based spatial search in honeybees. I. , 1999, Animal Cognition.

[33]  東京都立大学理学部地理学科.  Geographical reports of Tokyo Metropolitan University , 1966 .

[34]  Alinda Friedman,et al.  Spatial location judgments: A cross-national comparison of estimation bias in subjective North American geography , 2002, Psychonomic bulletin & review.

[35]  Earl Hunt,et al.  ORIENTATION AND WAYFINDING: A REVIEW , 1999 .

[36]  Patricia Howlin,et al.  Origins of cognitive skills , 1986 .

[37]  Albert C. Stevens,et al.  Distortions in judged spatial relations , 1978, Cognitive Psychology.

[38]  Waldo R. Tobler,et al.  Computation of the correspondence of geographical patterns , 1965 .

[39]  Yoshiki Wakabayashi.  Spatial analysis of cognitive maps , 1994 .

[40]  Joël Fagot,et al.  Picture Perception in Animals , 2000 .

[41]  R. Hyman,et al.  Judgments of similarity and spatial models , 1967 .

[42]  Nancy Millette,et al.  How People Look at Pictures , 1935 .

[43]  Anthony C. Gatrell,et al.  Distance and Space: A Geographical Perspective , 1983 .

[44]  W.,et al.  MEDIEVAL DISTORTIONS : THE PROJECTIONS OF ANCIENT MAPS , 2004 .

[45]  E. Tolman.  Cognitive maps in rats and men. , 1948, Psychological review.

[46]  A. Kimball Romney,et al.  SCALING TECHNIQUES IN THE ANALYSIS OF ENVIRONMENTAL COGNITION DATA , 1981 .

[47]  L. Hedges,et al.  Categories and particulars: prototype effects in estimating spatial location. , 1991, Psychological review.

[48]  Jan de Leeuw,et al.  Introducing Multilevel Modeling , 1998 .

[49]  Alinda Friedman,et al.  The development of geographic categories and biases. , 2003, Journal of experimental child psychology.

[50]  C. Allen,et al.  The Cognitive Animal: Empirical and Theoretical Perspectives on Animal Cognition , 2002 .

[51]  J. Schafer,et al.  Missing data: our view of the state of the art. , 2002, Psychological methods.

[52]  Alinda Friedman,et al.  A basis for bias in geographical judgments , 2002, Psychonomic bulletin & review.

[53]  William L. Hays,et al.  Statistics, 5th ed. , 1994 .