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.

The authors examined whether absolute and relative judgments about global-scale locations and distances were generated from common representations. At the end of a 10-week class on the regional geography of the United States, participants estimated the latitudes of 16 North American cities and all possible pairwise distances between them. Although participants were relative experts, their latitude estimates revealed the presence of psychologically based regions with large gaps between them and a tendency to stretch North America southward toward the equator. The distance estimates revealed the same properties in the representation recovered via multidimensional scaling. Though the aggregated within- and between-regions distance estimates were fitted by Stevens’s law (S. S. Stevens, 1957), this was an averaging artifact: The appropriateness of a power function to describe distance estimates depended on the regional membership of the cities. The authors conclude that plausible reasoning strategies, combined with regionalized representations and beliefs about the location of these relative to global landmarks, underlie global-scale latitude and distance judgments.

Population counts and longitude and latitude coordinates were estimated for the 50 largest cities in the United States by computational linguistic techniques and by human participants. The mathematical technique Latent Semantic Analysis applied to newspaper texts produced similarity ratings between the 50 cities that allowed for a multidimensional scaling (MDS) of these cities. MDS coordinates correlated with the actual longitude and latitude of these cities, showing that cities that are located together share similar semantic contexts. This finding was replicated using a first-order co-occurrence algorithm. The computational estimates of geographical location as well as population were akin to human estimates. These findings show that language encodes geographical information that language users in turn may use in their understanding of language and the world.

We examined some potential causes of bias in geographic location estimates by comparing location estimates of North American cities made by Canadian, U.S., and Mexican university students. All three groups placed most Mexican cities near the equator, which implies that all three groups were influenced by shared beliefs about the locations of geographical regions relative to global reference points. However, the groups divided North America into different regions and differed in the relative accuracy of the estimates within them, which implies that there was an influence of culture-specific knowledge. The data support a category-based system of plausible reasoning, in which biases in judgments are multiply determined, and underscore the utility of the estimation paradigm as a tool in cross-cultural cognitive research.

Seven independent groups estimated the location of North American cities using both spatial and numeric response modes and a variety of perceptual and memory supports. These supports included having location markers for each city color coded by nation and identified by name, giving participants the opportunity to see and update all their estimates throughout the task, and allowing them to respond directly on a map. No manipulation mitigated the influence of categories on the judgments, but some manipulations improved within-region ordinal accuracy. The data provide evidence that the city and regional levels are independent, spatial and numeric response modalities affect accuracy differently at the different levels, biases at the regional level have multiple sources, and accurate spatial cues improve estimates primarily by limiting the use of global landmarks to partition the response space. Results support J. Huttenlocher, L. V. Hedges, and S. Duncan’s (1991) theory of spatial location estimates and extend it to the domain of real-world geography.

www.elsevier.com/locate/jecp The development of geographic categories and biases

Distributional methods have proven to ex-cel at capturing fuzzy, graded aspects of meaning (Italy is more similar to Spain than to Germany). In contrast, it is diffi-cult to extract the values of more specific attributes of word referents from distribu-tional representations, attributes of the kind typically found in structured knowledge bases (Italy has 60 million inhabitants). In this paper, we pursue the hypothesis that distributional vectors also implicitly en-code referential attributes. We show that a standard supervised regres-sion model is in fact sufficient to retrieve such attributes to a reasonable degree of ac-curacy: When evaluated on the prediction of both categorical and numeric attributes of countries and cities, the model consis-tently reduces baseline error by 30%, and is not far from the upper bound. Further anal-ysis suggests that our model is able to “ob-jectify ” distributional representations for entities, anchoring them more firmly in the external world in measurable ways. 1

Several studies have demonstrated that language encodes geographical information. That is, the relative longitude and latitude of city locations can be extracted from language. Whether people actually rely on these linguistic features is less clear. Recent studies have suggested that language statistics plays a role in geographical estimates, but these studies rely on map drawings, a fundamentally perceptual task. The current study investigated the extent to which people rely on map representations and statistical linguistic frequencies by using a linguistic task. Participants saw U.S. city pairs in their iconic positions (a more northern city is presented above a more southern city, or a more western city is presented to the left of a more eastern city), and in their reverse-iconic positions (a more southern city is presented above a more northern city, or a more eastern city is presented to the left of a more western city). For iconic city pairs both in the east – west (Seattle – Boston) and north – south (Memphis – Miami) configurations, RTs were determined by the iconicity. No effect was obtained for statistical linguistic frequencies. However, when city pairs were presented in a reverse-iconic configuration, for both horizontal (Boston – Seattle) and vertical (Miami – Memphis) orientations, both perceptual and linguistic factors explained RTs. These findings support the idea that cognition relies on a shallow heuristic, a linguistic system, and a fine-grained and more precise perceptual simulation system.

There are several important reasons to study geographi-cal learning. First, knowledge of geographical or larger scale space is important for effective functioning in the modern world. Recent data show that American children and even adults have very little knowledge of world geog-raphy, leading to concern that the country is ill-equipped to consider important questions concerning international relations and an increasingly global economy (Liben & Downs, 1994). Second, studying geographical learning offers a real and complex context in which to examine the integration and the interaction of information from many disciplines and knowledge domains. Learning ge-ography requires more than simply encoding the spatial layout of cities and countries. It also involves learning the nature of the environments and climates in which these places are embedded, what natural resources these places possess, and the human aspects of such spatial contexts, such as cultures, political systems, and economic ac-tivities (National Geographic Research and Exploration, 1994). Third, in recent years, people working with geo-graphic information systems (GISs) have called for input from cognitive scientists, because understanding of how human minds process geographical information is vital to building and improving the application of GIS tech-