Abstract

A class of geometric models for individual differences in preferential choice or other ‘dominance’ data are considered, primarily spatial models in which psychological stimuli or other objects (e.g., political candidates in a voting situation) are represented as points in a multidimensional space, while subjects/data sources (e.g., consumers, voters, or demographic subgroups) are represented as vectors (or directed line segments), ideal points (i.e., the most preferred or highest ranked stimulus/object), or other entities (e.g., ‘weighted’ ideal points, with different weights for dimensions defining distances for different subjects/sources, or ‘generalized’ ideal points, with an even more general Euclidean metric defining distance between actual and ideal points). The ideal point models are often called ‘unfolding models.’ In the vector model preferences/dominances are modeled by projection of stimulus/object points onto vectors, while in the ideal point/unfolding models the closer (less distant) an actual point is to the ideal point the more preferred/higher ranked is the corresponding stimulus/object for that subject/source. Methods of fitting this class of models, collectively called the ‘linear-quadratic hierarchy of models,’ are described—both for ‘internal analysis,’ in which all parameters are fitted based on the preference/dominance data alone, and for ‘external analysis,’ where the stimulus/object points are defined a priori (e.g., via multidimensional scaling of proximity data) while subject/source parameters are ‘mapped into’ this fixed stimulus/object space.

Full Text
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