Spatial generalization and peak shift in humans

Using a computer betting game, five experiments tested university students on spatial generalization and peak shift. On each trial, one location was marked and the subject was invited to bet 0–4 points. At the winning location (S+), bets won four times the points betted. At nearby losing locations (S)s), points betted were lost. Generalization gradients were exponential in shape, supporting Shepard’s (1987), law (Experiment 1). With peak shift manipulations, three kinds of peak shift or area shift were found. (1) Subjects betted more on the S+ side than on the S) side (Experiments 2–4). (2) When asked if a location was the winning location, subjects responded ‘‘yes’’ more often to locations on the S+ side than to locations on the S) side (Experiments 3–5). (3) When asked to point to the winning location on the screen, subjects’ errors indicated peak shift (Experiment 5). 2002 Elsevier Science (USA). All rights reserved. When an organism has been rewarded for a particular behavior in a particular stimulus situation, it is likely to exhibit the same behavior in similar stimulus situations that are nevertheless different. This ubiquitous phenomenon is known as stimulus generalization. Experimentally, generalization is studied by first training a subject to perform a response to one stimulus (the S+). Unrewarded tests are then given with a range of stimuli, including the Learning and Motivation 33 (2002) 358–389 www.academicpress.com Corresponding author. Fax: +780-492-1768. E-mail address: [email protected] (M.L. Spetch). 0023-9690/02/$ see front matter 2002 Elsevier Science (USA). All rights reserved. PII: S0023-9690 (02 )00003-6 S+. Typically, only one dimension of the stimulus is varied, and the amount of responding the organism makes to each stimulus is recorded. In a classic example, Guttman and Kalish (1956) reinforced pigeons for pecking a key in the presence of a particular wavelength of light. Different animals were trained with different wavelengths as S+. After training, the pigeons were tested in extinction with a range of wavelengths, including S+. The pigeons pecked most to S+ and pecked less to stimuli with increasing wavelength difference from S+. Mechanisms proposed for generalization, going back to Spence (1937), rely on the notion of spreading activation. Basically, excitation or activation of a representation of S+ spreads to representations of stimuli similar to S+. The spreading process has been implemented in diverse ways (e.g., Blough, 1975; Cheng, Spetch, & Johnston, 1997; Ghirlanda & Enquist, 1998, 1999; Gluck, 1991; Reid & Staddon, 1998; Saksida, 1999; Shepard, 1958a; Spetch & Cheng, 1998; review: Cheng, 2002). Based on functional considerations, Shepard (1965, 1987) proposed a law of generalization. The gradient should have an exponential shape when plotted over the appropriate scale of stimulus values (discussed shortly). The equation for the universal law is y 1⁄4 expð kxÞ, where y is a measure of the amount or probability of responding relative to responding at S+, k is a scaling parameter, and x is the psychological distance between the test stimulus and S+. It is important to note the conditions under which the law is said to hold (Shepard, 1986). The stimuli tested in generalization must be clearly discriminable to the subject. If discriminating between stimuli is a problem, the shape of the generalization gradient may turn out Gaussian (Ennis, 1988; Nosofsky, 1986, 1988; Shepard, 1986, 1988). When the stimuli are discriminable, the task of generalization is to classify which stimuli belong in the same functional class as the S+. Shepard (1987) noted that the probability that two stimuli belong in the same class is likely to reflect the exponential function over a wide range of assumptions about the structure of the world. This provides a functional reason for his law of generalization. Mechanistically, a variety of models, with the right parameters, can generate exponential gradients (e.g., Cheng et al., 1997; Reid & Staddon, 1998; Saksida, 1999; Shepard, 1958a,b; Spetch & Cheng, 1998; review: Cheng, 2002). To derive the psychological scale, two methods may be used. One is multidimensional scaling (Shepard, 1965). A number of overlapping generalization gradients with different S+s are obtained (such as the data of Guttman & Kalish, 1956, which featured as an example in Shepard, 1965). The spacing along the physical scale is then adjusted by multidimensional scaling, subject to monotonicity, to render the gradients as similar as possible when their S+s are lined up. The resulting scale is taken to be the psychological scale, and the form of their common gradient the generalization function. A different approach is to take a theoretically specified scale for the stimulus K. Cheng, M.L. Spetch / Learning and Motivation 33 (2002) 358–389 359