Judgments Based on Different Functional Relationships between Interacting Cues and a Criterion

Summers, Stanley A.; Summers, Rita C.; Karkau, Virginia T.

doi:10.2307/1421244

Cited by 21 publications

(13 citation statements)

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“…On the other hand, the results seem to be in conflict with other previous results showing that people learn additive combination rules and linear functions more easily than nonadditive combination rules and nonlinear functions (Brehmer, 1969(Brehmer, , 1974Carroll, 1963;Deane et al, 1972;Hammond & D. A. Summers, 1965;S. A. Summers et al, 1969).…”

Section: Relation To Past Studies Of Function Learningcontrasting

confidence: 99%

“…The results also demonstrate that people can easily induce a power-function relation between angle and duration. These results, however, are surprising in light of the widely accepted view that additive combinations of linear functions are most easily learned (Brehmer, 1969;S. A. Summers et al, 1969).…”

Section: Discussionmentioning

confidence: 69%

“…The other specifies the combination rule-that is, how the component functions are combined (e.g., additively or multiplicatively). Previous studies of function learning have typically concluded that (1) linear component functions are learned faster than nonlinear (e. g., Ushaped) ones (Brehmer, 1974;Carroll, 1963;Deane, Hammond, & D. A. Summers, 1972;Hammond & D. A. Summers, 1965), and that (2) additive combination rules are learned more easily than nonadditive (e.g., multiplicative) ones (Brehmer, 1969;S. A. Summers, R. A. Summers, & Karkau, 1969).…”

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confidence: 99%

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Induction of combination rules in two-dimensional function learning

Koh

1993

Memory & Cognition

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Previous studies have typically found that when people learn to combine two dimensions of a stimulus to select a response, they learn additive combination rules more easily than nonadditive (e.g., multiplicative) ones. The present experiments demonstrate that in some situations people can learn multiplicative rules more easily than other (e.g., additive) rules. Subjects learned to produce specified response durations when presented with stimulus lines varying in length and angle of orientation. When stimuli and correct responses were related by a multiplicative combination of power functions, learning was relatively easy (Experiment 1). In contrast, systematic response biases occurred during the early phases of learning an additive combination of linear functions (Experiment 2) and a more complex (nonadditive and nonmultiplicative) combination oflinear functions (Experiment 3), suggesting that people have a tendency to induce a multiplicative combination of power functions. However, the initial biases decreased with practice. These results are explained in terms of a revised adaptive regression model of function learning originally proposed by Koh and Meyer (1991). Differences between the present results and previous results in the literature are discussed.

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Section: Relation To Past Studies Of Function Learningcontrasting

confidence: 99%

Section: Discussionmentioning

confidence: 69%

mentioning

confidence: 99%

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Induction of combination rules in two-dimensional function learning

Koh

1993

Memory & Cognition

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“…This manipulation is important because, if analogous effects are observed for both positive and negative functions, then we have evidence that the effects are due to learned functional relationships, and are not an artifact of previously existing biases toward positive linear relationships (e.g. Sawyer, 1991;Summers, Summers, & Karkau, 1969).…”

Section: Experiment: Blocking and Highlightingmentioning

confidence: 81%

Cue competition in function learning: Blocking and highlighting

Kruschke¹

2001

PsycEXTRA Dataset

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In function learning, people learn to predict a continuous outcome from continuous cues. In category learning, people learn to predict a nominal outcome. The present research demonstrates that two complementary forms of cue competition, previously found in category learning, also occur in function learning. One form of cue competition is blocking of learning about a redundant cue (Kamin, 1968). A second form of cue competition is highlighting of a diagnostic cue (a.k.a. the inverse base rate effect; Medin & Edelson, 1988). For tests with conflicting cues, the results show bimodality of responses, as opposed to averaging, which implies exclusive selectivity that cannot be discerned from category learning paradigms. It is argued that these effects are caused, in both category and function learning, by attentional shifts. No previously published model of function learning can account for these effects, but a model by Kalish, Lewandowsky, and Kruschke (2001) is promising.

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“…For the function shown in Figure 1, an extrapolation response would be of a smaller magnitude than those learned during training. Numerous studies have investigated the relative learning rate of different types of functions (e.g., Brehmer, 1974;Deane, Hammond, & Summers, 1972;Summers, Summers, & Karkau, 1969; for a review, see Busemeyer, Byun, et aL, in press), but only three function-learning studies have investigated transfer to extrapolation tests. One is an unpublished technical report (Carroll, 1963), and another is a briefly mentioned experiment that was peripheral to the thrust of the chapter in which it was reported (Surber, 1987).…”

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confidence: 99%

Extrapolation: The sine qua non for abstraction in function learning.

DeLosh¹,

Busemeyer²,

McDaniel³

1997

Journal of Experimental Psychology: Learning, Memory, and Cogni

165

378

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ion was investigated by examining extrapolation behavior in a function-learning task. During training, participants associated stimulus and response magnitudes (in the form of horizontal bar lengths) that covaried according to a linear, exponential, or quadratic function. After training, novel stimulus magnitudes were presented as tests of extrapolation and interpolation. Participants extrapolated well beyond the range of learned responses, and their responses captured the general shape of the assigned functions, with some systematic deviations. Notable individual differences were observed, particularly in the quadratic condition. The number of unique stimulus-response pairs given during training (i.e., density) was also manipulated but did not affect training or transfer performance. Two rule-learning models, an associative-learning model, and a new hybrid model with associative learning and rule-based responding (extrapolation-association model [EXAM]) were evaluated with respect to the transfer data. EXAM best approximated the overall pattern of extrapolation performance. Research on conceptual behavior has historically focused on category learning and the application of categorical knowledge. So dominant is this focus that the terms concept and category are often used interchangeably (e.g., see Bourne, 1966; Smith & Medin, 1981). It is useful to distinguish these two terms, however, because there are many types of concepts that can not be adequately characterized as categories (Busemeyer, McDaniel, & Byun, 1997; Estes, 1995). In general, concepts also pertain to causal variables (e.g., intelligence) and relationships between these variables (e.g., income is correlated with intelligence). This article investigates functions, which conceptualize the relationship between causal variables. By definition, a function maps a set of input values (called the domain of the function) into a set of output values (called the range of the function), such that each input value is assigned only one output value. In function-learning situations, the range is composed of a continuous set of response magnitudes (e.g., predict a student's GPA on the basis of IQ scores). In category learning, on the other hand, outputs consist of discrete and nominal response categories (e.g.,

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Judgments Based on Different Functional Relationships between Interacting Cues and a Criterion

Cited by 21 publications

References 0 publications

Induction of combination rules in two-dimensional function learning

Induction of combination rules in two-dimensional function learning

Cue competition in function learning: Blocking and highlighting

Extrapolation: The sine qua non for abstraction in function learning.

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