Multivariate stochastic processes compatible with “aspect” models of similarity and choice

Various recent works have developed feature or aspect models of similarity and preference. These models are more concerned with the fine detail of the judgment process than were prior models, but nevertheless they have not in general developed an underlying stochastic process compatible with the assumed structure. In this paper, we show that a particular class of multivariate stochastic processes, namely those associated with the Marshall-Olkin multivariate exponential distribution, generates several of these models. In particular, such stochastic processes (appropriately interpreted) yield Tversky's elimination by aspects model, Edgell and Geisler's (normal) additive random aspects model, and Shepard and Arabie's additive cluster model.This work was supported by Natural Science and Engineering Research Council of Canada Grant A8124 to A.A.J. Marley.     

Preference for mixed versus constant delays of reinforcement: Effect of probability of the short, mixed delay

Preference for mixed versus constant delays of reinforcement was studied with a concurrent-chain procedure. Lever pressing by rats in concurrently available variable-interval 60-second initial links occasionally produced mutually exclusive terminal-link reinforcement delays. A constant delay of reinforcement (either 15 seconds or 30 seconds) composed one terminal link and mixed delays (.2 second and twice the value of the constant delay) were arranged in the other terminal link. The proportion of .2-second delays in the mixed-delay terminal link took on values of 0, .1, .25, .5, .75, .9, and 1.0 over experimental conditions. Based on relative rates of responding in the initial links, preference for the mixed delays was a negatively accelerated function of the proportion of short, mixed delays. Three of five rats preferred the mixed delays to the constant delays when the proportion of short, mixed delays was .1 or higher, and all five rats preferred the mixed delays when the proportion of short, mixed delays was .25 or higher. Neither Squires and Fantino's (1971) delay-reduction model of choice nor a model based on the harmonic mean reinforcement delay provided a close estimate of choice proportions over the range of short-delay proportions studied. The delay-reduction model underestimated choice for the mixed delays at low and intermediate proportions of short delays, and the harmonic-mean-delay model overestimated choice for the mixed delays at intermediate and high proportions of short delays.     

Choice as a function of local versus molar reinforcement contingencies.

Rats were trained on a discrete-trial probability learning task. In Experiment 1, the molar reinforcement probabilities for the two response alternatives were equal, and the local contingencies of reinforcement differentially reinforced a win-stay, lose-shift response pattern. The win-stay portion was learned substantially more easily and appeared from the outset of training, suggesting that its occurrence did not depend upon discrimination of the local contingencies but rather only upon simple strengthening effects of individual reinforcements. Control by both types of local contingencies decreased with increases in the intertrial interval, although some control remained with intertrial intervals as long as 30 s. In Experiment 2, the local contingencies always favored win-shift and lose-shift response patterns but were asymmetrical for the two responses, causing the molar reinforcement rates for the two responses to differ. Some learning of the alternation pattern occurred with short intertrial intervals, although win-stay behavior occurred for some subjects. The local reinforcement contingencies were discriminated poorly with longer intertrial intervals. In the absence of control by the local contingencies, choice proportion was determined by the molar contingencies, as indicated by high exponent values for the generalized matching law with long intertrial intervals, and lower values with short intertrial intervals. The results show that when molar contingencies of reinforcement and local contingencies are in opposition, both may have independent roles. Control by molar contingencies cannot generally be explained by local contingencies.     

Violations of stochastic transitivity on concurrent chains: Implications for theories of choice

The concurrent-chains procedure has been used to measure how choice depends on various aspects of reinforcement, such as its delay and its magnitude. Navarick and Fantino (1972, 1974, 1975) have found that choice in this procedure can violate the condition of stochastic transitivity that is required if a unidimensional scale for reinforcements is to be possible. It is shown in this paper that two simple unidimensional models of choice on concurrent chains can produce violations of stochastic transitivity. It is argued that such violations may result from the complex contingencies of the concurrent-chains procedure.     

The second offspring of General Process Learning Theory: Overt behavior as the ambassador of the mind

Wasserman suggested in a recent book review that the study of intervening cognitive processes represents a current focus of interest in animal learning and that this has led to a revitalization of comparative psychology. An examination of the volume reviewed suggests that he may have overstated the case. Most of the authors to whom he refers expressed dissatisfaction with traditional stimulus-response associationism but few argued for the extreme (information processing) sort of cognitive approach described by Wasserman.     

The acquisition of observing.

Pigeons were exposed to stimuli correlated with the presence or absence of a variable-interval 60-second schedule of reinforcement only while they depressed a crossbar or "perch." In the first experiment, the stimuli were different tilts of a line displayed on the key. When the difference in brightness between the line and the background (salience) was maximal, seven of eight birds acquired the discrimination, but when the difference was reduced by 50%, only one succeeded. In the second experiment, wavelength of chamber illumination served as the relevant dimension. Neither experiment showed a large effect attributable to the magnitude of the difference (disparity) between the positive and the negative stimulus. Individual differences in time spent observing were positively correlated with level of discrimination in the presence of the stimuli. All birds produced the positive stimulus for a greater proportion of the available time than they did the negative stimulus. This may be the mechanism that provides selective reinforcement of observing. Finally, the formation of a discrimination was analyzed in terms of changes in the proportion of time spent in contact with the discriminative stimuli.     

Serial learning in the pigeon.

Three pigeons learned to peck four colors in a particular sequence, regardless of how these colors were positioned on four response keys and without feedback following each response. This demonstrates that serial learning is possible in subprimate animals.     

SELF-STIMULATION AND LEARNING IN AUTISTIC CHILDREN: PHYSICAL OR FUNCTIONAL INCOMPATIBILITY?1

This study investigated whether an observed inverse relationship between self-stimulation and learning in autistic children is due to a physical inability of the subject to use the same body part for self-stimulation and task responding, or whether self-stimulation “distracts” the subject from task responding. Four actively self-stimulating autistic children were taught two discrimination tasks; one required a response that physically interferred with their self-stimulation; the other did not. Results were: (a) all subjects responded similarly across both tasks; (b) the three subjects with higher mental age scores learned both tasks without external suppression of self-stimulation; and (c) none of the subjects showed an inverse relationship between self-stimulation and learning. The study demonstrated that elimination of self-stimulation is not a necessary prerequisite for the acquisition of a new behavior in all autistic children.     

THE ROLE OF FEEDBACK IN VOLUNTARY CONTROL OF BLOOD PRESSURE IN INSTRUCTED SUBJECTS1

Forty normal male volunteers were randomly assigned to one of four experimental conditions and instructed to raise and lower their systolic blood pressure. Subjects received either beat-to-beat feedback contingent on pressure changes, noncontingent beat-to-beat feedback, noncontingent feedback presented randomly with respect to the occurrence of each heart beat, or instructions alone. The order of increase and decrease trial blocks was counterbalanced across groups. Subjects receiving contingent feedback were monetarily rewarded for appropriate pressure changes. Subjects receiving noncontingent feedback received rewards and feedback equal to the mean received by the contingent group. Subjects in the instructions-only condition were also paid this bonus but were informed of their earnings only at the conclusion of the experiment. Results indicated that in the presence of instructions, feedback, whether contingent or noncontingent, added little to subjects' ability to control pressure during a single session. Theoretical and clinical implications are discussed.     

On Herrnstein's equation and related forms

In 1970, Herrnstein proposed a simple equation to describe the relation between response and reinforcement rates on interval schedules. Its empirical basis is firm, but its theoretical foundation is still uncertain. Two approaches to the derivation of Herrnstein's equation are discussed. It can be derived as the equilibrium solution to a process model equivalent to familiar linear-operator learning models. Modifications of this approach yield competing power-function formulations. The equation can also be derived from the assumption that response strength is proportional to reinforcement rate, given that there is a ceiling on response rate. The proportional relation can, in turn, be derived from a threshold assumption equivalent to Shimp's “momentary maximizing”. This derivation implies that the two parameters of Herrnstein's equation should be correlated, and may explain its special utility in application to internal schedules.