An efficient adaptive procedure for psychophysical discrimination experiments

We present an adaptive procedure to conduct psychophysical discrimination experiments. In a discrimination experiment, an observer senses (sees, hears, feels, etc.) two stimuli (separated in space or time) and is asked to order these stimuli with respect to a particular parameter (say,s). Under the usual assumption of a locally linear internal representation ofs, perturbed by additive Gaussian noise, the probabilityP(s ₂)—of judging test stimuluss ₂ “larger” than a reference stimuluss ₁—is an error function (a cumulative normal distribution). Such an error function,Erf [(s ₂μ)/σ], is parametrized by two parameters: μand σ. The parameter μ is the value for whichP(s ₂) = 50% and is related to possible bias effects in the internal representation of the observer. The parameter σ is √2 times the standard deviation of the noise distribution and is generally called thediscrimination threshold. In this paper, we present (1) an algorithm to estimate μ and σ given the data generated by such an observer, (2) an analysis of the efficiency of a stimulus presentation with respect to the estimation of μ and σ , and (3) a method that controls the specific choice of stimulus values during an experiment so that an optimal estimation of μ and σ is obtained.     

Top-down design for a system to control operant choice experiments

STATIONS, a FORTRAN program to control operant choice experiments, was developed based on the principles of top-down design and structured programming. As a consequence, the program consists of modules organized in a hierarchical fashion. Separate modules deal with different types of reinforcement schedules, such as variable ratio (VR) and variable interval (VI). These modules produce specific schedules with different parameters by using sequences of values read in at ran time and then randomly sampled. This form of organization permits modifications to be made via changes confined to one module without global repercussions. The clarity of structure that results from the application of top-down design and structured programming should enable future users to more easily adapt this package to suit their specific needs.     

Transitivity as a property of choice

Pigeons' pecks in the presence of two concurrently available initial-link stimuli occasionally produced one of two stimuli associated with mutually exclusive terminal links. Pecks during either terminal link produced food according to aperiodic (variable-interval and variable-ratio) or periodic (fixed-interval and fixed-ratio) schedules of reinforcement. Aperiodic and periodic schedules to which the pigeons were indifferent, in the sense that these schedules maintained equal responding in the initial links, often yielded different preferences in separate choice tests with a third schedule. Conversely, aperiodic and periodic schedules that were equally preferred to a third schedule often failed to generate indifference. These intransitivities imply that (1) aperiodic and periodic schedules are not functionally equivalent in their effects upon choice, and (2) efforts to find a simple method for transforming aperiodic schedules into their periodic equivalents will fail.     

A random-walk model of accuracy and reaction time applied to three experiments on pigeon visual discrimination

A random-walk model of visual discrimination is described and applied to reaction time (RT) distributions from three discrete-trial experiments with pigeons. Experiment 1 was a two-choice hue discrimination task with multiple hues. Choice percentages changed with hue discriminability; RTs were shortest for the least and most discriminable stimuli. Experiments 2 and 3 used go/no-go hue discriminations. Blocks of sessions differed in reward probability associated with a variable red stimulus in Experiment 2 and with a constant green stimulus in Experiment 3. Changes in hue had a large effect on response percentage and a small effect on RT; changes in reward shifted RT distributions on the time axis. The "random-walk, pigeon" model applied to these data is closely related to Ratcliff's diffusion model (Ratcliff, 1978; Ratcliff & Rouder, 1998). Simulations showed that stimulus discriminability affected the speed with which evidence accumulated toward a response threshold, in line with comparable effects in human subjects. Reward probability affected bias, modeled as the amount of evidence needed to reach one threshold rather than the other. The effects of reward probability are novel, and their isolation from stimulus effects within the decision process can guide development of a broader model of discrimination.     

An associative model of geometry learning: a modified choice rule

In a recent article, the authors (Miller & Shettleworth, 2007) showed how the apparently exceptional features of behavior in geometry learning ("reorientation") experiments can be modeled by assuming that geometric and other features at given locations in an arena are learned competitively as in the Rescorla-Wagner model and that the probability of visiting a location is proportional to the total associative strength of cues at that location relative to that of all relevant locations. Reinforced or unreinforced visits to locations drive changes in associative strengths. Dawson, Kelly, Spetch, and Dupuis (2008) have correctly pointed out that at parameter values outside the ranges the authors used to simulate a body of real experiments, our equation for choice probabilities can give impossible and/or wildly fluctuating results. Here, the authors show that a simple modification of the choice rule eliminates this problem while retaining the transparent way in which the model relates spatial choice to competitive associative learning of cue values.     

Responses and pauses: discrimination and a choice catastrophe.

Pigeons produced a stimulus change either by responding or by not responding for a specified time period (by pausing). They then had to choose between two responses to obtain food. One choice was correct if the first component had been completed by a response; the other was correct if the component had been completed by a pause. The pigeons usually chose correctly, thereby indicating that they used their own prior behavior as a discriminative stimulus. Fixed pause requirements did not produce equal first component completions by a response and by a pause. To obtain equality, the pause requirement was titrated as a function of current performance. Titration resulted in equal completions and also produced accurate discrimination. In addition to showing that pigeons discriminated whether they had responded or paused, the data displayed and discontinuous functions predicted by catastrophe theory. Another procedure used forced choice rather than titration to produce equal completions by pausing and responding and also showed accurate discrimination of behavior.     

Two-stage model for order discrimination

Ulrich (1987), exploring the shapes of psychometric functions obtained in the ternary-response paradigm, indicated several inconsistencies between observed and predicted relationships providing evidence against most popular models of temporal-order judgment. In this paper, a new model is presented. It assumes that there are two mechanisms involved in the order discrimination task: one is responsible for the recognition of whether or not the stimuli are successive, and the second is able to determine their order. The model was tested using Allan's (1975a, 1975b) and Ulrich's (1987) data; the model predictions were found to be consistent with the experimental results.     

Test of a psychological cost-benefit model for career choice

A psychological cost-benefit model for career choice was applied to the choice situation after high school graduation. Especially tested were the construct validity and predictive validity of the components of the model. Psychological cost, benefit, and profit scales, with regard to continued education, were constructed on the basis of questionnaire data from 421 high school seniors. The analyses showed a clear, positive relationship between psychological benefit-profit and level of aspiration with regard to continued education. This outcome was regarded as an indication of construct validity for the components of the model. Moreover, groups differing as to post high school choice differed markedly, and in the expected direction, as to psychological cost-benefit-profit. Thus, the model showed high predictive validity with respect to post high school choice, which was also supported by a probability analysis. The results were, in general, more pronounced for boys than for girls.     

From recurrent choice to skill learning: a reinforcement-learning model

The authors propose a reinforcement-learning mechanism as a model for recurrent choice and extend it to account for skill learning. The model was inspired by recent research in neurophysiological studies of the basal ganglia and provides an integrated explanation of recurrent choice behavior and skill learning. The behavior includes effects of differential probabilities, magnitudes, variabilities, and delay of reinforcement. The model can also produce the violation of independence, preference reversals, and the goal gradient of reinforcement in maze learning. An experiment was conducted to study learning of action sequences in a multistep task. The fit of the model to the data demonstrated its ability to account for complex skill learning. The advantages of incorporating the mechanism into a larger cognitive architecture are discussed.     

A markov model for discrimination learning

A theory for discrimination learning which incorporates the concept of an observing response is presented. The theory is developed in detail for experimental procedures in which two stimuli are employed and two responses are available to the subject. Applications of the model to cases involving probabilistic and nonprobabilistic schedules of reinforcement are considered; some predictions are derived and compared with experimental results.This research was supported by a grant from the National Science Foundation.     

A multivariate model for discrimination methods

We describe a multivariate model for a certain class of discrimination methods in this paper and discuss a multivariate Euclidean model for a particular method, the triangular method. The methods of interest involve the selection or grouping of stimuli drawn from two stimulus sets on the basis of attributes invoked by the subject. These methods are commonly used for estimation and hypothesis testing concerning possible differences between foods, beverages, odorants, tastants and visual stimuli.Mathematical formulation of the bivariate model for the triangular method is provided as well as extensive Monte Carlo results for up to 10-dimensional cases. The effect of correlation structure and variance inequality are discussed. Results from these methods (as probability of a correct response) are not monotonically related to the distance between the means of the stimulus sets from which the stimuli are drawn but depend in a particular way on dimensionality, correlation structure, and the relative orientation of the momentary sensory values in a multidimensional space. The importance of these results to the validity of these methods as currently employed is discussed and the possibility of developing a new approach to multidimensional scaling on the basis of this new theory is considered.     

Toward a psychological cost-benefit model for educational and vocational choice

The usefulness of cost-benefit models for analyzing the individual's educational and occupational choice is discussed, with the choice after high school graduation as an example. As a background, the economic approach linked to the human capital concept is described as well as the use of cost-benefit analysis within this framework. Cost-benefit analysis is then discussed as a possible model within the area of educational and occupational choice. First, the traditional, strictly economic model is analyzed and criticized. A psychological economic alternative is proposed which, in contrast to the economic model, is based on the individual's perceptions and expectations regarding costs and benefits. As a third step, a purely psychological cost-benefit model is suggested, where the cost and benefit concepts are broadened to include all types of personal sacrifices and rewards. This model is regarded as more realistic for the individual's career choice than the economic prototypes.     

An olfactory discrimination procedure for mice

This paper describes an olfactory discrimination procedure for mice that is inexpensively implemented and leads to rapid discrimination learning. Mice were first trained to dig in small containers of sand to retrieve bits of buried chocolate. For discrimination training, two containers were presented simultaneously for eight trials per session. One container held sand mixed with cinnamon, and the other held sand mixed with nutmeg. Both containers were baited with chocolate buried in the sand. One odor was designated S+, and mice were allowed to dig and retrieve the chocolate from this container. The other odor was S-, and both containers were removed immediately if subjects began to dig in an S- container. After meeting a two-session acquisition criterion, subjects were given a series of discrimination reversals. In Experiment 1, 12 Swiss-Webster mice (6 male and 6 female) acquired the olfactory discrimination in three to five sessions and completed 3 to 10 successive discrimination reversals within a 50-session testing limit. In Experiment 2, subjects were 14 Pah(enu2) mice, the mouse mutant for phenylketonuria; 7 were homozygotes in which the disorder was expressed (PKU), and 7 were heterozygotes with normal metabolism (non-PKU). Thirteen mice completed pretraining in four to seven sessions, acquisition required 3 to 12 sessions, and all mice completed at least three reversals. Learning rates were similar in PKU and non-PKU mice. We discuss issues related to implementation and several potentially useful procedural variations.