Molecular contingencies: reinforcement probability

Pigeons obtained food by responding in a discrete-trials two-choice probability-learning experiment involving temporal stimuli. A given response alternative, a left- or right-key peck, had 11 associated reinforcement probabilities within each session. Reinforcement probability for a choice was an increasing or a decreasing function of the time interval immediately preceding the choice. The 11 equiprobable temporal stimuli ranged from 1 to 11 sec in 1-sec classes. Preference tended to deviate from probability matching in the direction of maximizing; i.e., the percentage of choices of the preferred response alternative tended to exceed the probability of reinforcement for that alternative. This result was qualitatively consistent with probability-learning experiments using visual stimuli. The result is consistent with a molecular analysis of operant behavior and poses a difficulty for molar theories holding that local variations in reinforcement probability may safely be disregarded in the analysis of behavior maintained by operant paradigms.     

Validating a selection test,a predictive probability approach

The problem of inferring the validity of a selection test (x) as a predictor of some criterion (y) when completexy data are not available is investigated. The basic approach is to construct the predictive probability distribution of the unobservedy scores and then derive interval estimates of the least squares regression weights, the difference in averagey scores for selected and unselected cases, and the residual variance in predictingy fromx. Further, an approximation to the predictive distribution of the squared correlation betweenx andy in a future group is derived.     

Choice with certain and uncertain reinforcers in an adjusting-delay procedure.

A discrete-trials adjusting-delay procedure was used to investigate the conditions under which pigeons might show a preference for partial reinforcement over 100% reinforcement, an effect reported in a number of previous experiments. A peck on a red key always led to a delay with red houselights and then food. In each condition, the duration of the red-houselight delay was adjusted to estimate an indifference point. In 100% reinforcement conditions, a peck on a green key always led to a delay with green houselights and then food. In partial-reinforcement conditions, a peck on the green key led either to the green houselights and food or to white houselights and no food. In some phases of the experiment, statistically significant preference for partial reinforcement over 100% reinforcement was found, but this effect was observed in only about half of the pigeons. The effect was largely eliminated when variability in the delay stimulus colors was equated for 50% reinforcement conditions and 100% reinforcement conditions. Idiosyncratic preferences for certain colors or for stimulus variability may be at least partially responsible for the effect.     

Precurrent contingencies: Behavior reinforced by altering reinforcement probability for other behavior

The present study explored the effects of a precurrent contingency in which one (precurrent) activity increased the reinforcement probability for another (current) activity. Four human subjects responded on a two-key computer mouse. Each right-key press was reinforced (points exchangeable for money) with .02 probability. In one condition (no precurrent contingency), pressing the left key had no scheduled consequence; in another condition (precurrent contingency), pressing the left key increased the reinforcement probability for right-key responding to .08 for 15 s. Initial exposure to the precurrent contingency resulted in acquisition of precurrent left-key responding for 3 subjects, but for the 4th subject a special contingency was required. Right-key responding occurred at a high stable rate across the conditions. Changeovers to left-key responding dropped to near zero when the precurrent contingency was absent and were maintained at enhanced levels when the precurrent contingency was present. Contacts with the left key consisted of short response runs. Right-key responses were more frequently emitted within 15 s of a left-key response when the precurrent contingency was present, an efficient adaptation to the contingency. Continued research on precurrent behavior may produce insights into complex phenomena such as autoclitics and self-control.     

Leaving patches: An investigation of a laboratory analogue

Five pigeons were trained on a procedure that has been used as a laboratory analogue to natural patch residence. Trials commenced with two responses available. One of these might provide a reinforcer if the patch was a prey patch; the other ended the residence time in the patch and, after a fixed travel time in blackout, produced another patch that might or might not provide a reinforcer. Patch residence also ended, and was followed by the same travel time, after a reinforcer was obtained or after a fixed maximum time was spent in the patch. The dependent variable was patch residence time, from the commencement of the patch to the time at which the subject emitted a response to exit from the patch or until the maximum patch residence time had elapsed. In Parts 1 to 3, the duration of the imposed travel time was varied from 0.25 to 16 s at three different probabilities (.05, .1, and .2) of food per second (λ) in prey patches. As reported in previous research, both increasing travel time and decreasing probabilities of reinforcers per second increased patch residence time. In Parts 4 to 7, the probability of prey trials (ρ) was varied in an irregular order from .1, through .2, .5, and .7, to .9 for different combinations of λ and travel time. Respectively, these were in Part 4, .05 per second and 0.25 s; in Part 5, .05 per second and 16 s; in Part 6, .2 per second and 0.25 s; and in Part 7, .2 per second and 16 s. A previously offered model, based on optimization assumptions, substantially and consistently underpredicted patch residence time. However, a modification of that model, which assumes that the subjects could not accurately discriminate the residence time that provided the minimum interreinforcer interval, described the data well. The same model also described previously reported residence times in a different species with a uniform distribution of prey-arrival times.     

Conditioned reinforcement and choice with delayed and uncertain primary reinforcers.

In an adjusting-delay choice procedure, pigeons could peck on either a red key or a green key. A peck on the red key always led to a delay associated with red houselights and then food. The delay was adjusted over trials to estimate an indifference point--a delay at which the two keys were chosen about equally often. In some conditions, a peck on the green key led to food on all trials after delays of either 10 s or 30 s, and green houselights were lit during the delays. In other conditions, food was presented on only half of the green-key trials. If the green houselights continued to occur on both reinforcement and nonreinforcement trials, preference for the green key always decreased. Preference for the green key also decreased if half of the trials had 30-s houselights followed by food and the other half had no green houselights and no food. However, preference for the green key actually increased if half of the trials had 10-s green houselights followed by food and the other half had no green houselights followed by no food. The latter condition therefore demonstrated a case in which preference for an alternative increased when food was removed from half of the trials. The results suggest that the red and green houselights served as conditioned reinforcers. A hyperbolic decay model (Mazur, 1989) provided good predictions for all conditions by assuming that the strength of a conditioned reinforcer is inversely related to the total time spent in its presence before food is delivered.     

Robust and powerful nonorthogonal analyses

Numerous types of analyses for factorial designs having unequal cell frequencies have been discussed in the literature. These analyses test either weighted or unweighted marginal means which, in turn, correspond to different model comparisons. Previous research has indicated, however, that these analyses result in biased (liberal or conservative) tests when cell variances are heterogeneous. We show how to obtain a generally robust and powerful analysis with any of the recommended nonorthogonal solutions by adapting a modification of the Welch-James procedure for comparing means when population variances are heterogeneous.This research was supported by a Social Sciences and Humanities Research Council (SSHRC) grant (# 410-92-0430) to the first author, a Manitoba Health Research Council Scholar Award and a grant from Natural Sciences and Engineering Research Council to the second author, and a SSHRC Doctoral Fellowship (# 752-92-1628) to the third author. The authors would like to express their gratitude to Joanne Keselman and three anonymous reviewers for their many helpful substantive comments on earlier drafts of this paper.     

A Simple, Unified Approach to Bayesian Risk Calculations

A simple, unified approach for calculating Bayesian risks is presented and illustrated with examples. Although new genetic tools have reduced the need for these risk calculations, situations still exist in which consultands need to know these kinds of risks (for example, when no direct test is available for a particular deleterious mutation, or when a consultand wants to know his/her risk before deciding whether to undergo a direct test). The Unified Approach presented here is straightforward and ensures calculating the correct risks. It can be applied to a wide variety of genetic counseling situations, including but not limited to: calculating recurrence or carrier risks for dominant and recessive diseases; incorporating false-positive and false-negative rates on genetic tests into risk calculations; and determining the probability that an isolated case in a family represents a new mutation. The method is based on basic principles of probability and likelihood theory but can be used without sophisticated knowledge of this theory. The method relies on two rules, the Rule of All Configurations and the Rule of Fundamental Probabilities, which are explained and illustrated. The Unified Approach does not represent new or original mathematics but should make it easier for users to calculate risks accurately. A warning is included that complex calculations should always be independently verified by another individual.     

Effects of stimulus frequency and reinforcement variables on reaction time

Pigeons pecked at one of two black forms, “+” or “O,” either of which could appear alone on a white computer monitor screen. In baseline series of sessions, each form appeared equally often, and two pecks at it produced food reinforcement on 10% of trials. Test series varied the relative probability or duration of reinforcement or frequency of appearance of the targets. Peck reaction times, measured from target onset to the first peck, were found to vary as a function of reinforcement probability but not as a function of relative target frequency or of reinforcement duration. Reaction times to the two targets remained approximately equal as long as the probability of reinforcement, per trial, was equal for the targets, even if the relative frequency of the targets differed by as much as 19 to 1. The results address issues raised in visual search experiments and indicate that attentional priming is unimportant when targets are easy to detect. The results also suggest that equalizing reinforcement probability per trial for all targets removes differential reinforcement as an important variable. That reaction time was sensitive to the probability but not the duration of reinforcement raises interesting questions about the processes reflected in reaction time compared with rate as a response measure.     

The probabilistic import of illatives

It is not only overtly probabilistic illatives like makes it certain that but also apparently non-probabilistic ones like therefore that have probabilistic import. Illatives like therefore convey the meaning that the premise confers on the conclusion a probability not only greater than 0 but also greater than 1/2. But because they do not say whether that probability is equal to or less than 1, these illatives are appropriately called neutral.