Evidence against a constant-difference effect in concurrent-chains schedules

Savastano and Fantino (1996) reported that in concurrent-chains schedules, initial-link choice proportions remained constant as terminal-link durations increased as long as the subtractive difference between the two terminal-link schedules remained constant. Two experiments with pigeons were conducted to examine this constant-difference effect. Both experiments used equal variable-interval schedules as initial links. The terminal links were fixed delays to reinforcement in Experiment 1 and variable delays to reinforcement in Experiment 2. The durations of the terminal links were varied across conditions, but the difference between pairs of terminal links was always 10 s. In both experiments, preference for the shorter terminal link became less extreme as terminal-link durations increased, so a constant-difference effect was not found. It is argued, however, that this choice situation does not provide clear evidence for or against delay-reduction theory versus other theories of choice.     

Preratio pausing: effects of an alternative reinforcer on fixed- and variable-ratio responding

Seven rats responding under fixed-ratio or variable-ratio schedules of food reinforcement had continuous access to a drinking tube inserted into the operant chamber. Under different conditions they could drink either tap water or one of two saccharin solutions. In a baseline condition, the drinking bottle was empty. Preratio pausing was observed with both schedules, more so with the fixed-ratio than the variable-ratio schedule, and increasing the concentration of the saccharin solution increased the duration of pausing. Comparisons with baseline performances revealed that the additional pausing was largely, but not entirely, spent drinking. The results support the view that pausing under ratio schedules is a consequence of competition between the scheduled reinforcer and alternative reinforcers that also are available within the experimental environment.     

Operating on Functions with Variable Domains

The sum, difference, product and quotient of two functions with different domains are usually defined only on their common domain. This paper extends these definitions so that the sum and other operations are essentially defined anywhere that at least one of the components is defined. This idea is applied to propositions and events, expressed as indicator functions, to define conditional propositions and conditional events as three-valued indicator functions that are undefined when their condition is false. Extended operations of and, or, not and conditioning are then defined on these conditional events with variable conditions. The probabilities of the disjunction (or) and of the conjunction (and) of two conditionals are expressed in terms of the conditional probabilities of the component conditionals. In a special case, these are shown to be weighted averages of the component conditional probabilities where the weights are the relative probabilities of the various conditions. Next, conditional random variables are defined to be random variables X whose domain has been restricted by a condition on a second random variable Y. The extended sum, difference, product and conditioning operations on functions are then applied to these conditional random variables. The expectation of a random variable and the conditional expectation of a conditional random variable are recounted. Theorem 1 generalizes the standard result that the conditional expectation of the sum of two conditional random variables with disjoint and exhaustive conditions is a weighted sum of the conditional expectations of the component conditional random variables. Because of the extended operations, the theorem is true for arbitrary conditions. Theorem 2 gives a formula for the expectation of the product of two conditional random variables. After the definition of independence of two random variables is extended to accommodate the extended operations, it is applied to the formula of Theorem 2 to simplify the expectation of a product of conditional random variables. Two examples end the paper. The first concerns a work force of n workers of different output levels and work shifts. The second example involves two radars with overlapping surveillance regions and different detection error rates. One radar's error rate is assumed to be sensitive to fog and the other radar's error rate is assumed to be sensitive to air traffic density. The combined error rate over the combined surveillance region given heavy fog and moderate air traffic is computed.     

The effect of signaled reinforcement on rats' fixed-interval responding

Four experiments examined the effect on rats' response rate of presenting a brief (500 ms) stimulus simultaneously with the delivery of food on fixed-interval (FI) schedules. In Experiment 1, reinforcement signals that were spatially diffuse (both tones and lights) elevated rates of responding, but responding was attenuated by localized visual stimuli. The remaining experiments examined the signal-induced potentiation of responding. In Experiment 2, a tone reinforcement signal potentiated response rates on an FI schedule, but attenuated response rates on a variable-interval (VI) schedule. This difference was obtained even though the overall rate of responding was equated on the two schedules before the introduction of the signal. Signal-induced potentiation of responding occurred over a range of FI values employed in Experiment 3. In Experiment 4, presenting a reinforcement signal when high local rates of response had occurred immediately before reinforcement resulted in potentiated rates of responding on an FI schedule. The opposite effect on response rate occurred when the reinforcement signal followed only low local rates of response. These results indicate that a variety of factors influence the effects of a reinforcement signal. They imply, however, that the local rate of response at the time of reinforcement is a key factor in establishing the nature of the signaling effect.     

Bouts of responding from variable-interval reinforcement of lever pressing by rats

Four rats obtained food pellets by lever pressing. A variable-interval reinforcement schedule assigned reinforcers on average every 2 min during one block of 20 sessions and on average every 8 min during another block. Also, at each variable-interval duration, a block of sessions was conducted with a schedule that imposed a variable-ratio 4 response requirement after each variable interval (i.e., a tandem variable-time variable-ratio 4 schedule). The total rate of lever pressing increased as a function of the rate of reinforcement and as a result of imposing the variable-ratio requirement. Analysis of log survivor plots of interresponse times indicated that lever pressing occurred in bouts that were separated by pauses. Increasing the rate of reinforcement increased total response rate by increasing the rate of initiating bouts and, less reliably, by lengthening bouts. Imposing the variable-ratio component increased response rate mainly by lengthening bouts. This pattern of results is similar to that reported previously with key poking as the response. Also, response rates within bouts were relatively insensitive to either variable.     

Stimulus generalization of behavioral history

Undergraduates responded under a variable-ratio 30 schedule in the presence of a 25-mm long line and on a differential-reinforcement-of-low-rate 6-s schedule when a 13-mm long line was present. Following this, a line-length continuum generalization test was administered under a fixed-interval 6-s schedule (Experiment 1) or extinction (Experiment 2). In both experiments, obtained generalization gradients conformed to typical postdiscrimination gradients. Responses were frequent under stimuli physically similar to the 25-mm line and infrequent under stimuli physically similar to the 13-mm line. The generalization gradients were generally asymmetric with peak response rates occurring at line lengths greater than 25 mm.     

Variable-interval reinforcement schedule value influences responding following REM sleep deprivation

The effects of rapid-eye movement sleep deprivation (REMSD) in rats were studied in relation to variable-interval (VI) reinforcement schedule value. Initially, lever pressing was maintained on a VI 30-s schedule of food pellet delivery. After a baseline was established, rats were repeatedly exposed to 96 hr of REMSD and control conditions of an equivalent duration. Responding decreased following REMSD but not after exposure to control conditions. Lever pressing was then maintained on a VI 15-s schedule of food pellet delivery and exposure to the REMSD and control conditions was repeated. Under this condition following repeated REMSD exposures, rates of lever pressing became similar to baseline responding. A VI 30-s schedule of food pellet delivery was then reinstated and REMSD and control conditions were repeated. Lever pressing following exposure to the REMSD condition decreased for 3 of 4 rats. Results suggest that VI schedule value influences the effects of REMSD on responding.     

Variable-time reinforcement schedules in the treatment of socially maintained problem behavior

Noncontingent reinforcement (NCR) consists of delivering a reinforcer on a time-based schedule, independent of responding. Studies evaluating the effectiveness of NCR as treatment for problem behavior have used fixed-time (FT) schedules of reinforcement. In this study, the efficacy of NCR with variable-time (VT) schedules was evaluated by comparing the effects of VT and FT reinforcement schedules with 2 individuals who engaged in problem behavior maintained by positive reinforcement. Both FT and VT schedules were effective in reducing problem behavior. These findings suggest that VT schedules can be used to treat problem behavior maintained by social consequences.     

Testing indirect effect with a complete or incomplete dichotomous mediator

Past methodological research on mediation analysis mainly focused on situations where all variables were complete and continuous. When issues of categorical data occur combined with missing data, more methodological considerations are involved. Specifically, appropriate decisions need to be made on estimation methods of the indirect effects and on confidence intervals for testing the indirect effects with accommodations of missing data. We compare strategies that address these issues based on a model with a dichotomous mediator, aiming to provide guidelines for researchers facing such challenges in practice.     

A latent variable model for discrete multivariate psychometric waiting times

A version of the discrete proportional hazards model is developed for psychometrical applications. In such applications, a primary covariate that influences failure times is a latent variable representing a psychological construct. The Metropolis-Hastings algorithm is studied as a method for performing marginal likelihood inference on the item parameters. The model is illustrated with a real data example that relates the age at which teenagers first experience various substances to the latent ability to avoid the onset of such behaviors.We thank Michael Newton and Daode Huang for their helpful comments and suggestions.