Bouts of responding on variable-interval schedules: effects of deprivation level

Rats obtained food pellets on a variable-interval schedule of reinforcement by nose poking a lighted key. After training to establish baseline performance (with the mean variable interval set at either 60, 120, or 240 s), the rats were given free access to food during the hour just before their daily session. This satiation operation reduced the rate of key poking. Analysis of the interresponse time distributions (log survivor plots) indicated that key poking occurred in bouts. Prefeeding lengthened the pauses between bouts, shortened the length of bouts (less reliably), and had a relatively small decremental effect on the response rate within bouts. That deprivation level affects mainly between-bout pauses has been reported previously with fixed-ratio schedules. Thus, when the focus is on bouts, the performances maintained by variable-interval schedules and fixed-ratio schedules are similarly affected by deprivation.     

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.     

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.     

Obtaining Systematic Teacher Reports of Disruptive Behavior Disorders Utilizing DSM-IV

This study examines the psychometric properties of the Vanderbilt AD/HD Diagnostic Teacher Rating Scale (VADTRS) and provides preliminary normative data from a large, geographically defined population. The VADTRS consists of the complete list of DSM-IV AD/HD symptoms, a screen for other disruptive behavior disorders, anxiety and depression, and ratings of academic and classroom behavior performance. Teachers in one suburban county completed the scale for their students during 2 consecutive years. Statistical methods included (a) exploratory and confirmatory latent variable analyses of item data, (b) evaluation of the internal consistency of the latent dimensions, (c) evaluation of latent structure concordance between school year samples, and (d) preliminary evaluation of criterion-related validity. The instrument comprises four behavioral dimensions and two performance dimensions. The behavioral dimensions were concordant between school years and were consistent with a priori DSM-IV diagnostic criteria. Correlations between latent dimensions and relevant, known disorders or problems varied from .25 to .66.     

Joint Modeling of Ability and Differential Speed Using Responses and Response Times

With computerized testing, it is possible to record both the responses of test takers to test questions (i.e., items) and the amount of time spent by a test taker in responding to each question. Various models have been proposed that take into account both test-taker ability and working speed, with the many models assuming a constant working speed throughout the test. The constant working speed assumption may be inappropriate for various reasons. For example, a test taker may need to adjust the pace due to time mismanagement, or a test taker who started out working too fast may reduce the working speed to improve accuracy. A model is proposed here that allows for variable working speed. An illustration of the model using the Amsterdam Chess Test data is provided.     

Distractor selection ratios

A latent variable representation for multiple-choice item and option characteristic curves is presented. Under standard assumptions of conditional independence of item responses and monotonicity of item characteristic curves, a criterion for distractors is proposed based on distractor selection ratios. A connection is made between the proposed criterion and the theory of individual choice behavior, providing new insight. The main results allow for the testing of the criterion from observable data without first specifying a parametric form for the characteristic curves. A series of examples apply the method.