Response latency as an index of response strength during functional analyses of problem behavior

Dependent variables in research on problem behavior typically are based on measures of response repetition, but these measures may be problematic when behavior poses high risk or when its occurrence terminates a session. We examined response latency as the index of behavior during assessment. In Experiment 1, we compared response rate and latency to the first response under acquisition and maintenance conditions. In Experiment 2, we compared data from existing functional analyses when graphed as rate versus latency. In Experiment 3, we compared results from pairs of independent functional analyses. Sessions in the first analysis were terminated following the first occurrence of behavior, whereas sessions in the second analysis lasted for 10 min. Results of all three studies showed an inverse relation between rate and latency, indicating that latency might be a useful measure of responding when repeated occurrences of behavior are undesirable or impractical to arrange.     

A comparison of the key-peck and treadle-press operants in the pigeon: differential-reinforcement-of-low-rate schedule of reinforcement

Key pecking and treadle pressing in pigeons were compared under concurrent (key-treadle) and single-operant differential-reinforcement-of-low-rate schedules of food reinforcement ranging from 5 to 60 sec (concurrent procedure) or 5 to 120 sec (single-operant procedure). Under both procedures, the two operants followed the same general law: decreasing response rate and reinforcement rate and increasing number of responses per reinforcement as a function of increasing schedule interval. High correlations were found between key pecking and treadle pressing for the measures of response rate, reinforcement rate, and responses per reinforcement. Regression equations allowed the prediction of treadle pressing from key pecking. More bursting occurred in responding to the key, and key pecking showed a more precise temporal discrimination than treadle pressing. A test for sequential dependencies between key and treadle responses showed significant dependencies not only under the concurrent procedure but also in data created artificially by merging key and treadle sequences from different pigeons under the concurrent procedure and from the same pigeon under the single-operant procedure. It seems likely that the sequential dependencies found were due to the independent action of the schedule on each operant and that behavioral dependencies did not occur with the concurrent training procedure. The key-peck operant does not appear to have any special qualities that preclude its use in discovering general laws of behavior, at least under the differential-reinforcement-of-low-rate schedule. The usefulness of the key peck in other situations requires direct experimental study.     

Baseline response rates affect resistance to change

The effect of response rates on resistance to change, measured as resistance to extinction, was examined in two experiments. In Experiment 1, responding in transition from a variable‐ratio schedule and its yoked‐interval counterpart to extinction was compared with pigeons. Following training on a multiple variable‐ratio yoked‐interval schedule of reinforcement, in which response rates were higher in the former component, reinforcement was removed from both components during a single extended extinction session. Resistance to extinction in the yoked‐interval component was always either greater or equal to that in the variable‐ratio component. In Experiment 2, resistance to extinction was compared for two groups of rats that exhibited either high or low response rates when maintained on identical variable‐interval schedules. Resistance to extinction was greater for the lower‐response‐rate group. These results suggest that baseline response rate can contribute to resistance to change. Such effects, however, can only be revealed when baseline response rate and reinforcement rate are disentangled (Experiments 1 and 2) from the more usual circumstance where the two covary. Furthermore, they are more cleanly revealed when the programmed contingencies controlling high and low response rates are identical, as in Experiment 2.     

Polytomous IRT models and monotone likelihood ratio of the total score

In a broad class of item response theory (IRT) models for dichotomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait. In this study, it is shown that for polytomous items MLR holds for the partial credit model and a trivial generalization of this model. MLR does not necessarily hold if the slopes of the item step response functions vary over items, item steps, or both. MLR holds neither for Samejima's graded response model, nor for nonparametric versions of these three polytomous models. These results are surprising in the context of Grayson's and Huynh's results on MLR for nonparametric dichotomous IRT models, and suggest that establishing stochastic ordering properties for nonparametric polytomous IRT models will be much harder.Hemker's research was supported by the Netherlands Research Council, Grant 575-67-034. Junker's research was supported in part by the National Institutes of Health, Grant CA54852, and by the National Science Foundation, Grant DMS-94.04438.     

Molecular analyses of the effects of d-amphetamine on fixed-interval schedule performances of rats.

A series of doses (0.5 to 2.0 mg/kg) of d-amphetamine was administered to rats whose lever pressing was maintained by fixed-interval 30-s, 60-s, or 120-s schedules of reinforcement by sucrose delivery. Under both saline and d-amphetamine conditions, molecular features of responding were reliably described in terms of the distribution of postreinforcement pauses and local response rate following the onset of responding. Postreinforcement pause always varied from interval to interval but, on average, shortened under the drug. Local response rate (response rate exclusive of pause time) tended to decrease under the drug, and where acceleration occurred within runs of responses, it was reduced by the drug. All of these effects were dose-related. These findings suggest that fixed-interval behavior can be analyzed effectively at a molecular level, and that the effects of d-amphetamine are best described as disruption of temporal discrimination.     

The living legacy of the Harvard Pigeon Lab: quantitative analysis in the wide world

From the Harvard Pigeon Lab of the 1960s arose a behavior-analytic approach that was quantitative and rigorous, rooted in Herrnstein's matching law. Researchers modified the matching law to describe choice behavior in a variety of different settings and examined its relations with other quantitative models. Beginning in the early 1970s, researchers began using the Harvard Pigeon Lab's quantitative framework to study in the laboratory specific aspects of the world outside the laboratory. Much of this work concerned investigations of self-control-choice of a larger, more delayed reinforcer over a smaller, less delayed reinforcer. Experiments using a quantitative framework derived from the matching law have also been conducted outside the laboratory; however, these have been far less frequent. Current and future researchers will benefit the field by devising new, creative ways to investigate the matching law and related quantitative models outside the laboratory. Such research can help to demonstrate the validity of these models as basic principles of behavior, can enhance public opinion of and rewards for such research, and can stimulate further development of the Harvard Pigeon Lab's quantitative approach by using that approach with new variables.     

Effects of reinforcer probability, delay, and response requirements on the choices of rats and pigeons: possible species differences

In Experiment 1 with rats, a left lever press led to a 5-s delay and then a possible reinforcer. A right lever press led to an adjusting delay and then a certain reinforcer. This delay was adjusted over trials to estimate an indifference point, or a delay at which the two alternatives were chosen about equally often. Indifference points increased as the probability of reinforcement for the left lever decreased. In some conditions with a 20% chance of food, a light above the left lever was lit during the 5-s delay on all trials, but in other conditions, the light was only lit on those trials that ended with food. Unlike previous results with pigeons, the presence or absence of the delay light on no-food trials had no effect on the rats' indifference points. In other conditions, the rats showed less preference for the 20% alternative when the time between trials was longer. In Experiment 2 with rats, fixed-interval schedules were used instead of simple delays, and the presence or absence of the fixed-interval requirement on no-food trials had no effect on the indifference points. In Experiment 3 with rats and Experiment 4 with pigeons, the animals chose between a fixed-ratio 8 schedule that led to food on 33% of the trials and an adjusting-ratio schedule with food on 100% of the trials. Surprisingly, the rats showed less preference for the 33% alternative in conditions in which the ratio requirement was omitted on no-food trials. For the pigeons, the presence or absence of the ratio requirement on no-food trials had little effect. The results suggest that there may be differences between rats and pigeons in how they respond in choice situations involving delayed and probabilistic reinforcers.     

The Dutch Identity: A new tool for the study of item response models

The Dutch Identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions (IRFs) and the latent trait distribution. The identity may be exploited in several ways. For example: (a) to suggest how item response models behave for large numbers of items—they are approximate submodels of second-order loglinear models for 2 ^J tables; (b) to suggest new ways to assess the dimensionality of the latent trait—principle components analysis of matrices composed of second-order interactions from loglinear models; (c) to give insight into the structure of latent class models; and (d) to illuminate the problem of identifying the IRFs and the latent trait distribution from sample data.This research was supported in part by contract number N00014-87-K-0730 from the Cognitive Science Program of the Office of Naval Research. I realized the usefulness of the identity in Theorem 1 while lecturing in the Netherlands during October, 1986. Because this was in no small part due to the stimulating psychometric atmosphere there, I call the result the Dutch Identity.     

Timing the second response in two-response avoidance.

Rats were trained on a free-operant avoidance task requiring two lever presses within R seconds, with the opportunity for each response distinguished by differing stimuli. Response latencies at a variety of response-shock intervals were found to be proportional to the time available for the response. These results are shown to be consonant with a scalar expectancy model of timing behavior.     

Quantitative analyses of matching-to-sample performance

Six pigeons performed a simultaneous matching-to-sample (MTS) task involving patterns of dots on a liquid-crystal display. Two samples and two comparisons differed in terms of the density of pixels visible through pecking keys mounted in front of the display. Selections of Comparison 1 after Sample 1, and of Comparison 2 after Sample 2, produced intermittent access to food, and errors always produced a time-out. The disparity between the samples and between the comparisons varied across sets of conditions. The ratio of food deliveries for the two correct responses varied over a wide range within each set of conditions, and one condition arranged extinction for correct responses following Sample 1. The quantitative models proposed by Davison and Tustin (1978), Alsop (1991), and Davison (1991) failed to predict performance in some extreme reinforcer-ratio conditions because comparison choice approached indifference (and strong position biases emerged) when the sample clearly signaled a low (or zero) rate of reinforcement. An alternative conceptualization of the reinforcement contingencies operating in MTS tasks is advanced and was supported by further analyses of the data. This model relates the differential responding between the comparisons following each sample to the differential reinforcement for correct responses following that sample.     

Constituents of response rates

Response rate and the proportion of time pigeons allocated to a key-pecking activity were measured on several basic types of reinforcement schedules. Reinforcement frequency was varied within each type of basic schedule, and the effects on two constituents of response rate were noted. Propensity, the proportion of time the birds spent on a platform in front of the key, showed very consistent effects as reinforcement frequency varied: in general, it decreased when reinforcement frequency markedly decreased and it increased when reinforcement frequency increased. Speed, key pecks per unit of time spent on the platform, showed inconsistent effects when reinforcement frequency varied. Consequently, response rate showed less consistent effects than did propensity. Cumulative response records demonstrated the existence of several different types of transitions or boundary states between the key-pecking activity and other activities. The types of transitions that occurred between activities depended on both the type of reinforcement schedule and the frequency of reinforcement. The propensity data support the position that general laws of behavior can be based on temporal measures of behavior. The speed data suggest that, if a complete assessment of the dynamic properties of behavior is to be achieved, measures of behavior must incorporate the structural variations in the operant unit.     

On measurement properties of continuation ratio models

Three classes of polytomous IRT models are distinguished. These classes are the adjacent category models, the cumulative probability models, and the continuation ratio models. So far, the latter class has received relatively little attention. The class of continuation ratio models includes logistic models, such as the sequential model (Tutz, 1990), and nonlogistic models, such as the acceleration model (Samejima, 1995) and the nonparametric sequential model (Hemker, 1996). Four measurement properties are discussed. These are monotone likelihood ratio of the total score, stochastic ordering of the latent trait by the total score, stochastic ordering of the total score by the latent trait, and invariant item ordering. These properties have been investigated previously for the adjacent category models and the cumulative probability models, and for the continuation ratio models this is done here. It is shown that stochastic ordering of the total score by the latent trait is implied by all continuation ratio models, while monotone likelihood ratio of the total score and stochastic ordering on the latent trait by the total score are not implied by any of the continuation ratio models. Only the sequential rating scale model implies the property of invariant item ordering. Also, we present a Venn-diagram showing the relationships between all known polytomous IRT models from all three classes.     

Within-session changes in responding during concurrent schedules with different reinforcers in the components.

Rats and pigeons responded on several concurrent schedules that provided different reinforcers in the two components (food and water for rats, Experiment 1; wheat and mixed grain for pigeons, Experiment 2). The rate of responding and the time spent responding on each component usually changed within the session. The within-session changes in response rates and time spent responding usually followed different patterns for the two components of a concurrent schedule. For most subjects, the bias and sensitivity to reinforcement parameters of the generalized matching law, as well as the percentage of the variance accounted for, decreased within the session. Negative sensitivity parameters were sometimes found late in the session for the concurrent food-water schedules. These results imply that within-session changes in responding could cause problems for assessing the validity of quantitative theories of concurrent-schedule responding when the components provide different reinforcers. They question changes in a general motivational state, such as arousal, as a complete explanation for within-session changes in responding. The results are compatible with satiation for, or sensitization-habituation to, the reinforcers as explanations.     

The effect of foreperiod duration on reaction time and its relation to interval schedules of reinforcement

Two groups of pigeons were exposed to a simple reaction-time procedure in which mean foreperiod duration was 5, 10, or 20 seconds. For one group, the foreperiods had an arithmetic, or rectangular, distribution; for the second group, they had a constant-probability, or Bernoulli, distribution. Under both distributions, mean response latency was an increasing, negatively accelerated function of mean foreperiod duration. On a given trial, response latency was a function of its associated foreperiod duration: latency was a decreasing function of foreperiod duration in the arithmetic distribution, and an increasing function of foreperiod duration in the constant-probability distribution. Examination of the distribution of latencies revealed a harmonic structure reminiscent of distributions of interresponse times under variable-interval schedules of reinforcement. Taken together, the results confirm and extend previous findings with human subjects, and also suggest numerous similarities to behavior maintained by variable-interval schedules.     

Delay or rate of food delivery as determiners of response rate

Pigeons were confronted with two keys: a green food key and a white changeover key. Food became available for a peck to the green key after variable intervals of time (mean = 113 seconds). A single peck on the changeover key changed the color of the food key to red for a fixed period of time during which the timing of the variable-interval schedule in green was suspended and the switching option eliminated and after which the conditions associated with green were reinstated. In Experiment 1 a single food presentation was obtainable during each red-key period after a minimum delay timed from the switch. This delay and the duration of the red-key period were held constant during a condition but varied between conditions (delay = 2.5, 7.5, 15, or 30 seconds; red-period duration = 30, 60, 120, 240, or 480 seconds). In Experiment 2 additional food presentations were scheduled during a 240-second red-key period with the delay to the first food delivery held constant at 30 seconds, and the delays to later food deliveries varied over conditions. Considering the data from both experiments, the rate of switching to red was a decreasing function of the delay to the first food, the delay to the second food, and perhaps the delay to the third food after a switch. There was no clear evidence that the rate of food in the red-key period made an independent contribution. The ordering of response rates among conditions was consistent with the view that each food presentation after a response adds an incremental effect to the rate of the response and that each food presentation's contribution is a decreasing function of its delay timed from the response.     

Resistance to change of forgetting functions and response rates

This experiment examined the effects of reinforcement probability on resistance to change of remembering and response rate. Pigeons responded on a two-component multiple schedule in which completion of a variable-interval 20-s schedule produced delayed matching-to-sample trials in both components. Each session included four delays (0.1 s, 2 s, 4 s, and 8 s) between sample termination and presentation of comparison stimuli in both components. The two components differed in the probability of reinforcement arranged for correct matches (i.e., rich, p = .9; lean, p = .1). Response rates during the variable-interval portion of the procedure were higher in the rich component during baseline and more resistant to the disruptive effects of intercomponent food and extinction. Forgetting functions were constructed by examining matching accuracy as a function of delay duration. Baseline accuracy was higher in the rich component than in the lean component as measured by differences in the gamma-intercept of the forgetting functions (i.e., initial discrimination), rather than from differences in the slope of the forgetting function (i.e., rate of forgetting). Intercomponent food increased the rate of forgetting relatively more in the lean component than in the rich component, but initial discrimination was not systematically affected. Extinction reduced initial discrimination relatively more in the lean component than in the rich component, but did not systematically affect rate of forgetting. These results are consistent with our previous data suggesting that, as for response rate, accuracy and resistance to change of discriminating are positively related to rate of reinforcement. These data also suggest that the disruptability of remembering depends on the conditions of reinforcement, but the way in which remembering is disrupted depends on the nature of the disruptor.     

The sensitivity of response rate to the rate of variable-interval reinforcement for pigeons and rats: a review

The relation between the rate of a response (B) and the rate of its reinforcement (R) is well known to be approximately hyperbolic: B = kR/(R + Ro), where k represents the maximum response rate, and Ro indicates the rate of reinforcers that will engender a response rate equal to half its maximum value. A review of data reported in 17 published papers revealed that, under variable-interval schedules of reinforcement, Ro was usually lower when pigeons were the subjects than when rats were the subjects. The value of k, in contrast, did not differ consistently between pigeons and rats. Some accounts interpret Ro as the rate of alternative, unscheduled reinforcers in the situation, expressed in units of the scheduled reinforcer. So interpreted, the difference in Ro implies that less alternative reinforcement (relative to the scheduled reinforcement) typically is available to pigeons in their operant conditioning chambers than it is to rats in theirs. Whether or not that interpretation of Ro is valid, the pigeon-rat difference in Ro ensures that for reinforcer rates above about 10 per hour, response rate will be noticeably less sensitive to changes in reinforcer rate (and presumably to changes in other incentive and motivational operations) with pigeons than with rats as subjects, at least with the experimental conditions typically employed.     

Assessing the stability of principal components using regression

This paper presents an analysis, based on simulation, of the stability of principal components. Stability is measured by the expectation of the absolute inner product of the sample principal component with the corresponding population component. A multiple regression model to predict stability is devised, calibrated, and tested using simulated Normal data. Results show that the model can provide useful predictions of individual principal component stability when working with correlation matrices. Further, the predictive validity of the model is tested against data simulated from three non-Normal distributions. The model predicted very well even when the data departed from normality, thus giving robustness to the proposed measure. Used in conjunction with other existing rules this measure will help the user in determining interpretability of principal components.The authors would like to thank the four anonymous reviewers and the two editors for their valuable comments. Atanu R. Sinha gratefully acknowledges the research support received from the Marketing Studies Center, AGSM, UCLA. Send requests for reprints to Atanu R. Sinha, B418 Gold Hall, 110 Westwood Plaza, Los Angeles, CA 90095.