Relationship between response rate and reinforcement frequency in variable-interval schedules: the effect of the concentration of sucrose reinforcement

Four rats were exposed to variable-interval schedules specifying a range of different reinforcement frequencies, using sucrose of two different concentrations and distilled water as the reinforcer. With sucrose, the rates of responding of all four rats were increasing negatively accelerated functions of reinforcement frequency, the data conforming closely to Herrnstein's equation; this was also true of the data from three of the four rats when distilled water was used as the reinforcer. The values of both constants in Herrnstein's equation were related to the sucrose concentration: the asymptotic response rate decreased, and the reinforcement frequency corresponding to the half-maximal response rate increased, with decreasing sucrose concentration.     

Constrained multidimensional scaling inN spaces

A gradient method is used to obtain least squares estimates of parameters of them-dimensional euclidean model simultaneously inN spaces, given the observation of all pairwise distances ofn stimuli for each space. The procedure can estimate an additive constant as well as stimulus projections and the metric of the reference axes of the configuration in each space. Each parameter in the model can be fixed to equal some a priori value, constrained to be equal to any other parameter, or free to take on any value in the parameter space. Two applications of the procedure are described.     

Trace autoshaping: Acquisition, maintenance, and path dependence at long trace intervals

The pigeon's tendency to acquire and maintain signal-directed key pecking under a trace conditioning procedure was parametrically examined. In Experiment 1, the percentage of CS trials with a key peck response was a decreasing function of the trace interval for separate groups of pigeons. The majority of subjects acquired signal-directed key pecking with trace intervals as long as 36 sec. In Experiment 2, differential maintenance of key pecking occurred across trace intervals in a within-subject procedure. Maintenance of key pecking at 36- and 60-sec trace intervals was path dependent in that responding depended on the subject's performance under the preceding trace interval.     

Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm

Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an EM algorithm are used. By characterizing the ability distribution empirically, arbitrary assumptions about its form are avoided. The Em procedure is shown to apply to general item-response models lacking simple sufficient statistics for ability. This includes models with more than one latent dimension.Supported in part by NSF grant BNS 7912417 to the University of Chicago and by SSRC (UK) grant HR6132 to the University of Lancaster.We are indebted to Mark Reiser and Robert Gibbons for computer programming. David Thissen clarified a number of points in an earlier draft.     

On the existence and uniqueness of maximum-likelihood estimates in the Rasch model

Necessary and sufficient conditions for the existence and uniqueness of a solution of the so-called unconditional (UML) and the conditional (CML) maximum-likelihood estimation equations in the dichotomous Rasch model are given. The basic critical condition is essentially the same for UML and CML estimation. For complete data matricesA, it is formulated both as a structural property ofA and in terms of the sufficient marginal sums. In case of incomplete data, the condition is equivalent to complete connectedness of a certain directed graph. It is shown how to apply the results in practical uses of the Rasch model.Paper read at the European Meeting of the Psychometric Society, Groningen, June 19–21, 1980.Part of the research reported herein was done while the author was staying at the Pulmologisches Zentrum der Stadt Wien; he is indebted to Professor Dr. F. Muhar and Dr. R. Mutschlechner for providing excellent working conditions.     

Studies of operant and reflexive key pecks in the pigeon

The duration of pigeons' key pecks was studied in three experiments. Experiment I revealed that key pecks early in exposure to continuous reinforcement were of short duration, as were key pecks observed on an omission procedure in which pecks prevented food delivery. Key pecks later in exposure to continuous reinforcement, and those that occurred on positive automaintenance procedures, were of long duration. In Experiment II, pigeons were exposed to fixed-interval and fixed-ratio reinforcement schedules, and durations were recorded separately for each quarter of each interval or ratio. On fixed interval, durations were shorter in the first quarter of each interval than in subsequent quarters; on fixed ratio, durations were longer in the first quarter of the ratio than in subsequent quarters. These data parallel observations of concurrent operant responding and salivation in dogs. In Experiment III, pigeons were exposed to a discrete trial, differential-reinforcement-of-low-rate 6-sec schedule. Durations of responses in the first 2 sec of the trial were substantially shorter than those of responses that occurred later. The data from all three experiments support the view that the pigeon's "key peck" actually consists of two subclasses of peck, one reflexive and one operant.     

Evaluating interobserver reliability of interval data

Previous recommendations to employ occurrence, nonoccurrence, and overall estimates of interobserver reliability for interval data are reviewed. A rationale for comparing obtained reliability to reliability that would result from a random-chance model is explained. Formulae and graphic functions are presented to allow for the determination of chance agreement for each of the three indices, given any obtained per cent of intervals in which a response is recorded to occur. All indices are interpretable throughout the range of possible obtained values for the per cent of intervals in which a response is recorded. The level of chance agreement simply changes with changing values. Statistical procedures that could be used to determine whether obtained reliability is significantly superior to chance reliability are reviewed. These procedures are rejected because they yield significance levels that are partly a function of sample sizes and because there are no general rules to govern acceptable significance levels depending on the sizes of samples employed.     

Schedule-induced defecation.

Excessive defecation, typically considered to be a concomitant of stress, was experimentally induced or eliminated under specific schedules of positive reinforcement of lever pressing by rats. The schedules were, by and large, those under which polydipsia is typically induced. In the first of three experiments, rats under fixed-interval 32-second schedules and variable interval 32-second schedules for food and water reinforcers defecated profusely, but not under fixed-interval one-second schedules or other small interval schedules. Somewhat higher rates of defecation were observed on variable interval 32-second schedules than on fixed-interval 32-second schedules. In a second experiment, fixed-ratio schedules were used, some of which resulted in responding such that reinforcement densities were similar to those on the interval schedules that induced defecation. Defecation was not systematically induced by these ratio schedules. In a third experiment, fixed-time schedules of food presentations were utilized. High rates of defecation were induced comparable to those induced by interval schedules of the same time parameter. No other behavior commonly termed "emotional" was observed in any of these experiments.     

Delayed choice responding by pigeons when the correct response is not predictable from the sample stimulus.

Food-deprived pigeons were presented with a row of four response keys situated above a grain hopper aperture. At the start of a trial, three of four keys were randomly selected and illuminated white for six seconds. After a variable blackout period, one of the three previously white keys and the previously dark key were illuminated green, and the remaining white keys were reilluminated as before. A response to the green key that was previously white was reinforced with three-second access to gain, a response to any other key resulted in a three-second blackout and the start of a new trial. Five of six subjects responded to the correct green key more often than chance at an interstimulus interval of 1.5 seconds, and they displayed maximal performance at different intertrial interval values ranging from 15 to 60 seconds. Choice accuracy decreased for all but one subject as the interstimulus interval was increased. For the range of interstimulus interval durations employed, decrements in choice accuracy were qualitatively similar to, but lower than those typically obtained from, delayed-matching-to-sample or delayed-pair comparison procedures.     

A bayesian alternative to least squares and equal weighting coefficients in regression

This paper details a Bayesian alternative to the use of least squares and equal weighting coefficients in regression. An equal weight prior distribution for the linear regression parameters is described with regard to the conditional normal regression model, and resulting posterior distributions for these parameters are detailed. Some interesting connections between this Bayesian procedure and several other methods for estimating optimal weighting coefficients are discussed. In addition, results are presented of a Monte Carlo investigation which compared the effectiveness of the Bayesian procedure relative to least squares, equal weight, ridge, and Bayesian exchangeability estimations.