Optimality And Concurrent Variable-interval Variable-ratio Schedules

Despite claims to the contrary, all leading theories about operant choice may be seen as models of optimality. Although melioration is often contrasted with global maximization, both make the same core assumptions as other versions of optimality theory, including momentary maximizing, hill climbing, and the various versions of optimal foraging theory. The present experiment aimed to test melioration against more global optimality and to apply the visit-by-visit analysis suggested by foraging theory. Rats were exposed to concurrent schedules in which one alternative was always variable-ratio 10 and the other alternative was a variable-interval schedule. Although choice relations varied from rat to rat, the overall results roughly confirmed the matching law, a result often taken to support melioration. Pooling the data across sessions and across rats, however, resulted in no increment in unsystematic variance, lending support to the contention by Ziriax and Silberberg (1984) that the choice relation is partly constrained. When the data were analyzed at the level of visits, the results either disconfirmed predictions of melioration or showed regularities about which melioration is silent. Instead, performance tended toward a rough optimization, in which responding favored the variable ratio, but with relatively brief visits to the variable interval. There were no asymmetries in travel or variability that would indicate that different processes were involved in generating visits at the two different schedules. The findings point toward a more global optimality model than melioration and demonstrate the value of per-visit analysis in the study of concurrent performances.     

Tail-measurability in monotone latent variable models

We consider latent variable models for an infinite sequence (or universe) of manifest (observable) variables that may be discrete, continuous or some combination of these. The main theorem is a general characterization by empirical conditions of when it is possible to construct latent variable models that satisfy unidimensionality, monotonicity, conditional independence, andtail-measurability. Tail-measurability means that the latent variable can be estimated consistently from the sequence of manifest variables even though an arbitrary finite subsequence has been removed. The characterizing,necessary and sufficient, conditions that the manifest variables must satisfy for these models are conditional association and vanishing conditional dependence (as one conditions upon successively more other manifest variables). Our main theorem considerably generalizes and sharpens earlier results of Ellis and van den Wollenberg (1993), Holland and Rosenbaum (1986), and Junker (1993). It is also related to the work of Stout (1990).The main theorem is preceded by many results for latent variable modelsin general—not necessarily unidimensional and monotone. They pertain to the uniqueness of latent variables and are connected with the conditional independence theorem of Suppes and Zanotti (1981). We discuss new definitions of the concepts of true-score and subpopulation, which generalize these notions from the stochastic subject, random sampling, and domain sampling formulations of latent variable models (e.g., Holland, 1990; Lord & Novick, 1968). These definitions do not require the a priori specification of a latent variable model.The authors made equivalent contributions to the results of this article. Ellis' research was supported by the Dutch Interuniversitary Graduate School of Psychometrics and Sociometrics. Junker's research was supported by ONR Grant N00014-87-K-0277, NIMH Grant MH15758, and a Carnegie Mellon University Faculty Development Grant. In addition Junker would like to acknowledge the hospitality of the Nijmegen Institute for Cognition and Information during his visit to the University of Nijmegen in August 5–10, 1993.     

The effect of punishment on free-operant choice behavior in humans

During Phase I, three female human subjects pressed a button for monetary reinforcement in five variable-interval schedules specifying different frequencies of reinforcement. On alternate days, responding was also punished (by subtracting money) according to a variable-ratio 34 schedule. In the absence of punishment, response rates conformed to Herrnstein's equation for single variable-interval schedules. Punishment suppressed responding at all frequencies of reinforcement. This was reflected in a change in the values of both constants in Herrnstein's equation: the value of the theoretical maximum response-rate parameter was reduced, and the parameter describing the reinforcement frequency corresponding to the half-maximal response rate was elevated. During Phase II, the same five schedules (A) were in operation (without punishment), but in addition, a concurrent variable-interval schedule (B) of standard reinforcement frequency was introduced. On alternate days, responding in Component B was punished according to a variable-ratio 34 schedule. In the absence of punishment, absolute response rates conformed to equations proposed by Herrnstein to describe performance in concurrent schedules; the ratios of the response rates in the two components and the ratios of the times spent in the two components conformed to the Matching Law. When responding in Component B was punished, response rates in Component B were reduced and those in Component A were elevated, these changes being reflected in distortions of the matching relationship.     

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.     

INTERRESPONSE TIME STRUCTURES IN VARIABLE-RATIO AND VARIABLE-INTERVAL SCHEDULES

The interresponse-time structures of pigeon key pecking were examined under variable-ratio, variable-interval, and variable-interval plus linear feedback schedules. Whereas the variable-ratio and variable-interval plus linear feedback schedules generally resulted in a distinct group of short interresponse times and a broad distribution of longer interresponse times, the variable-interval schedules generally showed a much more continuous distribution of interresponse times. The results were taken to indicate that a log survivor analysis or double exponential fit of interresponse times may not be universally applicable to the task of demonstrating that operant behavior can be dichotomized into bouts of engagement and periods of disengagement.     

The reductive effects of noncontingent reinforcement fixed-time versus variable-time schedules.

The effects of fixed‐time (FT) and variable‐time (VT) schedules on responding were evaluated with 2 adults with mental retardation. Multielement and reversal designs were used to compare the effects of FT and VT schedules in reducing responses previously maintained on variable‐ratio reinforcement schedules. The schedules were equally effective in reducing the target behavior.     

Psychometrics in Psychological Research: Role Model or Partner in Science?

This is a reaction to Borsboom's (2006) discussion paper on the issue that psychology takes so little notice of the modern developments in psychometrics, in particular, latent variable methods. Contrary to Borsboom, it is argued that latent variables are summaries of interesting data properties, that construct validation should involve studying nomological networks, that psychological research slowly but definitely will incorporate latent variable methods, and that the role of psychometrics in psychology is that of partner, not role model. Requests for reprints should be sent to Klaas Sijtsma, Department of Methodology and Statistics, FSW, Tilburg University, PO Box 90153, 5000 LE, Tilburg, The Netherlands.     

Rats' performance on variable-interval schedules with a linear feedback loop between response rate and reinforcement rate

Three experiments investigated whether rats are sensitive to the molar properties of a variable-interval (VI) schedule with a positive relation between response rate and reinforcement rate (i.e., a VI+ schedule). In Experiment 1, rats responded faster on a variable ratio (VR) schedule than on a VI+ schedule with an equivalent feedback function. Reinforced interresponse times (IRTs) were shorter on the VR as compared to the VI+ schedule. In Experiments 2 and 3, there was no systematic difference in response rates maintained by a VI+ schedule and a VI schedule yoked in terms of reinforcement rate. This was found both when the yoking procedure was between-subject (Experiment 2) and within-subject (Experiment 3). Mean reinforced IRTs were similar on both the VI+ and yoked VI schedules, but these values were more variable on the VI+ schedule. These results provided no evidence that rats are sensitive to the feedback function relating response rate to reinforcement rate on a VI+ schedule.     

The Future of Research on Intimate Partner Violence: Person-Oriented and Variable-Oriented Perspectives

This article uses the distinction between the person and the variable orientations as a frame for structuring (1) research on IPV, (2) results of this research, and (3) an agenda for future research. The main tenet of this agenda is that causes, processes, and effects of IPV are person and context specific; therefore, results that relate variables to each other are of limited value if it can be shown that the processes that take place, the meaning of the variables, the profile of the transgressors and the women who experience IPV depend on time, environment, and research design. Examples of valuable variable-oriented research are given; examples of the growing contribution made by person-oriented research are given as well. Sample theories are sketched out, for the variable-oriented, the person-oriented, and the theoretical research arenas, the need for future research is derived from inconsistencies and shortcomings in both current research and theory. Sample research questions are proposed. The contributions made by the authors of this Special Section are embedded within the discussion of research and theory of IPV. It is shown that each of the contributions is valuable within a particular segment of the research landscape.     

Time ordering in frontal lobe patients: a stochastic model approach

Frontal lobe patients reproduced a sequence of capital letters or abstract shapes. Immediate and delayed reproduction trials allowed the analysis of short- and long-term memory for time order by means of suitable Markov chain stochastic models. Patients were as proficient as healthy subjects on the immediate reproduction trial, thus showing spared encoding and short-term memory. They failed, instead, on the delayed trials with capital letters, but not with random shapes, suggesting that their long-term memory impairment did not depend on primary deficits for ordering, but on inability to benefit from the organisational strategies that improve the retention and retrieval in normal subjects.