Human performance on negative slope schedules of points exchangeable for money: a failure of molar maximization

Panel pressing was generated and maintained in 5 adult humans by schedules of points exchangeable for money. Following exposure to a variable-interval 30-s schedule and to a linear variable-interval 30-s schedule (which permitted points to accumulate in an unseen "store" in the absence of responding), subjects were exposed to a series of conditions with a point-subtraction contingency arranged conjointly with the linear variable-interval schedule. Specifically, points were added to the store according to the linear-variable interval 30-s schedule and were subtracted from the store according to a ratio schedule. Ratio value varied across conditions and was determined individually for each subject such that the subtraction contingency would result in an approximately 50% reduction in the rate of point delivery. Conditions that included the subtraction contingency were termed negative slope schedules because the feedback functions were negatively sloped across all response rates greater than the inverse of the variable-interval schedule, in this case, two per minute. Overall response rates varied inversely with the subtraction ratio, indicating sensitivity to the negative slope conditions, but were in excess of that required by accounts based on strict maximization of overall reinforcement rate. Performance was also not well described by a matching-based account. Detailed analyses of response patterning revealed a consistent two-state pattern in which bursts of high-rate responding alternated with periods of prolonged pausing, perhaps reflecting the joint influence of local and overall reinforcement rates.     

Concurrent ratio schedules: Fixed vs. variable response requirements

Rats were trained on concurrent fixed-ratio variable-ratio or concurrent fixed-ratio mixed-ratio schedules of food reinforcement. The variable-ratio schedule was composed of an arithmetic sequence of 11 ratios that averaged 50; the mixed-ratio schedule consisted of equiprobable ratios of 1 and 99. Fixed-ratio values, varied over experimental conditions, included 25, 35, 50, 60, and 99. The proportion of responses and time allocated to the variable- or mixed-ratio schedule increased as the size of the fixed ratio increased. For most subjects, higher proportions of responses and time were maintained on the fixed-ratio schedule at fixed-ratio values of 25 and 35; higher proportions of responses and time were maintained on the variable- or mixed-ratio schedule at fixed-ratio values of 50 or higher. On concurrent variable-ratio fixed-ratio schedules, the tendency for responding to be maintained exclusively by one schedule was related to the difference in local reinforcement rates obtained from those schedules. Exclusive responding was approximated when the difference in local reinforcement rates obtained from those schedules was large; responding was more evenly distributed between the schedules as the difference in the rates at which reinforcement was obtained from each decreased.     

Test theory without true scores?

This paper traces the course of the consequences of viewing test responses as simply providing dichotomous data concerning ordinal relations. It begins by proposing that the score matrix is best considered to be items-plus-persons by items-plus-persons, and recording the wrongs as well as the rights. This shows how an underlying order is defined, and was used to provide the basis for a tailored testing procedure. It also was used to define a number of measures of test consistency. Test items provide person dominance relations, and the relations provided by one item can be in one of three relations with a second one: redundant, contradictory, or unique. Summary statistics concerning the number of relations of each kind are easy to get and provide useful information about the test, information which is related to but different from the usual statistics. These concepts can be extended to form the basis of a test theory which is based on ordinal statistics and frequency counts and which invokes the concept of true scores only in a limited sense.1979 Psychometric Society presidential address.I want to recognize the contributions which others have made to whatever I have accomplished. First to mention here are my teachers: principally Harold Gulliksen, Ledyard Tucker, and the late Edith Jay. Second, I would like to recognize the importance of my graduate students. Tom Reynolds has been especially important in developing the ideas that I will talk about here today, but at various times, the others have made major contributions in this and other topics. I would like to express also a debt to my family, primarily my wife, Rosemary, who herself has a longterm interest in the psychometric area. Finally, I must acknowledge the financial support of the NIMH some time ago, the Office of Naval Research, until about a year ago, and of the James McKeen Cattell Fund this past year.     

Relationship between response rate and reinforcement frequency in variable-interval schedules: II. Effect of the volume of sucrose reinforcement

Three rats were exposed to variable-interval schedules specifying a range of different reinforcement frequencies, using three different volumes of .32 molar sucrose (.10, .05, and .02 milliliters) as the reinforcer. With each of the three volumes, the rates of responding of all three rats were increasing, negatively accelerated functions of reinforcement frequency, the data conforming closely to Herrnstein's equation. In each rat the value of the constant K_H, which expresses the reinforcement frequency needed to obtain the half-maximal response rate, increased with decreasing reinforcer volume, the values obtained with .02 milliliters being significantly greater than the values obtained with .10 milliliters. The values of the constant R_max, which expresses the theoretical maximum response rate, were not systematically related to reinforcer volume. The effect of reinforcer volume upon the relationship between response rate and reinforcement frequency is thus different from the effect of the concentration of sucrose reinforcement: In a previous experiment (Bradshaw, Szabadi, & Bevan, 1978) it was found that sucrose concentration influenced the values of both constants, R_max increasing and K_H decreasing with increasing sucrose concentration.     

Differential effects of fixed- and variable-time feedback on production rates of elementary school children

The performance of 26 third-grade students who worked on individual weekly academic tasks was compared under fixed- and variable-time "home reports". During fixed-time home reports, each student was given a report to take home on Friday that indicated the quantity of work the student had completed that week, contained comments concerning the quality of the work, and had a space for parental remarks and signature. The same report was given during the variable-time reports, except that seven to nine students were randomly selected each day to receive a home report. During variable-time reporting, students completed more assignments and completed assignments on a greater percentage of available workdays than during fixed-time reporting. The teachers' preference for the variable-time reporting was one additional advantage for the variable system.     

The matching law in and within groups of rats

In each of the two experiments, a group of five rats lived in a complex maze containing four small single-lever operant chambers. In two of these chambers, food was available on variable-interval schedules of reinforcement. In Experiment I, nine combinations of variable intervals were used, and the aggregate lever-pressing rates (by the five rats together) were studied. The log ratio of the rates in the two chambers was linearly related to the log ratio of the reinforcement rates in them; this is an instance of Herrnstein's matching law, as generalized by Baum. Summing over the two food chambers, food consumption decreased, and response output increased, as the time required to earn each pellet increased. In Experiment II, the behavior of individual rats was observed by time-sampling on selected days, while different variable-interval schedules were arranged in the two chambers where food was available. Individual lever-pressing rates for the rats were obtained, and their median bore the same “matching” relationship to the reinforcement rates as the group aggregate in Experiment I. There were differences between the rats in their distribution of time and responses between the two food chambers; these differences were correlated with differences in the proportions of reinforcements the rats obtained from each chamber.     

Estimating the parameters of the latent population distribution

Under consideration is a test battery of binary items. The responses ofn individuals are assumed to follow a Rasch model. It is further assumed that the latent individual parameters are distributed within a given population in accordance with a normal distribution. Methods are then considered for estimating the mean and variance of this latent population distribution. Also considered are methods for checking whether a normal population distribution fits the data. The developed methods are applied to data from an achievement test and from an attitude test.     

Stepwise variable selection in factor analysis

It is very important to choose appropriate variables to be analyzed in multivariate analysis when there are many observed variables such as those in a questionnaire. What is actually done in scale construction with factor analysis is nothing but variable selection.In this paper, we take several goodness-of-fit statistics as measures of variable selection and develop backward elimination and forward selection procedures in exploratory factor analysis. Once factor analysis is done for a certain numberp of observed variables (thep-variable model is labeled the current model), simple formulas for predicted fit measures such as chi-square, GFI, CFI, IFI and RMSEA, developed in the field of the structural equation modeling, are provided for all models obtained by adding an external variable (so that the number of variables isp + 1) and for those by deleting an internal variable (so that the number isp – 1), provided that the number of factors is held constant.A programSEFA (Stepwise variable selection in Exploratory Factor Analysis) is developed to actually obtain a list of the fit measures for all such models. The list is very useful in determining which variable should be dropped from the current model to improve the fit of the current model. It is also useful in finding a suitable variable that may be added to the current model. A model with more appropriate variables makes more stable inference in general.The criteria traditionally often used for variable selection is magnitude of communalities. This criteria gives a different choice of variables and does not improve fit of the model in most cases.The URL of the programSEFA is http://koko15.hus.osaka-u.ac.jp/~harada/factor/stepwise/.     

JEAB: Past,present, and future

The effects of response force on microstructure were evaluated. A strain-gauge operandum permitted the manipulation of the force required to produce reinforcers (criterion responses) independently from the force defining response threshold. Thus, we could detect subcriterion forces that fell short of the force criterion. Eight rats earned food according to variable-interval (VI) 30- and 120-s schedules. The force requirements were set to 5.6 or 32.0 g; the response threshold was fixed at 5.6 g. Interresponse times were computed when subcriterion responses were both included and omitted from the analysis. Log-survivor functions of interresponse times showed that increasing force requirements elevated the mean between-bout interval of the VI 120-s schedule, but only if subcriterion behavior was excluded. Omitting subcriterion responses thus leads to overestimation of intervals separating response bouts. Increasing force requirements also increased the skewness of the between-bout distribution. A subsequent analysis found that subcriterion responses are most plentiful following reinforcer delivery, which helps to explain why their omission might inflate between-bout intervals, as this period is an important transition from reinforcer consumption to engagement in operant activity. The data suggest caution interpreting the effects of force on microstructure when subcriterion behavior is not or cannot be measured.     

Variable-ratio versus variable-interval schedules: response rate, resistance to change, and preference

Two experiments asked whether resistance to change depended on variable-ratio as opposed to variable-interval contingencies of reinforcement and the different response rates they establish. In Experiment 1, pigeons were trained on multiple random-ratio random-interval schedules with equated reinforcer rates. Baseline response rates were disrupted by intercomponent food, extinction, and prefeeding. Resistance to change relative to baseline was greater in the interval component, and the difference was correlated with the extent to which baseline response rates were higher in the ratio component. In Experiment 2, pigeons were trained on multiple variable-ratio variable-interval schedules in one half of each session and on concurrent chains in the other half in which the terminal links corresponded to the multiple-schedule components. The schedules were varied over six conditions, including two with equated reinforcer rates. In concurrent chains, preference strongly overmatched the ratio of obtained reinforcer rates. In multiple schedules, relative resistance to response-independent food during intercomponent intervals, extinction, and intercomponent food plus extinction depended on the ratio of obtained reinforcer rates but was less sensitive than was preference. When reinforcer rates were similar, both preference and relative resistance were greater for the variable-interval schedule, and the differences were correlated with the extent to which baseline response rates were higher on the variable-ratio schedule, confirming the results of Experiment 1. These results demonstrate that resistance to change and preference depend in part on response rate as well as obtained reinforcer rate, and challenge the independence of resistance to change and preference with respect to response rate proposed by behavioral momentum theory.