Local contrast in behavior allocation during multiple-schedule components

Allocation of responses between two keys was studied during two alternating multiple-schedule components. Responses were recorded in successive quarters of each component. Variable-interval reinforcer schedules on the two keys were constant throughout the experiment for one (constant) component and were varied over conditions on one key for the other, producing changes in reinforcer ratios for the varied component. Behavior allocation for the first quarter of the constant component was inversely related to varied-component reinforcer ratios, a form of local contrast, but this relationship was not observed later in the component. During the first quarter of the varied component, slopes of matching lines were high and decreased later in the component. It is argued that this form of local contrast cannot be explained in terms of reallocation of extraneous reinforcers between components, and that the matching law for concurrent operants does not capture some sources of control over behavior allocation. A simple extension of the matching law is offered that adequately describes behavior changes during both components. A version of this formulation can predict contrast effects in absolute response rates.     

A re-examination of local contrast in multiple schedules

Pigeons were presented with multiple schedules of alternating 90-sec components. When components in which grain was never presented alternated with components in which grain was presented on a variable-interval schedule, the average rate of responding in the variable-interval components increased, showing overall positive behavioral contrast. Unlike previous reports, this study found that the response rates for all birds increased toward the end of the variable-interval components as training proceeded. This increase in local response rate disappeared when the multiple schedule was composed solely of variable-interval components and reappeared when the variable-interval components were again alternated with extinction. This finding cannot be predicted or explained by recent theories of behavioral contrast based on autoshaping, and thus questions their sufficiency. We suggest that this local response-rate increase results from the predictable change from high to low density of reinforcement at the end of the fixed-duration component. Thus, the present effect apparently illustrates a different type of interaction between components of a multiple schedule than that described by previous theories of contrast. In a given procedure, either or both types of interaction may occur; neither provides a complete account of behavioral contrast.     

Some exact conditional tests of independence forR ×C cross-classification tables

Exact conditional tests of independence in cross-classification tables are formulated based on the ² statistic and statistics with stronger operational interpretations, such as some nominal and ordinal measures of association. Guidelines for the table dimensions and sample sizes for which the tests are economically implemented on a computer are given. Some selected sample sizes and marginal distributions are used in a numerical comparison between the significance levels of the approximate and exact conditional tests based on the ² statistic.The authors are grateful for the suggestions of the referees and for computer funding provided by the Northeast Regional Data Center at the University of Florida.     

Testing a unidimensional,qualitative unfolding model for attitudinal or developmental data

Assuming that subject responses rank order stimuli by preference, statistical methods are presented for testing the hypothesis that responses conform to a unidimensional, qualitative unfolding model and to an a priori stimulus ordering. The model postulates that persons and stimulus variables are ordered along a single continuum and that subjects most prefer stimuli nearest their own position. The underlying continuum need not form an interval scale of the stimulus attribute. The general assumptions of the test for the unfolding model make it suitable for the analysis of structure in attitude responses, preference data, and developmental stage data.This research was supported by a grant from the U.S. Public Health Service (Grant No. 1-R01-MH27861-01) to the University of Minnesota. I wish to thank Sanford Weisberg for his helpful suggestions. I also wish to thank Karen Kitchener and Patricia King for letting me use their data.     

Exact conditional tests for cross-classifications: Approximation of attained significance levels

A procedure is proposed for approximating attained significance levels of exact conditional tests. The procedure utilizes a sampling from the null distribution of tables having the same marginal frequencies as the observed table. Application of the approximation through a computer subroutine yields precise approximations for practically any table dimensions and sample size.     

Contrast effects in multiple fixed-interval reinforcement schedules

Pigeons were exposed to a multiple fixed-interval one-minute fixed-interval three-minute schedule of reinforcement following training on either a multiple fixed-interval one-minute fixed-interval one-minute schedule or a multiple fixed-interval three-minute fixed-interval three-minute schedule. For all birds, large negative local contrast effects developed during the first of four three-minute intervals in a component; response rate was depressed and postreinforcement pause lengthened in this interval. Positive local contrast effects were evident during the first of 12 one-minute intervals in a component for five of six birds; at asymptote, the pause was very short and response rate slightly elevated during this interval. Overall positive contrast was generally transient and varied considerably across subjects, while overall negative contrast effects, if they occurred, appeared only after a large number of sessions.     

Habituation To The Reinforcer May Contribute To Multiple-schedule Behavioral Contrast

Habituation to the reinforcer may contribute to multiple-schedule behavioral contrast. According to this argument, reducing reinforcers in one component of a multiple schedule reduces habituation to the reinforcer. Reducing habituation enhances the value, or effectiveness, of the remaining reinforcers, producing positive contrast. Enriching the reinforcers in one component increases habituation to that reinforcer. Increasing habituation decreases the effectiveness of the reinforcer, producing negative contrast. Such an idea is simple and parsimonious. It is not contradicted by any well-established finding in the contrast literature. It makes several tested and untested predictions that are unusual. However, habituation cannot explain all contrast. A complete explanation requires postulating that at least one additional mechanism, controlled by the conditions of reinforcement in the following component, also contributes to contrast.     

Rasch models for item bundles

This paper discusses the application of a class of Rasch models to situations where test items are grouped into subsets and the common attributes of items within these subsets brings into question the usual assumption of conditional independence. The models are all expressed as particular cases of the random coefficients multinomial logit model developed by Adams and Wilson. This formulation allows a very flexible approach to the specification of alternative models, and makes model testing particularly straightforward. The use of the models is illustrated using item bundles constructed in the framework of the SOLO taxonomy of Biggs and Collis.The work of both authors was supported by fellowships from the National Academy of Education Spencer Fellowship.     

Response-reinforcer independence and the economic continuum: A preliminary analysis

Three pigeons were exposed to 1-hr and 4-hr sessions during which they earned food under a fixed-ratio 50 schedule of reinforcement while obtaining additional food according to either a variable-interval or a variable-time schedule. Postsession food was provided after the 1-hr sessions. The frequency of the variable-interval and variable-time food presentations was varied under the two session durations. The various combinations of within-session earned and unearned food, as well as the postsession food, defined conditions on the open-to-closed economy continuum. Key pecks tended to increase as the frequency of either variable-interval or variable-time food decreased. An economic-continuum analysis based on an independence quotient as a measure of response-reinforcer independence is presented to account for the effects.     

The functional independence of mands and tacts

This study demonstrates functional independence in the acquisition of mands and tacts. Some subjects first learned to mand the experimenter's placement of objects with the prepositional phrases “On the left” and “On the right.” They were regularly tested for collateral appearance of tacts with these same phrases. Other subjects learned to tact the location of objects with these prepositional phrases and were regularly tested for collateral appearance of mands. All subjects were next trained in the repertoire that had not been trained in the first condition (either tact or mand). After all subjects had learned both to mand and to tact correctly, another assessment of mand-tact independence was undertaken. Mands (tacts) were reversed and testing assessed collateral reversal of tacts (mands). The results demonstrated that tacts and mands, even when incorporating identical response forms, were functionally independent during acquisition. Subsequent modification of one repertoire (by reversal training) produced collateral reversal in three of nine subjects.