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J J McDowell

Publications and source records attributed to J J McDowell.

At least 19 recordsLinked to original sources
PubMed2005

A test of the formal and modern theories of matching.

The present study tested a formal, or purely mathematical, theory of matching, and a modern account derived by McDowell (1986) that incorporates deviations from strict matching-bias and sensitivity. Six humans pressed a lever for monetary reinforcers on five concurrent variable interval (VI) schedules of reinforcement. All schedules were presented during each session. The magnitude on one alternative remained constant, and five magnitudes were presented across sessions on the other alternative. To test the formal account, two absolute response rate equations were fitted to the response and reinforcement rates at each alternative at each magnitude. Although the equations accounted for a high percentage of variance, there was a significant negative correlation between the standardized residuals and the predicted response rates. To test the modern account, an ensemble of four equations was fitted to the data. The equations predicted relative and absolute responding, and the independent variables in each equation were adjusted for bias and sensitivity. The equations accounted for a high percentage of variance, and the standardized residuals were not correlated with the predicted response rates. The values of the parameters were consistent with empirical findings and theoretical predictions, including the prediction that k should remain constant across changes in reinforcer magnitude. The results suggest that the formal theory of matching does not describe the data, and that the modern theory may provide an accurate and coherent description of concurrent and single-alternative responding.

Adult↗
PubMed2005

On the classic and modern theories of matching.

Classic matching theory, which is based on Herrnstein's (1961) original matching equation and includes the well-known quantitative law of effect, is almost certainly false. The theory is logically inconsistent with known experimental findings, and experiments have shown that its central constant-k assumption is not tenable. Modern matching theory, which is based on the power function version of the original matching equation, remains tenable, although it has not been discussed or studied extensively. The modern theory is logically consistent with known experimental findings, it predicts the fact and details of the violation of the classic theory's constant-k assumption, and it accurately describes at least some data that are inconsistent with the classic theory.

Animals↗
PubMed2004

A computational model of selection by consequences.

Darwinian selection by consequences was instantiated in a computational model that consisted of a repertoire of behaviors undergoing selection, reproduction, and mutation over many generations. The model in effect created a digital organism that emitted behavior continuously. The behavior of this digital organism was studied in three series of computational experiments that arranged reinforcement according to random-interval (RI) schedules. The quantitative features of the model were varied over wide ranges in these experiments, and many of the qualitative features of the model also were varied. The digital organism consistently showed a hyperbolic relation between response and reinforcement rates, and this hyperbolic description of the data was consistently better than the description provided by other, similar, function forms. In addition, the parameters of the hyperbola varied systematically with the quantitative, and some of the qualitative, properties of the model in ways that were consistent with findings from biological organisms. These results suggest that the material events responsible for an organism's responding on RI schedules are computationally equivalent to Darwinian selection by consequences. They also suggest that the computational model developed here is worth pursuing further as a possible dynamic account of behavior.

Algorithms↗
PubMed2000

Falsification of matching theory's account of single-alternative responding: Herrnstein's k varies with sucrose concentration.

Eight rats pressed levers for varying concentrations of sucrose in water under eight variable-interval schedules that specified a wide range of reinforcement rate. Herrnstein's (1970) hyperbolic equation described the relation between reinforcement and responding well. Although the y asymptote, k, of the hyperbola appeared roughly constant over conditions that approximated conditions used by Heyman and Monaghan (1994), k varied when lower concentration solutions were included. Advances in matching theory that reflect asymmetries between response alternatives and insensitive responding were incorporated into Herrnstein's equation. After fitting the modified equation to the data, Herrnstein's k also increased. The results suggest that variation in k can be detected under a sufficiently wide range of reinforcer magnitudes, and they also suggest that matching theory's account of response strength is false. The results support qualitative predictions made by linear system theory.

Animals↗
PubMed1999

Falsification of matching theory: changes in the asymptote of Herrnstein's hyperbola as a function of water deprivation.

Five rats pressed levers on variable-interval schedules of water reinforcement at various levels of water deprivation. In one phase of the experiment, three deprivation conditions that replicated conditions in Heyman and Monaghan (1987) were arranged, along with three less extreme deprivation conditions. In a second phase, water deprivation was arranged so that subjects were exposed to a greater range of access to water per day. Herrnstein's hyperbola described the rats' response-rate data well. The y asymptote, k, of the hyperbola appeared roughly constant over the conditions that replicated those of Heyman and Monaghan, but decreased markedly when less extreme deprivation conditions were included. In addition, k varied systematically when the second method of arranging deprivation was used. These results falsify a strong form of matching theory and confirm predictions made by linear system theory.

Animals↗
PubMed1995

Response-reinforcement relationships in chronic pain syndrome: applicability of Herrnstein's law.

The quantitative relationship between chronic pain behavior and reinforcement has been generally found to be positive. Herrnstein's statement of the law of effect adds a qualification: it predicts that response rate varies hyperbolically with contingent reinforcement, and that response rate is also negatively related to extraneous reinforcement. The present study is an original investigation of the first of these assertions with regard to the naturally occurring behaviors in chronic pain syndrome. It was found that the stereotypic pain behaviors of 12 chronic pain patients were hyperbolically rather than proportionally related to contingent reinforcement from their significant others. Likewise, healthy behaviors in the same group were a hyperbolic function of contingent reinforcement. Estimates of extraneous reinforcement were also obtained for each category of behaviors. As a group, the subjects showed an inverse relationship between pain behaviors and healthy behaviors, consistent with previous research in the pain area. The present findings add generality to Herrnstein's matching law which serves as a descriptive model of target behaviors in chronic pain patients. The findings also have prescriptive implications for the modification of behavior among chronic pain sufferers.

Adult↗
PubMed1992

Application of Herrnstein's hyperbola to time allocation of naturalistic human behavior maintained by naturalistic social reinforcement.

Five college students talked to an experimenter about various topics. Time spent looking at the experimenter was reinforced by verbal statements of praise and interest on five variable-interval schedules. Herrnstein's hyperbola provided a good description of the time-allocation data for 4 of the 5 subjects, and accounted for 95% of the variance of the median time-allocation data. The hyperbola provided a significantly better description of the data than a two-parameter ramp function with similar differential properties. Estimates of the asymptote, k, of the hyperbola varied among subjects from about 2 to about 15 seconds of eye contact per minute. These estimates were much smaller than the constant 60 seconds of eye contact per minute required by Herrnstein's matching theory. These results support the conclusion that Herrnstein's hyperbola describes naturalistic human behavior maintained by naturalistic social reinforcement as well as it describes the behavior of humans and nonhumans in typical laboratory preparations. The results also indicate that the hyperbolic form of the time-allocation version of Herrnstein's equation is accurate, but that the constant k requirement of matching theory may not hold.

Journal Article↗
PubMed1992

Applying linear systems analysis to dynamic behavior.

In this paper we present an abbreviated discussion of the linear systems analysis in the time domain. We then consider the qualitative character of the behavioral dynamics predicted using the linear form of the analysis. The analysis is then extended to a second-order form. We illustrate some relevant new features introduced by the second-order form with a special case example.

Journal Article↗
PubMed1988

The linear system theory's account of behavior maintained by variable-ratio schedules.

The mathematical theory of linear systems, which has been used successfully to describe behavior maintained by variable-interval schedules, is extended to describe behavior maintained by variable-ratio schedules. The result of the analysis is a pair of equations, one of which expresses response rate on a variable-ratio schedule as a function of the mean ratio requirement (n) that the schedule arranges. The other equation expresses response rate on a variable-ratio schedule as a function of reinforcement rate. Both equations accurately describe existing data from variable-ratio schedules. The theory accounts for two additional characteristics of behavior maintained by variable-ratio schedules; namely, the appearance of strained, two-valued (i.e., zero or very rapid) responding at large ns, and the abrupt cessation of responding at a boundary n. The theory also accounts for differences between behavior on variable-interval and variable-ratio schedules, including (a) the occurrence of strained responding on variable-ratio but not on variable-interval schedules, (b) the abrupt cessation of responding on occurrence of higher response rates on variable-ratio than on variable-interval schedules. Furthermore, given data from a series of variable-interval schedules and from a series of concurrent variable-ratio variable-interval schedules, the theory permits quantitative prediction of many properties of behavior on single-alternative variable-ratio schedules. The linear system theory's combined account of behavior on variable-interval and variable-ratio schedules is superior to existing versions of six other mathematical theories of variable-interval and variable-ratio responding.

Animals↗
PubMed1986

On the falsifiability of matching theory.

Herrnstein's matching theory requires the parameter, k, which appears in the single-alternative form of the matching equation, to remain invariant with respect to changes in reinforcement parameters like magnitude or immediacy. Recent experiments have disconfirmed matching theory by showing that the invariant-k requirement does not hold. However, the theory can be asserted in a purely algebraic form that does not require an invariant k and that is not disconfirmed by the recent findings. In addition, both the original and the purely algebraic versions of matching theory can be asserted in forms that allow for commonly observed deviations from matching (bias, undermatching, and overmatching). The recent finding of a variable k does not disconfirm these versions of matching theory either. As a consequence, matching remains a viable theory of behavior, the strength of which lies in its general conceptualization of all behavior as choice, and in its unified mathematical treatment of single- and multialternative environments.

Animals↗
PubMed1986

Variable-ratio schedules as variable-interval schedules with linear feedback loops.

The mathematical theory of linear systems has been used successfully to describe responding on variable-interval (VI) schedules. In the simplest extension of the theory to the variable-ratio (VR) case, VR schedules are treated as if they were VI schedules with linear feedback loops. The assumption entailed by this approach, namely, that VR and VI-plus-linear-feedback schedules are equivalent, was tested by comparing responding on the two types of schedule. Four human subjects' lever pressing produced monetary reinforcers on five VR schedules, and on five VI schedules with linear feedback loops that reproduced the feedback properties of the VR schedules. Pressing was initiated by instructions in 2 subjects, and was shaped by successive approximation in the other 2. The different methods of response initiation did not have differential effects on behavior. For each of the 4 subjects, the VR and the comparable VI-plus-linear-feedback schedules generated similar average response rates and similar response patterns. The subjects' behavior on both types of schedule was similar to that of avian and rodent species on VR schedules. These results indicate that the assumption entailed by the VI-plus-linear-feedback approach to the VR case is valid and, consequently, that the approach is worth pursuing. The results also confute interresponse-time theories of schedule performance, which require interval and ratio contingencies to produce different response rates.

Adult↗
PubMed1985

Confirmation of linear system theory prediction: Rate of change of Herrnstein's kappa as a function of response-force requirement.

Four human subjects worked on all combinations of five variable-interval schedules and five reinforcer magnitudes ( cent/reinforcer) in each of two phases of the experiment. In one phase the force requirement on the operandum was low (1 or 11 N) and in the other it was high (25 or 146 N). Estimates of Herrnstein's kappa were obtained at each reinforcer magnitude. The results were: (1) response rate was more sensitive to changes in reinforcement rate at the high than at the low force requirement, (2) kappa increased from the beginning to the end of the magnitude range for all subjects at both force requirements, (3) the reciprocal of kappa was a linear function of the reciprocal of reinforcer magnitude for seven of the eight data sets, and (4) the rate of change of kappa was greater at the high than at the low force requirement by an order of magnitude or more. The second and third findings confirm predictions made by linear system theory, and replicate the results of an earlier experiment (McDowell & Wood, 1984). The fourth finding confirms a further prediction of the theory and supports the theory's interpretation of conflicting data on the constancy of Herrnstein's kappa.

Journal Article↗
PubMed1984

Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude.

Eight human subjects pressed a lever on a range of variable-interval schedules for 0.25 cent to 35.0 cent per reinforcement. Herrnstein's hyperbola described seven of the eight subjects' response-rate data well. For all subjects, the y-asymptote of the hyperbola increased with increasing reinforcer magnitude and its reciprocal was a linear function of the reciprocal of reinforcer magnitude. These results confirm predictions made by linear system theory; they contradict formal properties of Herrnstein's account and of six other mathematical accounts of single-alternative responding.

Journal Article↗
PubMed1981

Dynamic equilibrium on a cyclic-interval schedule with a ramp.

Five human subjects pressed a panel for money on a cyclic-interval schedule that arranged recurring periods of linearly increasing reinforcement rates (ramps). Response rate versus time functions for all subjects showed recurring periods of linearly increasing response rates. The responding of four of the five subjects was in phase with the reinforcement input. The remaining subject showed a two-minute phase shift. These results suggest that organisms may act like simple amplifiers on cyclic-interval schedules, that is, the form of the input signal is not changed by the organism, but is returned with amplification. By analogy with the variable-interval case, the controlling variable on cyclic-interval schedules with rate ramps may be the constant reinforcement acceleration that is arranged by the schedule.

Journal Article↗
PubMed1980

An analytic comparison of Herrnstein's equations and a multivariate rate equation.

Herrnstein's equations are approximations of the multivariate rate equation at ordinary rates of reinforcement and responding. The rate equation is the result of a linear system analysis of variable-interval performance. Rate equation matching is more comprehensive than ordinary matching because it predicts and specifies the nature of concurrent bias, and predicts a tendency toward undermatching, which is sometimes observed in concurrent situations. The rate equation contradicts one feature of Herrnstein's hyperbola, viz., the theoretically required constancy of k. According to the rate equation, Herrnstein's k should vary directly with parameters of reinforcement such as amount or immediacy. Because of this prediction, the rate equation asserts that the conceptual framework of matching does not apply to single alternative responding. The issue of the constancy of k provides empirical grounds for distinguishing between Herrnstein's account and a linear system analysis of single alternative variable-interval responding.

Journal Article↗