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.

[1]  A. M. Schrier,et al.  RESPONSE RATES OF MONKEYS (MACACA MULATTA) UNDER VARYING CONDITIONS OF SUCROSE REINFORCEMENT. , 1965, Journal of comparative and physiological psychology.

[2]  J. Staddon,et al.  On matching and maximizing in operant choice experiments. , 1978 .

[3]  P. Killeen On the temporal control of behavior. , 1975 .

[4]  D. Kraeling,et al.  Analysis of amount of reward as a variable in learning. , 1961, Journal of comparative and physiological psychology.

[5]  J J McDowell,et al.  A multivariate rate equation for variable-interval performance. , 1979, Journal of the experimental analysis of behavior.

[6]  B. Campbell,et al.  Response strength as a function of drive level and amount of drive reduction. , 1953, Journal of experimental psychology.

[7]  R. Herrnstein On the law of effect. , 1970, Journal of the experimental analysis of behavior.

[8]  R J Herrnstein,et al.  Formal properties of the matching law. , 1974, Journal of the experimental analysis of behavior.

[9]  H. L. Miller Matching-based hedonic scaling in the pigeon. , 1976, Journal of the experimental analysis of behavior.

[10]  H Rachlin,et al.  On the tautology of the matching law. , 1971, Journal of the experimental analysis of behavior.

[11]  W M Baum,et al.  The correlation-based law of effect. , 1973, Journal of the experimental analysis of behavior.

[12]  R. Herrnstein,et al.  Toward a law of response strength. , 1976 .

[13]  D L Myers,et al.  Undermatching: a reappraisal of performance on concurrent variable-interval schedules of reinforcement. , 1977, Journal of the experimental analysis of behavior.

[14]  P Killeen,et al.  The matching law. , 1972, Journal of the experimental analysis of behavior.

[15]  W M Baum,et al.  On two types of deviation from the matching law: bias and undermatching. , 1974, Journal of the experimental analysis of behavior.

[16]  J. Staddon,et al.  OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR SPACED RESPONDING AND CHOICE : A PRELIMINARY ANALYSIS ' , 2005 .

[17]  R. E. Keesey DURATION OF STIMULATION AND THE REWARD PROPERTIES OF HYPOTHALAMIC STIMULATION. , 1964, Journal of comparative and physiological psychology.

[18]  W M Baum,et al.  Choice as time allocation. , 1969, Journal of the experimental analysis of behavior.

[19]  H. Rachlin A molar theory of reinforcement schedules. , 1978, Journal of the experimental analysis of behavior.

[20]  M C Davison,et al.  Performance in concurrent interval schedules. , 1972, Journal of the experimental analysis of behavior.