The logistics of choice

Abstract

The generalized matching law (GML) is reconstructed as a logistic regression equation that privileges no particular value of the sensitivity parameter, a. That value will often approach 1 due to the feedback that drives switching that is intrinsic to most concurrent schedules. A model of that feedback reproduced some features of concurrent data. The GML is a law only in the strained sense that any equation that maps data is a law. The machine under the hood of matching is in all likelihood the very law that was displaced by the Matching Law. It is now time to return the Law of Effect to centrality in our science.

Syntax for calculation of discounting indices from the monetary choice questionnaire and probability discounting questionnaire

“…These are among the most commonly used metrics (for a review see Green & Myerson, 2004) and provide investigators with model-based indices (i.e., k and h ) and model-free indices (i.e., ICR and RCR); however, other approaches are also used. These include alternative discounting models, such as a nonlinear curve fitted with logistic transformation, exponential models, hyperboloid models, and heuristic models, (Green, Fry, & Myerson, 1994; Killeen, 2015; Marzilli Ericson, White, Laibson, & Cohen, 2015; Prelec & Loewenstein, 1991; Rachlin et al, 1991), as well as other model-free methods, such as area under the curve (Myerson, Green, & Warusawitharana, 2001). Although the MCQ and PDQ were originally designed to be analyzed using Mazur’s (1987) hyperbolic discounting model, these other models of discounting are viable alternatives and researchers should consider exploring the pros and cons of each method of generating overall discounting.…”

Bayesian methods applied to the generalized matching law

“…This perspective opens the possibility of interpreting the model under different possible theoretical frameworks. The first, consistent with the motivations for its development, is its interpretation as a psychophysical model (Stevens, ) or as an instance of a random utility model (Killeen, ). The second interpretation is as a probabilistic response rule, as an instance of a quantal response model (Goeree, Holt, & Palfrey, ).…”

“…As noted by Killeen (), however, the generalized matching law can also be seen as an instance of a logistic function. This perspective opens the possibility of interpreting the model under different possible theoretical frameworks.…”

“…In terms of bias, values of β 0 < 0 represent a bias toward option 2, while values of β 0 > 0 represent a bias toward option 1, which explains the geometric interpretation of sensitivity and bias. As noted by Killeen (2015), however, the generalized matching law can also be seen as an instance of a logistic function. This perspective opens the possibility of interpreting the model under different possible theoretical frameworks.…”

Addendum to Killeen's (2019) Bidding for Delayed Rewards

“…If the animal is placed in a concurrent‐chain choice experiment, it again need merely approach the better option. If it is differences in a/d that drive the discrimination of which side promises the best value, the data will be well described with logit or logistic functions on those values (Killeen, 2015a, 2015b). Understanding behavior through our models of it is often, as the case here, more complex than the heuristics that may govern that behavior.…”