Scaling N from 1 to 1,000,000: Application of the Generalized Matching Law to Big Data Contexts

The generalized matching law (GML) has been used to describe the behavior of individual organisms in operant chambers, artificial environments, and nonlaboratory human settings. Most of these analyses have used a handful of participants to determine how well the GML describes choice in the experimental arrangement or how some experimental manipulation influences estimated matching parameters. Though the GML accounts very well for choice in a variety of contexts, the generality of the GML to all individuals in a population is unknown. That is, no known studies have used the GML to describe the individual behavior of all individuals in a population. This is likely because the data from every individual in the population has not historically been available or because time and computational constraints made population-level analyses prohibitive. In this study, we use open data on baseball pitches to provide an example of how big data methods can be combined with the GML to: (1) scale within-subjects designs to the population level; (2) track individual members of a population over time; (3) easily segment the population into subgroups for further analyses within and between groups; and (4) compare GML fits and estimated parameters to performance. These were accomplished for each of 2,374 individuals in a population using 8,467,473 observations of behavior-environment relationships spanning 11 years. In total, this study is a proof of concept for how behavior analysts can use data-science techniques to extend individual-level quantitative analyses of behavior to the population-level focused on domains of social relevance.