The Natural Mathematics of Behaviour Analysis: Multivariate Computational Modelling in Behaviour Analysis

Abstract

In a behavioural experiment, a subject is presented with stimuli, and their interactions with a set of operanda are recorded. This generates an event record, a list of events and timestamps. The standard practice in behaviour analysis is to summarise the event record with a single variable. Then, an algebraic model is typically applied to model the covariation between that variable and the independent variable(s). An alternative approach is to use computational models, which generate responses in the context of a simulated environment and thus yield a simulated event record. The typical approach is to extract the dependent variable of interest from the simulated event record. However, we are not restricted to extracting only a single variable from the predicted event records generated by our computational models. Instead, we may generate predictions for any number of variables that are computable from our subjects' event records. This makes computational models convenient for multivariate analysis. The novelty of this thesis lies in exploring the use of computational models for multivariate analysis in behaviour analysis. In multivariate analysis, we face issues concerning the selection of dependent variables and trade-offs between the quality of fit between variables. This forms the central theme of the present thesis. To illustrate, we demonstrate multiple models, including Catania's Operant Reserve, McDowell's Evolutionary Theory of Behaviour Dynamics, Shimp's Associative Learner, and extended implementations of these models. For model fitting, we use a range of algorithms including Approximate Bayesian Computation, Differential Evolution, Particle Swarm Optimisation, and Harmony Search. To deal with the trade-offs between variables, we explore and discuss a range of techniques for contending with the trade-offs between variables, including scalarisation, the conditional compromise heuristic, Fonseca-Fleming rankings, and lexicographic methods. We also demonstrate and explore issues surrounding model development and model comparison. Overall, because there are qualitative differences between the variables of interest, there is often ambiguity around which solutions are considered "best". Our recommendation for multivariate analysis is to analyse jointly the model and dataset from multiple perspectives to get a comprehensive representation of performance under different model-fitting situations and different variables.