Decision Field Theory: Equivalence with probit models and guidance for identifiability

Abstract

We examine identifiability and distinguishability in Decision Field Theory (DFT) models and highlight pitfalls and how to avoid them. In the past literature, the models’ parameters have been put forward as being able to capture the psychological processes in a decision maker’s mind during deliberation. DFT models have been widely used to analyse human decision making behaviour, and many empirical applications in the choice modelling domain rely solely on data concerning the observed final choice. This raises the question if such data are rich enough to allow for the identification of the model’s parameters. Insight into identifiability and distinguishability is crucial as it allows the researcher to determine which behavioural and psychological conclusions can or cannot be drawn from the estimated DFT model and how a DFT model can be specified in such a way that resulting parameters have meaningful interpretations. In this paper, we address this issue. To do this, we first show which specifications of DFT are equivalent to conventional probit models. Then, building on this equivalence result, we apply established analytical methods to highlight and explain the identification and distinguishability issues that arise when estimating DFT models on conventional choice data. We find evidence that some of the DFT models’ special cases suffer from identifiability issues. Our results warrant caution when DFT models are used to infer psychological processes and human behaviour from conventional choice data, and they help researchers choose the correct specification of DFT models.