Exploring intertemporal decision-making dynamics through functional data analysis: investigating variations in different discount function's dimensions

Intertemporal preferences are closely related to essential aspects of an individual’s emotional and cognitive domains. Discount functions are used to quantify these preferences, which can help us understand conditions such as addiction, depression, and Attention Deficit Hyperactivity Disorder (ADHD). However, traditional parametric models are limited when dealing with intertemporal preferences, mainly when behavioural biases are involved. This study exploits Functional Data Analysis (FDA) to investigate the properties of discount functions in intertemporal choices comparing people suffering from the Hikikomori pathology (a condition that involves social withdrawal) and normal people. Notably, the goal of this research is to look for statistically significant differences in the dynamics of intertemporal decision-making according to different gravity of the Hikikomori condition through the magnified FDA lens on different functional dimensions; the distinctive curves of discount functions categorised by Hikikomori scores prompted a more profound investigation via the so-called augmented functional analysis of variance. The original curves and their derivatives, and the discount rates and their first derivatives provide the different functional dimensions explored. This original approach of analyzing differences between subgroups according to decision-making behaviours is exciting from a methodological and practical perspective.