Zero-and-one-inflated generalized Dirichlet distribution to estimate the decision order of resource allocation

Abstract In real life and in social psychology experiments, we allocate a given amount of resources (e.g., time or money) to multiple recipients. It is desirable to have a method to understand the cognitive process of the allocation decision from such data. This study proposes a novel method to estimate the order of allocation using a new statistical model of sequential allocation. We introduce an extension of the generalized Dirichlet distribution, namely zero-and-one-inflated generalized Dirichlet distribution, and describe some of its properties. Through simulation studies, we show that the model can correctly estimate the parameters and the decision order via model selection based on marginal likelihoods. Additionally, we demonstrate the usefulness of this approach with an example of real data analysis, in which the interpretation of the results is more meaningful and psychologically principled than previous analyses based only on the amount allocated.