Multi-stage sequential sampling models with finite or infinite time horizon and variable boundaries

Abstract

The multi-stage decision model, aka multiattribute attention switching model, assumes a separate sampling process for each attribute and switching attention from one attribute to the next in a sequential fashion during one trial. Here the model is extended to finite and infinite time horizons and to non-constant boundaries. For a finite time horizon the model predicts a probability of not deciding within the available time. Two different families of non-constant boundaries are implemented, one with a nonlinear decrease, one with a constant boundary at the beginning and a linear decrease towards the deadline. Furthermore, it is shown how the stochastic process underlying each attribute of the multi-stage model (Wiener or Ornstein–Uhlenbeck process) can be discretized by a birth–death chain to implement all the relevant model features and how to provide speeded calculations. Several numerical examples are provided demonstrating the effect of the order of attribute processing (order schedule) and boundary properties. It is shown that, regardless of the time horizon or the non-constant boundaries, the order schedule is the determinant to predict a consistent choice probability/choice response time pattern including preference reversals and fast errors.