Parameter identifiability in evidence-accumulation models: The effect of error rates on the diffusion decision model and the linear ballistic accumulator.

Abstract

A variety of different evidence-accumulation models (EAMs) account for common response time and accuracy patterns in two-alternative forced choice tasks by assuming that subjects collect and sum information from their environment until a response threshold is reached. Estimates of model parameters mapped to components of this decision process can be used to explain the causes of observed behavior. However, such explanations are only meaningful when parameters can be identified, that is, when their values can be uniquely estimated from data generated by the model. Prior studies suggest that parameter identifiability is poor when error rates are low but have not systematically compared this issue across different EAMs. We conducted a simulation study investigating the identifiability and estimation properties of model parameters at low error rates in the two most popular EAMs: The diffusion decision model (DDM) and the linear ballistic accumulator (LBA). We found poor identifiability at low error rates for both models but less so for the DDM and for a larger number of trials. The DDM also showed better identifiability than the LBA at low trial numbers for a design with a manipulation of response caution. Based on our results, we recommend tasks with error rates between 15% and 35% for small, and between 5% and 35% for large trial numbers. We explain the identifiability problem in terms of trade-offs caused by correlations between decision-threshold and accumulation-rate parameters and discuss why the models differ in terms of their estimation properties.