On the relation between the (censored) shifted Wald and the Wiener distribution as measurement models for choice response times

TL;DR

This paper demonstrates that the shifted Wald distribution, modeled as censored data, can reliably recover diffusion model parameters from response time data even with high or perfect accuracy, expanding modeling options in cognitive psychometrics.

Contribution

It introduces a novel approach to diffusion modeling by using censored shifted Wald distribution to estimate parameters from high-accuracy response data, overcoming limitations of the Wiener distribution.

Findings

Censored shifted Wald accurately recovers diffusion parameters with high accuracy data.

Modeling error RTs as censored correct RTs improves parameter recovery.

The approach works well even with increased omission errors due to trial timeout.

Abstract

Inferring processes or constructs from performance data is a major hallmark of cognitive psychometrics. Particularly, diffusion modeling of response times (RTs) from correct and erroneous responses using the Wiener distribution has become a popular measurement tool because it provides a set of psychologically interpretable parameters. However, an important precondition to identify all of these parameters is a sufficient number of RTs from erroneous responses. In the present article, we show by simulation that the parameters of the Wiener distribution can be recovered from tasks yielding very high or even perfect response accuracies using the shifted Wald distribution. Specifically, we argue that error RTs can be modeled as correct RTs that have undergone censoring by using techniques from parametric survival analysis. We illustrate our reasoning by fitting the Wiener and (censored) shifted Wald distribution to RTs from six participants who completed a Go/No-go task. In accordance with our simulations, diffusion modeling using the Wiener and the shifted Wald distribution yielded identical parameter estimates when the number of erroneous responses was predicted to be low. Moreover, the modeling of error RTs as censored correct RTs substantially improved the recovery of these diffusion parameters when premature trial timeout was introduced to increase the number of omission errors. Thus, the censored shifted Wald distribution provides a suitable means for diffusion modeling in situations when the Wiener distribution cannot be fitted without parametric constraints.