2021/12/10 by Thomas J. Faulkenberry, Faulkenberry, Thomas J.
Computer Science · Decision Sciences · Psychology · #Applications (stat.AP) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Forecasting Techniques and Applications #Mental Health Research Topics #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.2112.05503
openalex publication_date 2021/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To investigate the structure of individual differences in performance on behavioral tasks, Haaf and Rouder (2017) developed a class of hierarchical Bayesian mixed models with varying levels of constraint on the individual effects. The models are then compared via Bayes factors, telling us which model best predicts the observed data. One common criticism of their method is that the observed data are assumed to be drawn from a normal distribution. However, for most cognitive tasks, the primary measure of performance is a response time, the distribution of which is well known to not be normal. In this paper, I investigate the assumption of normality for two datasets in numerical cognition. Specifically, I show that using a shifted lognormal model for the response times does not change the overall pattern of inference. Further, since the model-estimated effects are now on a logarithmic scale, the interpretation of the modeling becomes more difficult, particularly because the estimated effect is now multiplicative rather than additive. As a result, I recommend that even though response times are not normally distributed in general, the simplification afforded by the Haaf and Rouder (2017) approach provides a pragmatic approach to modeling individual differences in behavioral tasks.