Assessing the evidence for response time mixture distributions

I describe a technique for comparing two simple accounts of a distribution of response times: A mixture model and a generalized-shift model. In the mixture model, a target distribution is assumed to be a mixture of response times from two other (reference) distributions. In the generalized-shift model, the target distribution is assumed to be a quantile average of the reference distributions. In order to distinguish these two possibilities, quantiles for the target distribution are estimated from the quantiles of the reference distributions assuming either a shift or a mixture, and the predicted quantiles are used to calculate the multinomial likelihood of the obtained data. Monte Carlo simulations reported here demonstrate that the index is relatively unbiased, is effective with moderate sample sizes and modest spreads between the reference distributions, is relatively unaffected by changes in the number of bins or by data trimming, can be used with data aggregated across subjects, and is relatively insensitive to a range of subject variations in distribution shape and in mixture or shift proportion. As an illustration, the index is applied to the interpretation of three effects from distinct paradigms: residual switch costs in the task-switching paradigm, the psychological refractory period effect, and sequential effects in the Simon task. I conclude that the multinomial likelihood index provides a useful and easily applied tool for the interpretation of effects on response time distributions.