Problematic usage of the Zhang and Luck mixture model

Abstract

A common method, due to Zhang and Luck (2008), for analyzing delayed-estimation data with a circular stimulus variable is to fit a mixture of a Von Mises distribution and a uniform distribution. The uniform distribution represents random guesses, presumably made when an item is not kept in memory. When I generate synthetic data from a variable-precision model with zero guessing, the method estimates the guess rate to be nonzero and often high. This is due to model mismatch: the fitted model is not matched to the data-generating (true) model. In real data, this could be a problem if one considers the variable-precision model a plausible candidate model and draws conclusions based on the estimated guess rates. I describe five solutions to this problem: analyzing the residual, ruling out the variable-precision model, robust inference, fitting a hybrid model, and using model-free statistics. I hope that these solutions can contribute to good data analysis practices in the study of working memory.