The consistency of element transformations affects the visibility but not the direction of illusory motion

Easy, bias-free Bayesian hierarchical modeling of the psychometric function using the Palamedes Toolbox

A hierarchical Bayesian method is proposed that can be used to fit multiple psychometric functions (PFs) simultaneously across conditions and subjects. The method incorporates the generalized linear model and allows easy reparameterization of the parameters of the PFs, for example, to constrain parameter values across conditions or to code for experimental effects (e.g., main effects and interactions in a factorial design). Simulations indicate that fitting PFs for multiple conditions and observers simultaneously using the hierarchical structure effectively eliminates bias and improves precision in parameter estimates relative to fitting PFs individually in each condition. The method is further validated by analyzing human psychophysical data obtained in an experiment investigating the effect of attention on correspondence matching in an ambiguous long-range motion display. The method converges successfully, even for experiments that use a low number of trials per subject, without the need for fine-tuning by the user and while using the default essentially uninformative priors. The latter may make the method more acceptable to those critical of applying informative priors. The method is implemented in the freely downloadable Palamedes Toolbox, which also includes routines that graphically display the fitted psychometric functions alongside the data, and derive and display posterior distributions of parameters, summary statistics, and diagnostic measures. Overall, these features make hierarchical Bayesian modeling of PFs easily available to researchers who wish to use Bayesian statistics but lack the expertise to implement these methods themselves.

Relative roles of 3-D and 2-D coordinate systems in solving the correspondence problem in apparent motion

There has been a controversy in the apparent motion literature regarding the influence of 3-D distances between motion tokens on correspondence matching. The current series of experiments indicates that this discrepancy results because the effect of three-dimensional distance is too small to be detected unless the retinal coordinates of the motion tokens are carefully chosen so as to lead to ambiguous correspondence matches on identical trials. It is also shown that, even when the retinal coordinates of motion tokens are equated, such that the different solutions to the correspondence problem are generated with equal probability, the effect of 3-D distances obtained is relatively small when compared to the effect of the retinal coordinates of motion tokens.