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Application of Monte Carlo Methods to Psychometric Function Fitting

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84314

Wichmann,  FA
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Wichmann, F. (2002). Application of Monte Carlo Methods to Psychometric Function Fitting.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-E11B-5
Abstract
The psychometric function relates an observer's performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. Here I describe methods to (1) fitting psychometric functions, (2) assessing goodness-of-fit, and (3) providing confidence intervals for the function's parameters and other estimates derived from them. First I describe a constrained maximum-likelihood method for parameter estimation. Using Monte-Carlo simulations I demonstrate that it is important to have a fitting method that takes stimulus-independent errors (or "lapses") into account. Second, a number of goodness-of-fit tests are introduced. Because psychophysical data sets are usually rather small I advocate the use of Monte Carlo resampling techniques that do not rely on asymptotic theory for goodness-of-fit assessment. Third, a parametric bootstrap is employed to estimate the variability of fitted parameters and derived quantities such as thresholds and slopes. I describe how the bootstrap bridging assumption, on which the validity of the procedure depends, can be tested without incurring too high a cost in computation time. Finally I describe how the methods can be extended to test hypotheses concerning the form and shape of several psychometric functions. Software describing the methods is available (http://www.bootstrap-software.com/psignifit/), as well as articles describing the methods in detail (WichmannHill, PerceptionPsychophysics, 2001a,b).