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Application of Monte Carlo Methods to Psychometric Function Fitting




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 (Wichmann&Hill, Perception&Psychophysics, 2001a,b).

Author(s): Wichmann, FA.
Journal: Proceedings of the 33rd European Conference on Mathematical Psychology
Pages: 44
Year: 2002
Day: 0

Department(s): Empirical Inference
Bibtex Type: Poster (poster)

Digital: 0
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik


  title = {Application of Monte Carlo Methods to Psychometric Function Fitting},
  author = {Wichmann, FA.},
  journal = {Proceedings of the 33rd European Conference on Mathematical Psychology},
  pages = {44},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  year = {2002}