Abstract
A subject’s response to the strength of a stimulus is described by the psychometric function, from which summary measures, such as a threshold or a slope, may be derived. Traditionally, this function is estimated by fitting a parametric model to the experimental data, usually the proportion of successful trials at each stimulus level. Common models include the Gaussian and Weibull cumulative distribution functions. This approach works well if the model is correct, but it can mislead if not. In practice, the correct model is rarely known. Here, a nonparametric approach based on local linear fitting is advocated. No assumption is made about the true model underlying the data, except that the function is smooth. The critical role of the bandwidth is identified, and its optimum value is estimated by a cross-validation procedure. As a demonstration, seven vision and hearing data sets were fitted by the local linear method and by several parametric models. The local linear method frequently performed better and never worse than the parametric ones. Supplemental materials for this article can be downloaded from app.psychonomic-journals.org/content/supplemental.
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This work was supported by EPSRC Grant EP/C003470/1 and BBSRC Grant S08656.
Software packages for performing local linear fitting of psychometric functions, extracting thresholds and slopes, and estimating standard errors, as described in this article, are available for both MATLAB (The MathWorks, Inc., Natick, MA) and R (www.r-project.org/) computing environments at www.liv.ac.uk/maths/SP/HOME/K_Zychaluk.html, http://personalpages.manchester.ac.uk/staff /david.foster/, or www.eee.manchester.ac.uk/research/groups/sisp/software or by contacting the authors by e-mail.
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Zchaluk, K., Foster, D.H. Model-free estimation of the psychometric function. Attention, Perception, & Psychophysics 71, 1414–1425 (2009). https://doi.org/10.3758/APP.71.6.1414
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DOI: https://doi.org/10.3758/APP.71.6.1414