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Kamila Żychaluk, David H. Foster; Resolving inconsistencies between parametric estimates of psychometric functions by nonparametric fitting. Journal of Vision 2008;8(6):951. doi: https://doi.org/10.1167/8.6.951.
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© ARVO (1962-2015); The Authors (2016-present)
Traditionally, experimentalists assume that the psychometric function underlying a given set of stimulus-response data has a standard shape, i.e. that it belongs to a class of so-called parametric model functions such as Gaussian or Weibull functions. Once the model is chosen, its parameters are adjusted for best fit to the data. In practice, however, the correct model is rarely known. A consequence of this uncertainty is that the fit may be biased, leading to incorrect inferences such as the estimated threshold stimulus level for a particular criterion probability of response. Goodness-of-fit measures can be used to identify badly fitting psychometric functions but these measures are not always helpful in deciding which parametric model should be used. The problems of parametric models are illustrated by an experiment in which a subject had to detect a sinusoidal grating of varying orientation and contrast in a two-alternative forced-choice task. Different parametric models were fitted, including the logistic, Gaussian, Weibull, and reverse Weibull functions, and all gave acceptable fits as measured by the deviance. But the estimated thresholds for 75%-correct performance for each model were very different, sometimes exceeding 10% of the stimulus range tested. With closely similar deviances, fit itself could not be used to decide which curve, and therefore which threshold, should be taken as the final estimate. Instead, it is argued here that a nonparametric method offers a more consistent and neutral approach. The model curve is estimated by adjusting for best fit locally over neighbourhoods defined along the stimulus range. The results are much less dependent on the chosen model, freeing the analysis, and estimated thresholds, from arbitrary model choices.
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