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Nicolaas Prins; The Adaptive Psi Method and the Lapse Rate. Journal of Vision 2012;12(9):322. doi: 10.1167/12.9.322.
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As originally proposed, the adaptive psi method (Kontsevich & Tyler, 1999, Vision Research, 39, 2729-2737) requires that a specific value for the lapse rate is assumed, resulting in bias in parameter estimates when the generating lapse rate does not match this assumed value. However, we may free the lapse rate parameter if we subsequently fit results in a separate procedure. Unfortunately, this strategy also results in a significant bias in parameter estimates (Prins, VSS, 2011; doi:10.1167/11.11.1175). Here, I test two modifications to the original psi-method. In the first (and most obvious) modification, the parameter space across which the psi-method calculates the posterior probability distribution (in which it attempts to reduce uncertainty) was extended to include the lapse rate (as well as the threshold and slope) parameter. The second modification of the psi method combined trials in which stimulus placement was controlled by the original psi-method with a (smaller) number of trials which placed stimuli at an asymptotically high level of performance. Results were then fitted in a separate procedure using a maximum likelihood criterion. The behavior of both of these modifications was tested using computer simulations, as well as human observers. While parameter estimates obtained using the first modification did eventually converge on the generating parameter values without bias, the number of trials required to reach convergence would, in most practical cases, be prohibitive. Moreover, trial runs frequently contained long series (often consisting of more than a hundred) of consecutive stimulus placements near asymptotic levels of performance. Considering both the degree of bias and the efficiency of estimation, best results were instead obtained using the second modification of the psi-method in combination with the fitting of a model which assumed that any incorrect responses observed for the trials placed at the asymptotic stimulus intensity were due exclusively to lapses.
Meeting abstract presented at VSS 2012
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