Concepts borrowed from the General Linear Model can be applied to the fitting of psychometric functions (PFs) and testing of research hypotheses. The Palamedes toolbox (Prins & Kingdom, 2009) implements these concepts into routines which allow the user to fit multiple PFs simultaneously to several datasets (arising for example, from different conditions in an experiment). The user is given considerable flexibility in defining models. A model might specify for example that the guess rate equals 0.5, that the thresholds in the different conditions vary as a linear function of some IV (e.g., adaptation duration), that the slopes are equal between conditions and that the lapse rate equals 0.02. Users may compare statistically any two such custom models as long as one of the models is nested under the other. However, such comparisons are valid only insofar as the assumptions that the simpler of the two model makes are met. What if these assumptions are not met? I am addressing this question by running simulations.
The Psychometric Function (PF) relates some behavioral measure (e.g., proportion correct detection) to some task characteristic (e.g., stimulus intensity). Typically of interest is the 'threshold' stimulus intensity. The threshold is usually defined as that stimulus intensity at which observers reach a specific level of performance. Some suggest that, in order to obtain a threshold estimate which is as unbiased as possible, we should allow the upper asymptote of the PF or 'lapse rate' to vary during function fitting. In their highly influential paper, Wichmann and Hill (2001) claim that allowing the lapse rate to vary results in threshold and slope estimates which are 'essentially unbiased', seemingly irrespective of what stimulus placement regimen is used. I have attempted to replicate W&H's results, but was unsuccesful. Instead, I obtained systematic and significant biases in both thresholds and slopes (see Figure, click on it to view a larger version). I propose an alternative fitting scheme which does lead to threshold and slope estimates which are in fact 'essentially unbiased'. In the proposed method, stimulus placements are included at intensities so high that it can be reasonably assumed that an error made there could only have been due to a lapse (let's call these asymptotic performance intensities). Data so obtained may be fit in (at least) three ways: (1) as discussed by W&H. That is, the model fitted corresponds to the standard PF equation found in e.g., W&H (nAPLE: non-Asymptotic Performance Lapse Estimation); (2) Identically to (1), except that the probability correct at the asymptotic intensity is modeled to equal 1 - lambda (i.e., errors there are attributed exclusively to lapses) (jAPLE: joint APLE); (3) lapse rate is estimated solely from performance at asymptotic intensity, observations made at other placements are used to estimate threshold and slope while fixing the lapse rate at the value estimated at the asymptotic level (iAPLE: isolated APLE). The Figure shows median threshold and slope estimates for four conditions. From left to right: (1) original placements used by W&H, fitted nAPLE, (2) placements used by W&H but modified such that the highest stimulus intensity was moved to a near-asymptotic level (F = 0.9999), fitted nAPLE (3) same placement as in (2) but fitted jAPLE, (4) same placement as in (2) but fitted iAPLE. Click here to download paper which explains things in more detail.
The Psychometric Function (PF) relates some behavioral measure (e.g., proportion correct detection) to some task characteristic (e.g., stimulus intensity). Typically of interest is the 'threshold' stimulus intensity. The threshold is usually defined as that stimulus intensity at which observers reach a specific level of performance. Some suggest that, in order to obtain a threshold estimate which is as unbiased as possible, we should allow the upper asymptote of the PF or 'lapse rate' to vary during function fitting. In their highly influential paper, Wichmann and Hill (2001) claim that allowing the lapse rate to vary results in threshold and slope estimates which are 'essentially unbiased', seemingly irrespective of what stimulus placement regimen is used. I have attempted to replicate W&H's results, but was unsuccesful. Instead, I obtained systematic and significant biases in both thresholds and slopes (see Figure, click on it to view a larger version). I propose an alternative fitting scheme which does lead to threshold and slope estimates which are in fact 'essentially unbiased'. In the proposed method, stimulus placements are included at intensities so high that it can be reasonably assumed that an error made there could only have been due to a lapse (let's call these asymptotic performance intensities). Data so obtained may be fit in (at least) three ways: (1) as discussed by W&H. That is, the model fitted corresponds to the standard PF equation found in e.g., W&H (nAPLE: non-Asymptotic Performance Lapse Estimation); (2) Identically to (1), except that the probability correct at the asymptotic intensity is modeled to equal 1 - lambda (i.e., errors there are attributed exclusively to lapses) (jAPLE: joint APLE); (3) lapse rate is estimated solely from performance at asymptotic intensity, observations made at other placements are used to estimate threshold and slope while fixing the lapse rate at the value estimated at the asymptotic level (iAPLE: isolated APLE). The Figure shows median threshold and slope estimates for four conditions. From left to right: (1) original placements used by W&H, fitted nAPLE, (2) placements used by W&H but modified such that the highest stimulus intensity was moved to a near-asymptotic level (F = 0.9999), fitted nAPLE (3) same placement as in (2) but fitted jAPLE, (4) same placement as in (2) but fitted iAPLE. Click here to download paper which explains things in more detail.
Palamedes toolbox
Concepts borrowed from the General Linear Model can be applied to the fitting of psychometric functions (PFs) and testing of research hypotheses. The Palamedes toolbox (Prins & Kingdom, 2009) implements these concepts into routines which allow the user to fit multiple PFs simultaneously to several datasets (arising for example, from different conditions in an experiment). The user is given considerable flexibility in defining models. A model might specify for example that the guess rate equals 0.5, that the thresholds in the different conditions vary as a linear function of some IV (e.g., adaptation duration), that the slopes are equal between conditions and that the lapse rate equals 0.02. Users may compare statistically any two such custom models as long as one of the models is nested under the other. However, such comparisons are valid only insofar as the assumptions that the simpler of the two model makes are met. What if these assumptions are not met? I am addressing this question by running simulations.
It is known that observers improve their performance in texture segmentation with practice. The mechanism by which this improvement occurs, however, is not known. We are investigating the possibility that perceptual learning of texture segmentation occurs by perceptual template retuning at the level of the first-order filters which would serve to exclude information in irrelevant spatial frequency/orientation channels.
Features of motions tokens (e.g., planarity, depth, color, size) other than their retinal location influence which solution to the correspondence problem in apparent motion is generated. This is generally taken to mean that either the solution to the correspondence problem is generated at a relatively high level of visual processing or that such token features may in fact be fundamental visual properties that are available at a relatively early stage of visual processing. However, effects of motion token characteristics other than their retinal position are found only when the retinal positions are in a relatively narrow range where the visual system is relatively indecisive based on retinal position alone (such as shown here). And even then, the effect is small (chances are that you see vertical motion above which compromises the chromatic integrity of the tokens). Also, I have shown that the effects of features other than the location of tokens in the retinal image exert their influence relatively slow. This suggests that correspondence matches between tokens are assigned by a mechanism that acts on retinal location. Only when no solution can be generated fast may a slower, attentive conscious process sway the solution based on whatever the observer feels would make a good match (researchers have shown effects of color, spatial frequency, depth, co-planarity, and even intention by experimenter's instruction).
Features of motions tokens (e.g., planarity, depth, color, size) other than their retinal location influence which solution to the correspondence problem in apparent motion is generated. This is generally taken to mean that either the solution to the correspondence problem is generated at a relatively high level of visual processing or that such token features may in fact be fundamental visual properties that are available at a relatively early stage of visual processing. However, effects of motion token characteristics other than their retinal position are found only when the retinal positions are in a relatively narrow range where the visual system is relatively indecisive based on retinal position alone (such as shown here). And even then, the effect is small (chances are that you see vertical motion above which compromises the chromatic integrity of the tokens). Also, I have shown that the effects of features other than the location of tokens in the retinal image exert their influence relatively slow. This suggests that correspondence matches between tokens are assigned by a mechanism that acts on retinal location. Only when no solution can be generated fast may a slower, attentive conscious process sway the solution based on whatever the observer feels would make a good match (researchers have shown effects of color, spatial frequency, depth, co-planarity, and even intention by experimenter's instruction).
The coding of curvature in contours plays an important role in object recognition. Curvature may be coded by reference to changes in the local orientation of the contour or by changes in the local position of the contour. We have shown that at least for our stimuli, curvature detection is based on the local position, not orientation, of the contour.
Many surfaces are naturally textured. Modulations of the characteristics of such textures (such as changes in local orientation, spatial frequency, contrast, etc.) across visual space give us important information about the shape of the textured object or surface. Much is known about the mechanisms which extract local characteristics of the visual stimulus, such as orientation, spatial frequency, motion, etc. Much less, however, is known about how these local characteristics are combined to give rise to the perception of textured surfaces and how
Nick Prins
Research
Texture Perception
Perceptual Learning
Motion Perception
Contour Perception
information regarding the shape of these surfaces is extracted.
Psychology
Ole Miss
Nick Prins
order filters which would serve to exclude information in irrelevant spatial frequency/orientation channels.
The Psychometric Function and the Lapse Rate
Statistical Model Comparisons