With Psykinematix, collected data may be fitted with psychometric functions immediately after each session in addition to fitting automatically performed by a method (Bayesian or of constant stimuli). The curving fitting procedure provided by Psykinematix is based on the Levenberg-Marquardt least squares minimization technique. To access the fitting capabilities, click on the "Plotter" icon in the toolbar to display the Plotter Panel (or press shift–⌘R) and select a graphable data set (last level in the results hierarchy).
A typical scenario is illustrated below where a method provides 2 graphable data sets: a "Performance" set that plots % correct as function of the dependent variable, which can be freely fitted, and a "Model/Fit" set that plots the same data but pre-fitted with the psychometric function that was indicated under the Method Panel (the resulting fitted parameters are those shown under the "Fitting" tab in the data table associated to the 1st level of the session results). The "Model/Fit" fitting cannot be modified, and the fitting of the "Performance" set should be used at the pilot stage to discover the most appropriate psychometric function or when the pre-specified function does not seem to fit the data anymore.
Two kinds of data can be fitted:
XY Datasets
Reaction Times
The fitting of monotonic XY datasets, typically subject's performance (% correct) as a function of some stimuli parameters (dependent variable), can be customized by selecting the "XY" tab: the psychometric function, its direction (either increasing or decreasing), miss rate, chance level and threshold criterion should be chosen appropriately to reflect the experimental constraints.
All these functions are cumulative distribution function (CDF) types of the form:
 |
for a monotonic increase |
 |
for a monotonic decrease |
where 
is the performance as a function of some stimulus parameter x,
is the chance level (eg: 50% in a 2AFC),
is the miss rate,
is the cumulative distribution function, with 
being the stimulus parameter, 
and 
are the sensitivity parameters that control the shape of the function.
| Weibull CDF |  |
| Logistic CDF |  |
Gaussian CDF |
 |
| Gumbel CDF |  |
Note that for the Weibull function, and are analogous to the threshold and slope respectively, while for all other functions they are analogous to the offset and spread respectively.
The threshold (t) and slope (s) for a specified probability level (p) (threshold criterion) of the psychometric functions are then defined as:
and
All of these functions can be used as models for the Method of Constant Stimuli or the Bayesian Method.
The graphical representation of the reaction times can be customized by selecting the "RT" tab: reaction times below a given level (anticipatory responses) and above a given level (late responses) can be filtered out, and the bin width can be set to any value between 10 and 100 ms. Post-stimulus RTs are included by default, but can be excluded from the histogram representation by unchecking the related check box.
The reaction time distribution can be fitted with a Weibull distribution using its probability density function:
where k > 0 is the shape parameter, λ > 0 is the scale parameter of the distribution, and is a translation parameter.
The mean and standard deviation of the Weibull distribution are given by:
Note that the accuracy of the fitting procedure depends on the bin width.