I found that currently the form of psychometric function assumes that the proportion correct lies between 0.5-1 given the range of stimulus level, but how to fit a psychometric function when the subject's performance never goes to 1 (and it is not because of lapse)?
An example of how this situation can happen: suppose I want to study how stimulus presentation time affect a small target's visibility in a given peripheral visual field location by a 2AFC task. The target's feature is fixed throughout the experiment. I can imagine that with longer stimulus presentation time (like 1 ms vs. 200 ms), subject can make more correct responses, but because of the limit of peripheral vision, the correct response rate can never go to 100% even if you present the stimulus for a very long time. How can I fit a psychometric function (proportion correct ~ stimulus presentation time) to data like this?