I'm looking for a phenomenon, preferably within social sciences/economy, with available datasets that follow a sigmoidal relationship. For example, a relationship could be between the amount of money earned and the money spent. I would be grateful for any pointers.
Steep sigmoidal input-output relationships are very common in biological systems (see the review by Steven Frank). The input in such a setting typically corresponds to the concentration of some chemical ligand, while the output is the concentration of another chemical downstream in a biochemical pathway that responds to the input. The relationship is also termed the dose response or, in engineering terms, the response characteristic. Biological systems (networks) that give steep sigmoidal responses to inputs are called "ultra-sensitive" and typically modelled with Hill equation where the Hill coefficient is greater than 1.
In principle, the sigmoidal relationship that I'm looking for, should exist between two variables, e.g. the duration of advertisement block on TV (x-axis) vs. the time to switch the channel (y-axis), etc. In the best case scenario such a relationship would be measured for a number of individuals. Therefore, I could have the entire "response characteristic" for an ensemble of, say, 100 people.
What I'm not looking for, however, is the temporal behaviour of phenomena, e.g. the accumulation of wealth in time that could also follow a saturation-type sigmoidal curve.
