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.

Example of sigmoidal function

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.

  • hi, there are many easy to use, public use microdata sets with both income and expenditure values on asdfree.com Commented Nov 11, 2014 at 15:37
  • @AnthonyDamico thanks! Although I haven't found the right dataset yet, it does look promising.
    – mattek
    Commented Nov 11, 2014 at 21:35
  • datasets that i'm sure have income and some sort of spending include ce, cps, meps, sipp.. but each survey has strengths and weaknesses in collection of both spending an income Commented Nov 12, 2014 at 6:29

2 Answers 2


In technology forecasting, the market penetration of a new technology often follows a sigmoidal curve. Hence, with one variable being the time, the other variable being the market share of

  • ebooks
  • LED
  • organic food

could form examples. There is a classic paper by Fisher and Pry on this, however behind a paywall.

  • OK, this saturation type of dynamics might be interesting too. However, I wouldn't be too keen on analysing time-dependent phenomena. I edited the question to clarify this.
    – mattek
    Commented Nov 12, 2014 at 20:54

There is a quasi-sigmoidal relationship between time and the usage share of Netscape Classic (green):

Layout engine usage share

Data is available (public domain license) as CSV at https://commons.wikimedia.org/wiki/File:Layout_engine_usage_share-2009-01-07.svg, it is very rough though.

  • As in the comment above and the edit of my original question, I'm rather looking for sigmoids of two variables other than saturation-type of temporal dynamics. Thanks anyway!
    – mattek
    Commented Nov 12, 2014 at 20:57

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