Reading on a paper on factor analysis and measurement invariance I find the description of some functions as 'ogival' functions. Example text introducing functions as ogival functions without characterizing their analytic form)

In Google I find it referenced mostly in papers from the '70s and '80s. Seems a term that fell out of fashion as I see only one mention of 'ogives' in this whole site. The Wikipedia page says it describes an empirical CDF, but from some of these plots and articles (e.g. this article from 1975, p.317) it seems that ogival curves are used to refer to any sigmoidal function? Where is it defined?

  • $\begingroup$ In some circumstances "ogive" might indeed refer to any sigmoidal function but typically in statistics it implies a cdf (and often, one without jump discontinuities). You can generally figure out which was intended from context. $\endgroup$
    – Glen_b
    Nov 8 '20 at 22:22
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    $\begingroup$ While it's very much not my area of expertise, I believe the discussion there closely relates to the "normal ogive model" in the section on item bias (p538 onward) and presumably does relate specifically to a cdf. $\endgroup$
    – Glen_b
    Nov 8 '20 at 22:44
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    $\begingroup$ The general definition (see en.wikipedia.org/wiki/Ogive_(statistics)) suggests "ogival" is meant in the same sense many machine learning practitioners today use "sigmoidal." $\endgroup$
    – whuber
    Nov 9 '20 at 14:44
  • $\begingroup$ Oh well, I guess there will not be any more information or original sources than the ones already mentioned. Thanks for the in-context clarification @Glen_b. $\endgroup$
    – Kuku
    Nov 9 '20 at 21:56
  • $\begingroup$ If you're seeking references to the use of the word "ogive" in statstics there's a fair number n of them, going back a fair way, but I don't think it makes the intended meaning in your paper any clearer than you'll get from looking at the paper (and other related references to that specific application). $\endgroup$
    – Glen_b
    Nov 10 '20 at 23:11

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