Yes, and yet, including the bend is arguably a better model since we know the bend will come. It’s hard to get the details of models right, we shouldn’t let that be a reason not to get their basic shape right.
Fair enough. If nothing else, it’s best to state where you think the min value, max value, and midpoint are, and ideally put error bars around those.
Or, at least, you can state outright you think the midpoint and max are far enough away as to be irrelevant distractions to some particular practical purpose. Or that you expect other factors to intervene and change the trend long before the later parts of the sigmoid shape become relevant.
To add: It is in principle very easy for people to make equivalent prediction errors in either direction about when a particular exponential will level off, and to be wrong by many orders of magnitude. In practice, I usually encounter a vocal minority who happily ignores the fact that the sigmoid even exists, and a larger group who thinks that leveling off must be imminent and the trend can possibly continue much longer. The cynic in me thinks the former group tends to start getting believed just in time to be proven wrong, while the latter group misses out on a lot of opportunities but then helps ensure the leveling off has less catastrophic consequences when it happens.
I’m curious: was there a particular (set of) sigmoid(s) you had in mind when writing this post? And particular opinions about them you haven’t seen reflected in discussions?
Most of the times I’ve used sigmoid in my own modeling/forecasting have been about adoption and penetration of new technologies. Often the width of the sigmoid (say the time to get from 1% to 99% of the way from min to max) is relatively easy to approximate, driven by forces like “how incumbent institutions are governed” (yes, this is critical even for most extremely disruptive innovations). The midpoint and maximum are much harder to anticipate.
In practice, I usually encounter a vocal minority who happily ignores the fact that the sigmoid even exists, and a larger group who thinks that leveling off must be imminent and the trend can possibly continue much longer.
I suspect that most people see what they want to see in models, rather than actually evaluating the models.
I’m curious: was there a particular (set of) sigmoid(s) you had in mind when writing this post? And particular opinions about them you haven’t seen reflected in discussions?
No. I just see exponential models literally ever week and they disappointment me because they are leaving out half the model without even a nod to the fact they are doing this. It generally feels like the authors of models are failing to even consider the possibility that the growth of something will end.
Yes, and yet, including the bend is arguably a better model since we know the bend will come. It’s hard to get the details of models right, we shouldn’t let that be a reason not to get their basic shape right.
Fair enough. If nothing else, it’s best to state where you think the min value, max value, and midpoint are, and ideally put error bars around those.
Or, at least, you can state outright you think the midpoint and max are far enough away as to be irrelevant distractions to some particular practical purpose. Or that you expect other factors to intervene and change the trend long before the later parts of the sigmoid shape become relevant.
To add: It is in principle very easy for people to make equivalent prediction errors in either direction about when a particular exponential will level off, and to be wrong by many orders of magnitude. In practice, I usually encounter a vocal minority who happily ignores the fact that the sigmoid even exists, and a larger group who thinks that leveling off must be imminent and the trend can possibly continue much longer. The cynic in me thinks the former group tends to start getting believed just in time to be proven wrong, while the latter group misses out on a lot of opportunities but then helps ensure the leveling off has less catastrophic consequences when it happens.
I’m curious: was there a particular (set of) sigmoid(s) you had in mind when writing this post? And particular opinions about them you haven’t seen reflected in discussions?
Most of the times I’ve used sigmoid in my own modeling/forecasting have been about adoption and penetration of new technologies. Often the width of the sigmoid (say the time to get from 1% to 99% of the way from min to max) is relatively easy to approximate, driven by forces like “how incumbent institutions are governed” (yes, this is critical even for most extremely disruptive innovations). The midpoint and maximum are much harder to anticipate.
I suspect that most people see what they want to see in models, rather than actually evaluating the models.
No. I just see exponential models literally ever week and they disappointment me because they are leaving out half the model without even a nod to the fact they are doing this. It generally feels like the authors of models are failing to even consider the possibility that the growth of something will end.