Why fitting a logistic is nearly impossible from early data
8 hours ago
- Nothing grows exponentially forever; exponential curves often turn into S-curves like logistic curves.
- Data from only the left side of a logistic curve cannot predict the limiting value accurately due to sensitivity to errors.
- Data from both sides of the inflection point allows good prediction of the asymptotic value.
- Fitting a logistic curve to three evenly spaced time points has a closed-form solution for the limiting value L.
- The expression y₁² − y₀ y₂ in the derivatives becomes near zero when data is from the exponential tail, making L extremely sensitive to data changes.
- A small change in y values from the left tail can cause the forecasted L to vary from 1 to infinity.