I have a dataset of monthly ridership figures by transit route from 2007 to 2015. I am analyzing this data in R. When I go to predict on a new dataset with step increases in trips (ie 1,2,3,etc.) using any PLM, GLM, NLMER or GEE/GENLIM analysis my ridership predictions all increase linearly or exponentially.
I understand why, but am looking to find an alternate method where the ridership increases on a logistic scale. Because I am dealing with count data, I could transform the data to make all ridership values between 0 and 1. However any predicted cases where there is a large increase in this trips variable past the largest value in my dataset would see an extremely small change in ridership.
Is there a logistic approach out there that can be applied to count data or is there a way to allow that the maximum could be higher (ie delaying the decreasing rate of ridership given higher values of trips (for example))?