I'm trying to make a model to fit a rotated sigmoidal curve in R but don't know where to start when looking for an appropriate equation for the model.
Some example data and the type of fit I'm getting at the moment are shown below:
library(tidyverse)#example datadf <- data.frame(x = c(50,54,56,55,58,64,91,148,345,722,1641,4320,4931,5224), y = c(1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192))# 4th order polynomial fittingmodel1 <- lm(y ~ poly(x,4, raw = TRUE), data = df)# inverse log non-linear model?model2 <- nls(y ~ I(1 / x * a) + b * x, data = df, start = list(a = 1, b = 1))# make some evenly spaced points for x and fit modelsmodel_df <- data.frame(logx = seq(1.7, 3.7, by=0.01)) %>% mutate(x = 10^logx)model_df$fit1 <- predict(model1, model_df) model_df$fit2 <- predict(model2, model_df) # plot on log axesggplot(df) + aes(x = x, y = y) + geom_point(size = 4) + geom_point(data = model_df, aes(x = x, y = fit1), colour = "red", size = 1) + geom_point(data = model_df, aes(x = x, y = fit2), colour = "blue", size = 1) + scale_x_log10() + scale_y_log10() 
Does anyone know any suitable way to fit a curve like this?