Fitting a catenary to data
In catenary: Fits a Catenary to Given Points

Simulate dataset

We simulate a dataset with x-points from a uniform (0,4) distribution, the y-points are from the function

$$ y_i = c_1 \cosh\left(\frac{x_i-c_2}{c_1}\right) + \lambda + \epsilon_i, $$ where $\epsilon_i \sim N(0,\sigma=0.1)$.

library(catenary)
library(tidyverse)

sim_data <- data_frame(x = runif(100,0,4))
sim_data  <- sim_data %>% 
  mutate(y = f(x, c1 = 1, c2 = 2, lambda = 3))
sim_data  <- sim_data %>% 
  mutate(y = y + rnorm(100,0,0.1))

sim_data %>% ggplot(aes(x,y)) + geom_point()

Fitting a catenary to the data

We fit the catenary with the

sim_data_cat <- fittedCatenary(sim_data$x, sim_data$y)
plot(sim_data_cat,fit='cat', envelope='cat')
show(sim_data_cat)

Get summary statistics of goodness of fit

Unfortunately R-square values are not appropriate for non-linear methods, which is how the catenary model is fitted to the data - see for example why-is-there-no-r-squared-for-nonlinear-regression. Instead I have added a new method gof() which will take a fitted catenary object and return the summary statistics like Akaike's information criterion and Bayesian information criterion, which can be used to assess model fit.