Nonlinear optimization to fit the fitness-fatigue model

fitness-fatigue-optim.R

# Recover parameters using non-linear regression
rss <- function(theta) {
  int  <- theta[1] # performance baseline
  k1   <- theta[2] # fitness weight
  k2   <- theta[3] # fatigue weight
  tau1 <- theta[4] # fitness decay
  tau2 <- theta[5] # fatigue decay

  fitness <- sapply(1:nrow(train_df),
                    function(n) convolve_training(train_df$w, n, tau1))

  fatigue <- sapply(1:nrow(train_df),
                    function(n) convolve_training(train_df$w, n, tau2))

  perf_hat <- int + k1 * fitness - k2 * fatigue
  return(sum((train_df$perf - perf_hat) ^ 2))
}

optim_results <- optim(c(400, .05, .15, 20, 5), rss, method = "BFGS",
                       hessian = TRUE, control = list(maxit = 1000))