# Hyperbolic fit with nls ```r hyperbolic_fit(value, delay, initial_guess, max_iter = 1e+05, scale_offset = 0) ``` ## Arguments - `value`: A numeric vector of the subjective values (indifference points) - `delay`: A numeric vector of the delays used - `initial_guess`: A numeric value providing an initial start for k - `max_iter`: Positive integer with maximum number of iterations - `scale_offset`: A constant to be added if the residuals are close to 0. This is to avoid division by 0, which is know to cause problems of convergence. ## Returns An object of class nls ## Examples ```r # Simulated data with k = 0.5 data("hyp_data") delay <- hyp_data$delay sv <- hyp_data$sv real_k <- hyp_data$real_k model_hyp <- hyperbolic_fit(sv, delay, initial_guess = 0.01) summary(model_hyp) k_est <- coef(model_hyp) k_est # plot real and estimated sv delay_real <- seq(0, max(delay), len = 100) # first, simulate how the data should look with the real k real_sv <- eq_hyp(real_k, delay_real) # simulate estimated fitting line est_sv <- eq_hyp(k_est, delay_real) plot( delay, sv, pch = 21, col = 1, bg = 8, xlab = "Delay", ylab = "Subjective value" ) lines( delay_real, est_sv, col = "red", lwd = 2 ) # real data lines( delay_real, real_sv, type = "l", col = "blue", lwd = 2 ) legend( "topright", legend = c("data", "real", "fit"), text.col = "white", pch = c(21, NA, NA), col = c(1, NA, NA), pt.bg = c(8, NA, NA), bty = "n" ) legend( "topright", legend = c("data", "real", "fit"), pch = c(NA, NA, NA), lty = c(NA, 1, 1), col = c(NA, "blue", "red"), bty = "n" ) # Now an example with real data data("DD_data") # first, fit a linear model lineal_m <- lm(norm_sv ~ Delay, data = DD_data) # hyperbolic model hyp_m <- hyperbolic_fit(DD_data$norm_sv, delay = DD_data$Delay, 0.1) # exponential model exp_m <- exp_fit(DD_data$norm_sv, delay = DD_data$Delay, 0.1) AIC(lineal_m, hyp_m, exp_m) # compare visually k_hyp <- coef(hyp_m) k_exp <- coef(exp_m) k_lin <- coef(lineal_m) delay_vec <- seq(0, max(DD_data$Delay), len = 200) plot( DD_data$Delay, DD_data$norm_sv, ylim = c(0, 1), pch = 21, ylab = "SV", xlab = "Delay", bg = "orange", col = "black" ) lines( delay_vec, eq_hyp(k = k_hyp, delay_vec), col = "green4", lwd = 2 ) lines( delay_vec, exp(-k_exp * delay_vec), col = "steelblue", lwd = 2 ) abline(lineal_m, lty = 2, lwd = 2) legend( "topright", legend = c("data", "exp fit", "hyp fit", "linear fit"), text.col = "white", pch = c(21, NA, NA, NA), col = c(1, NA, NA, NA), pt.bg = c("orange", NA, NA, NA), bty = "n" ) legend( "topright", legend = c("data", "exp fit", "hyp fit", "linear fit"), pch = c(NA, NA, NA, NA), lty = c(NA, 1, 1, 2), col = c(NA, "steelblue", "green4", 1), bty = "n" ) # plot AIC values aic_val <- AIC(lineal_m, hyp_m, exp_m) |> round(2) leg <- sprintf(paste(rownames(aic_val), "= %s", sep = " "), aic_val$AIC) legend( "bottomleft", title = "AIC\n(the smaller, the better)", legend = leg, bty = "n" ) ```

hyperbolic_fit function