YEAB (version 1.0.6)

hyperbolic_fit: Hyperbolic fit with nls

Description

Hyperbolic fit with nls

Usage

hyperbolic_fit(value, delay, initial_guess, max_iter = 1e+05, scale_offset = 0)

Value

An object of class nls

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.

Examples

# 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"
)