Highlight median bootstrap output confidence interval in ggplot2

Question

I have a dataframe df (see below)

 dput(df) structure(list(x = c(49, 50, 51, 52, 53, 54, 55, 56, 1, 2, 3, 4, 5, 14, 15, 16, 17, 2, 3, 4, 5, 6, 10, 11, 3, 30, 64, 66, 67, 68, 69, 34, 35, 37, 39, 2, 17, 18, 99, 100, 102, 103, 67, 70, 72), y = c(2268.14043972082, 2147.62290922552, 2269.1387550775, 2247.31983098201, 1903.39138268307, 2174.78291538358, 2359.51909126411, 2488.39004804939, 212.851575751527, 461.398994384333, 567.150629704352, 781.775113821961, 918.303706148872, 1107.37695799186, 1160.80594193377, 1412.61328924168, 1689.48879626486, 260.737164468854, 306.72700499362, 283.410379620422, 366.813913489692, 387.570173754128, 388.602676983443, 477.858510450125, 128.198042456082, 535.519377609133, 1028.8780498564, 1098.54431357711, 1265.26965941035, 1129.58344809909, 820.922447928053, 749.343583476846, 779.678206156474, 646.575242339517, 733.953282899613, 461.156280127354, 906.813018662913, 798.186995701282, 831.365377249207, 764.519073183124, 672.076289062505, 669.879217186302, 1341.47673353751, 1401.44881976186, 1640.27575962036)), .Names = c("x", "y"), row.names = c(NA, -45L), class = "data.frame") 

I created non-linear regression (nls) based on my dataset.

 nls1 <- nls(y~A*(x^B)*(exp(k*x)), data = df, start = list(A = 1000, B = 0.170, k = -0.00295), algorithm = "port") 

Then I calculated the bootstrap for this function to get several sets of parameters (A, B and k).

 library(nlstools) Boo <- nlsBoot(nls1, niter = 200) 

Now I want to build the median curve, as well as the upper and lower confidence interval curves calculated from the bootstrap object, in one ggplot2. The parameters (A, B and K) of each curve are contained in Boo_Gamma$bootCI . Can anyone help me with this? Thank you in advance.

Answer 1

AFAIK, the nlstools package returns only loaded parameter estimates, not predicted values ​​...

Therefore, this is a quick solution, manually using estimates of the loaded parameters to calculate forecasts, and then recounts the statistics from the predictions, since the model here is non-linear. This is not the most elegant, but he must do it :)

 # Matrix with the bootstrapped parameter estimates Theta_mat <- Boo$coefboot # Model fun <- function(x, theta) theta["A"] * (x ^ theta["B"]) * (exp(theta["k"] * x)) # Points where to evaluate the model x_eval <- seq(min(df$x), max(df$x), length.out = 100) # Matrix with the predictions Pred_mat <- apply(Theta_mat, 1, function(theta) fun(x_eval, theta)) # Pack the estimates for plotting Estims_plot <- cbind( x = x_eval, as.data.frame(t(apply(Pred_mat, 1, function(y_est) c( median_est = median(y_est), ci_lower_est = quantile(y_est, probs = 0.025, names = FALSE), ci_upper_est = quantile(y_est, probs = 0.975, names = FALSE) )))) ) library(ggplot2) ggplot(data = Estims_plot, aes(x = x, y = median_est, ymin = ci_lower_est, ymax = ci_upper_est)) + geom_ribbon(alpha = 0.7, fill = "grey") + geom_line(size = rel(1.5), colour = "black") + geom_point(data = df, aes(x = x, y = y), size = rel(4), colour = "red", inherit.aes = FALSE) + theme_bw() + labs(title = "Bootstrap results\n", x = "x", y = "y") ggsave("bootpstrap_results.pdf", height = 5, width = 9)