boot.resid.quad.plateau: Quadratic plateau model estimation by bootstrapping residuals

In FertBoot: Fertilizer Response Curve Analysis by Bootstrapping Residuals

Description

boot.resid.quad.plateau is the core function to implement bootstrapping residuals on quadratic plateau models, which assumes y = (a + b * x + c *x^2) * (x <= -0.5*b/c) + (a + -b^2/(4 * c)) * (x > -0.5 * b/c). Note that this function may take minutes up to days. Parallel computing may be necessary. We suggest users start with a smaller B and moderate n.start to see if the bootstrap models can converge. In general, increasing n.start and plus_minus may help with ease of convergence. For rigorous statistical inference, B should be on the order of a thousand.

Usage

boot.resid.quad.plateau(
  mod,
  data,
  x.range = data.frame(x = seq(0, 280, by = 40)),
  B = 100 - 1,
  plus_minus = 100,
  n.start = 5000,
  print.progress = TRUE
)

Arguments

mod	a full model list, probably from f.quad.plateau()
data	data frame with two columns (x and y)
x.range	vector of data.frame with one column for range of N rate of interested for prediction interval
B	bootstrap sample size
plus_minus	radius of random initial values (default: 100)
n.start	total number of initial points considered (default: 1000)
print.progress	logical flag whether printing progress

Value

boot.resid.quad.plateau returns a list of two elements: result: matrix with B rows and columns containing bootstrap sample for parameter (a,b,c), optimal N and yield (max_x, max_y), log-likelihood (logLik) and N values of interest; x.range: range of x considered for prediction interval (same as x.range in vector form)

Examples

set.seed(1)
x <- rep(1:300, each=5)
a <- 8; b <- 0.05; c <- -1e-4
y <- (a + b * x + c *x^2) * (x <= -0.5*b/c) + (a + -b^2/(4 * c)) * (x > -0.5 * b/c) +
    rnorm(length(x), sd=0.1)
d <- cbind(x,y)

ans <- f.quad.plateau(d, start=list(a = 7, b = 0.02, c = 1e-5),
    plus_minus=10, n.start=10, msg=FALSE)


boot.resid.quad.plateau(ans, d, x.range=seq(0,280,by=40),
    B=1e1-1, plus_minus = 1e2, n.start=1000, print.progress=TRUE) # use larger B for inference

FertBoot documentation built on Feb. 20, 2021, 1:06 a.m.