Create an optimal design for measuring the slope divided by the intercept

Usage

oed_for_slope_over_intercept(
  n,
  xmin,
  xmax,
  theta0,
  f_hetero = NULL,
  MaxIter = 6000,
  MaxFunEvals = 6000,
  TolFun = 1e-06,
  NUM_RAND_STARTS = 50
)

Arguments

n: The number of experimental runs.
xmin: The minimum value of the independent variable.
xmax: The maximum value of the independent variable.
theta0: The guess of the true value of the slope / intercept.
f_hetero: Specification of heteroskedasticity: the h(x) which relates the value of the independent variable to the variance in the response around the line at that place or the proportional variance at that point. If NULL, homoskedasticity is assumed (this is the default behavior).
MaxIter: For the heteroskedastic design, a Nelder-Mead search is used (via the function fminbnd). This is the MaxIter value for the search. Default is 6000. Lower if n is high.
MaxFunEvals: For the heteroskedastic design, a Nelder-Mead search is used (via the function fminbnd). This is the MaxFunEvals value for the search. Default is 6000. Lower if n is high.
TolFun: For the heteroskedastic design, a Nelder-Mead search is used (via the function fminbnd). This is the TolFun value for the search. Default is 1e-6. Increase for faster execution.
NUM_RAND_STARTS: For the heteroskedastic design, a Nelder-Mead search is used (via the function fminbnd). The Nelder-Mead search must be given a starting location. Our implementation uses many starting locations. This parameter controls the number of additional random starting locations in the space [xmin, xmax]. Default is 50.

Value

An n-vector of x-values which specifies the optimal design

Author

Adam Kapelner

Examples

xmin = 5 / 15
xmax = 19 / 1
n = 10
theta0 = 0.053
opt_homo_design = oed_for_slope_over_intercept(n, xmin, xmax, theta0)
table(opt_homo_design)
#> opt_homo_design
#> 0.333333333333333                19 
#>                 7                 3