Plots a standard error estimate of thetahat (slope over intercept) over a range of possible theta0 values in order to investigate robustness of the the initial theta0 guess.

Usage

err_vs_theta0_plot_for_homo_design(
  n,
  xmin,
  xmax,
  theta,
  theta0_min,
  theta0_max,
  theta0 = NULL,
  beta0 = 1,
  sigma = 1,
  RES = 500,
  Nsim = 5000,
  error_est = function(est) {
quantile(est, 0.99) - quantile(est, 0.01)
 },
  theta_logged = TRUE,
  error_pct = TRUE,
  plot_rhos = FALSE,
  ...
)

Arguments

n: The number of experimental runs.
xmin: The minimum value of the independent variable.
xmax: The maximum value of the independent variable.
theta: The putative true value. This is used to see how much efficiency given up by designing it for theta0.
theta0_min: Simulating over different guesses of theta0, this is the minimum guess.
theta0_max: Simulating over different guesses of theta0, this is the maximum guess.
theta0: The guess used to construct the experimental design. Specify only if you wish to see this value plotted. Default is NULL.
beta0: A guess to be used for the intercept. Defaults to 1.
sigma: A guess to be used for the homoskedastic variance of the measurement errors. If known accurately, then the standard errors (i.e. the y-axis on the plot) will be accurate. Otherwise, the standard errors are useful only when compared to each other in a relative sense. Defaults to 1.
RES: The number of points on the x-axis to simulate. Higher numbers will give smoother results. Default is 20.
Nsim: The number of models to be simulated for estimating the standard error at each value on the x-axis. Default is 1000.
error_est: The error metric for the estimates. The sample standard deviation (i.e. sd) is unstable at low sample sizes. The default is the 90 percentile minus the 10 percentile.
theta_logged: Should the values of theta be logged? Default is TRUE.
error_pct: Plot error as a percentage increase from minimum. Default is TRUE.
plot_rhos: Plot an additional graph of rho by theta0. Default is FALSE.
...: Additional arguments passed to the plot function.

Value

A list with original parameters as well as data from the simulation

Author

Adam Kapelner

Examples

# \donttest{
xmin = 5 / 15
xmax = 19 / 1
n = 10
theta0 = 0.053
plot_info = err_vs_theta0_plot_for_homo_design(
  n, xmin, xmax, theta0, theta0_min = 0.001, theta0_max = 1
)

# }