ICAOD (version 0.9.2)

FIM_exp_2par: Fisher information matrix for the two-parameter exponential model.

Description

The mean of response variable is $$f(x, \bold{\theta}) = a + \exp(-bx)$$.

Usage

FIM_exp_2par(x, w, param)

Arguments

x

vector of design points.

w

vector of design weight. Its length must be equal to the length of x and sum(w) should be 1.

param

vector of model parameters \(\bold{\theta} = (a, b)\).

Value

Fisher information matrix.

Details

The Fisher information matrix does not depend on a. The locally D optimal design is independent of the nominal value of \(a\) and is equally supported at \(x = 0\) and \(x = 1/b\) only when \(x \in [0, 1]\). See "Examples".

References

Dette, H., & Neugebauer, H. M. (1997). Bayesian D-optimal designs for exponential regression models. Journal of Statistical Planning and Inference, 60(2), 331-349.

See Also

Other FIM: FIM_comp_inhibition, FIM_emax_3par, FIM_exp_3par, FIM_logisitic_1par, FIM_logistic_4par, FIM_logistic, FIM_loglin, FIM_michaelis, FIM_mixed_inhibition, FIM_noncomp_inhibition, FIM_power_logistic, FIM_uncomp_inhibition

Examples

# NOT RUN {
### finding the locally optimal design for different values for design interval
mica(fimfunc = "FIM_exp_2par", lx = 0, ux = 1, lp = c(1, 2), up = c(1, 2),
     iter = 100, k = 2, type = "locally", control = list(seed = 215))

mica(fimfunc = "FIM_exp_2par", lx = .0001, ux = 1, lp = c(1, 2), up = c(1, 2),
     iter = 100, k = 2, type = "locally", control = list(seed = 215))

mica(fimfunc = "FIM_exp_2par", lx = 0, ux = 10, lp = c(1, 2), up = c(1, 2),
     iter = 100, k = 2, type = "locally", control = list(seed = 215))

mica(fimfunc = "FIM_exp_2par", lx = .0001, ux = 10, lp = c(1, 2), up = c(1, 2),
     iter = 100, k = 2, type = "locally", control = list(seed = 215))

## it seems for design interval x = [x_l, x_u], when x_l > 0,
## the locally D-optimal design is a two-point equally weighted design
## with x1 = x_l, x2 = x_u

mica(fimfunc = "FIM_exp_2par", lx = .5, ux = 10, lp = c(1, 2), up = c(1, 2),
     iter = 100, k = 2, type = "locally", control = list(seed = 215))

mica(fimfunc = "FIM_exp_2par", lx = .0001, ux = 10, lp = c(1, 2), up = c(1, 2),
     iter = 100, k = 2, type = "locally", control = list(seed = 215))

mica(fimfunc = "FIM_exp_2par", lx = 1, ux = 10, lp = c(1, 2), up = c(1, 2),
        iter = 100, k = 2, type = "locally", control = list(seed = 215))


mica(fimfunc = "FIM_exp_2par", lx = 2, ux = 10, lp = c(1, 2), up = c(1, 2),
     iter = 100, k = 2, type = "locally", control = list(seed = 215))

mica(fimfunc = "FIM_exp_2par", lx = 3, ux = 9, lp = c(1, 2), up = c(1, 2),
     iter = 100, k = 2, type = "locally", control = list(seed = 215))

# }