Nothing
############################
# Exponential growth model
############################
# Verifying optimailty of a locally D-optimal design
senslocally(formula = ~a + exp(-b*x),
predvars = "x", parvars = c("a", "b"),
x = c(.1, 1), w = c(.5, .5),
lx = 0, ux = 1, inipars = c(1, 10))
##############################
# A model with two predictors
##############################
x0 <- c(30, 3.861406, 30, 4.600633, 0, 0, 5.111376, 4.168798)
w0 <- rep(.25, 4)
senslocally(formula = ~ V*S/(Km * (1 + I/Kic)+ S * (1 + I/Kiu)),
predvars = c("S", "I"),
parvars = c("V", "Km", "Kic", "Kiu"),
x = x0, w = w0,
lx = c(0, 0), ux = c(30, 60),
inipars = c(1.5, 5.2, 3.4, 5.6))
\dontrun{
# using package rgl for 3d plot:
res<- senslocally(formula = ~ V*S/(Km * (1 + I/Kic)+ S * (1 + I/Kiu)),
predvars = c("S", "I"),
parvars = c("V", "Km", "Kic", "Kiu"),
x = x0, w = w0,
lx = c(0, 0), ux = c(30, 60),
inipars = c(1.5, 5.2, 3.4, 5.6),
plot_3d = "rgl")
}
###################################
# user-defined optimality criterion
##################################
# When the model is defined by the formula interface
# Checking the A-optimality for the 2PL model.
# the criterion function must have argument x, w fimfunc and the parameters defined in 'parvars'.
# use 'fimfunc' as a function of the design points x, design weights w and
# the 'parvars' parameters whenever needed.
Aopt <-function(x, w, a, b, fimfunc){
sum(diag(solve(fimfunc(x = x, w = w, a = a, b = b))))
}
## the sensitivtiy function
# xi_x is a design that put all its mass on x in the definition of the sensitivity function
# x is a vector of design points
Aopt_sens <- function(xi_x, x, w, a, b, fimfunc){
fim <- fimfunc(x = x, w = w, a = a, b = b)
M_inv <- solve(fim)
M_x <- fimfunc(x = xi_x, w = 1, a = a, b = b)
sum(diag(M_inv %*% M_x %*% M_inv)) - sum(diag(M_inv))
}
senslocally(formula = ~1/(1 + exp(-b * (x-a))), predvars = "x",
parvars = c("a", "b"), family = "binomial",
inipars = c(0, 1.5),
crtfunc = Aopt,
lx = -2, ux = 2,
sensfunc = Aopt_sens,
x = c(-1, 1), w = c(.5, .5))
# not optimal
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