Description Usage Arguments Details Value Note Author(s) References See Also Examples
Finds Locally Doptimal designs for MichaelisMenten model which is defined as E(y) = (ax)/(1+bx) or E(y) = (ax)/(b+x) or E(y) = "x/(a+bx) with Var(y) = σ^2, where a, b and σ are unknown parameters.
1 2 
a 
initial value for paremeter a. 
b 
initial value for paremeter b. 
form 
must be 
lb 
lower bound of design interval, must be greater than or equal to 0. 
ub 
upper bound of design interval. 
user.points 
(optional) vector of user design points which calculation of its Defficiency is aimed. Each element of 
user.weights 
(optional) vector of weights which its elements correspond to 
... 
(optional) additional parameters will be passed to function

prec 
(optional) a number, the maximal precision to be used for Defficiency calculation, in bite. Must be at least 2 (default 53), see 'Details'. 
n.restarts 
(optional optimization parameter) number of solver restarts required in optimization process (default 1), see 'Details'. 
n.sim 
(optional optimization parameter) number of random parameters to generate for every restart of solver in optimization process (default 1), see 'Details'. 
tol 
(optional optimization parameter) relative tolerance on feasibility and optimality in optimization process (default 1e8). 
rseed 
(optional optimization parameter) a seed to initiate the random number generator, else system time will be used. 
While Defficiency is NaN
, an increase in prec
can be beneficial to achieve a numeric value, however, it can slow down the calculation speed.
Values of n.restarts
and n.sim
should be chosen according to the length of design interval.
plot of derivative function, see 'Note'.
a list containing the following values:
points 
obtained design points 
weights 
corresponding weights to the obtained design points 
det.value 
value of Fisher information matrix determinant at the obtained design 
user.eff 
Defficeincy of user design, if 
To verify optimality of obtained design, derivate function (symmetry of Frechet derivative with respect to the xaxis) will be plotted on the design interval. Based on the equivalence theorem (Kiefer, 1974), a design is optimal if and only if its derivative function are equal or less than 0 on the design interval. The equality must be achieved just at the obtained points.
Ehsan Masoudi, Majid Sarmad and Hooshang Talebi
Masoudi, E., Sarmad, M. and Talebi, H. 2012, An Almost General Code in R to Find Optimal Design, In Proceedings of the 1st ISM International Statistical Conference 2012, 292297.
Dette, H., Melas, V.B., Wong, W.K. (2005). Optimal design for goodnessoffit of the MichaelisMenten enzyme kinetic function. Journal of the American Statistical Association, 100:13701381.
Kiefer, J. C. (1974), General equivalence theory for optimum designs (approximate theory). Ann. Statist., 2, 849879.
1 2 3 4 5 6 7 8 9  ldmm(a = 1, b = 2, form = 1, lb = 0, ub =3) # $points: 0.375 3.000
ldmm(a = 1, b = 2, form = 2, lb = 0, ub =3) # $points: 0.8571428 3.0000000
ldmm(a = 1, b = 2, form = 3, lb = 0, ub =3) # $points: 0.375 3.000
## Deffecincy computation:
ldmm(a = 1, b = 2, form = 3, lb = 0, ub =3, user.points = c(.5, 3, 2),
user.weights = rep(.33, 3)) # $user.eff: 0.83174

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