Finds Locally D-optimal designs for Negative Binomial regression model which is defined as $E(y) = \lambda(x)$ with $Var(y) = \sigma^2\lambda(x)(1+(\lambda(x)/\theta))$, where $y ~ NB(\theta, \lambda(x))$, $\lambda(x) = a\exp(-bx)$ and $a$, $b$ and $\sigma$ are unknown parameters.
ldnbinom(a, b, theta, lb, ub, user.points = NULL, user.weights = NULL,
..., n.restarts = 1, n.sim = 1, tol = 1e-8, prec = 53, rseed = NULL)user.points must be within the design interval.user.points elements. The sum of weights should be $1$; otherwise they will be normalized.
curve.
user.design and user.weights are not NULL. NaN, an increase in the value of prec can be beneficial to achieve a numeric value, however, can slow down the calculation speed. Values of n.restarts and n.sim should be chosen according to the length of design interval.
Rodriguez-Torreblanca, C. Rodriguez-Diaz, J.M. (2007), Locally D- and c-optimal designs for Poisson and negative binomial regression models, Metrika, 66, 161-172.
Kiefer, J. C. 1974, General equivalence theory for optimum designs (approximate theory), Ann. Statist., 2, 849-879.
cfisher, cfderiv and eff.
ldnbinom(a = 2, b = 3, theta = 10, lb = -3, ub =3)
# $points: -3.0000000 -0.8115872
## D-effecincy computation:
ldnbinom(a = 2, b = 3, theta = 10, lb = -3, ub =3, user.points = c(2, -3),
user.weights = rep(.5, 2)) # $user.eff: 0.06099
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