The beta model is defined as $$ f(d,\theta)=E_0+E_{max}B(\delta_1,\delta_2)(d/scal)^{\delta_1}(1-d/scal)^{\delta_2} $$ where $$B(\delta_1,\delta_2)=(\delta_1+\delta_2)^{\delta_1+\delta_2}/(\delta_1^{\delta_1} \delta_2^{\delta_2})$$
betaMod(dose, e0, eMax, delta1, delta2, scal)
Dose variable
Placebo effect
Maximum effect
delta1 parameter
delta2 parameter
Scale parameter (not estimated in the code)
Response value
The beta model is intended to capture non-monotone
dose-response relationships and is more flexible than the quadratic model.
The kernel of the beta model
function consists of the kernel of the density function of a beta
distribution on the interval [0,scal]. The parameter
scal is not estimated but needs to be set to a value
larger than the maximum dose via the argument scal
.
logistic
, sigEmax
,
linlog
, linear
, quadratic
,
emax
, exponential