sbpsi {scaleboot} | R Documentation |
sbpsi.poly
and sbpsi.sing
are psi functions to
specify a polynomial model and a singular model, respectively.
sbpsi.poly(beta,s=1,k=1,sp=-1,aux=NULL,check=FALSE) sbpsi.sing(beta,s=1,k=1,sp=-1,aux=NULL,check=FALSE) sbmodelnames(m=3,poly=m,sing=m)
beta |
numeric vector of parameters;
β_0=beta[1] , β_1=beta[2] ,...
β_{m-1}=beta[m] , where m is the number of
parameters.
|
s |
σ_0^2. |
k |
numeric to specify the order of derivatives. |
sp |
σ_p^2. |
aux |
auxiliary parameter. Currently, not used. |
check |
logical for boundary check. |
m |
numeric to specify the maximum number of parameters. |
poly |
maximum number of parameters in poly models. |
sing |
maximum number of parameters in sing models. |
For k=1, sbpsi
functions return their psi function
values at σ^2=σ_0^2. Currently, two types of
sbpsi
functions are
implemented. sbpsi.poly
defines the polynomial model;
psi(σ^2 | β) = sum_{j=0}^{m-1} β_j σ^{2j}.
sbpsi.sing
defines the singular model;
psi(σ^2 | β) = β_0 + sum_{j=1}^{m-2} β_j σ^{2j} (1+a)/(1+a σ),
where a=β_{m-1}/(1-β_{m-1}) so that 0<= a <= infty for 0<=β_{m-1}<=1.
For k>1, sbpsi
functions return values extrapolated at
σ^2=σ_p^2 using derivatives up to order k-1
evaluated at σ^2=σ_0^2;
sum_{j=0}^{k-1} frac{(σ_p^2-σ_0^2)^j}{j!} frac{d^j psi(x|β)}{d x^j}Bigr|_{σ_0^2},
which reduces to psi(σ_0^2|β) for k=1.
sbpsi.poly
and sbpsi.sing
are examples of a sbpsi
function; users can develop their own sbpsi functions for better
model fitting by preparing sbpsi.xxx
and sbini.xxx
functions for model xxx
.
If check=FALSE, a sbpsi function returns
the psi function value or the extrapolation value.
If check=TRUE, a sbpsi function returns NULL when all
the elements of beta are included in the their valid
intervals. Otherwise, a sbpsi function returns a list with components
beta
for the parameter value being modified to be on a boundary
of the interval and mask
of a logical vector indicating which
elements are not on the boundary.
sbmodelnames
returns a character vector of model names.
Hidetoshi Shimodaira