sbpsi {scaleboot}R Documentation

Model Specification Functions

Description

sbpsi.poly and sbpsi.sing are psi functions to specify a polynomial model and a singular model, respectively.

Usage


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)

Arguments

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.

Details

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.

Value

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.

Author(s)

Hidetoshi Shimodaira

See Also

sbfit.


[Package scaleboot version 0.1-2 Index]