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,lambda=NULL,aux=NULL,check=FALSE)

sbpsi.sing(beta,s=1,k=1,sp=-1,lambda=NULL,aux=NULL,check=FALSE)

sbpsi.sphe(beta,s=1,k=1,sp=-1,lambda=NULL,aux=NULL,check=FALSE)

sbpsi.generic(beta,s=1,k=1,sp=-1,lambda=NULL,aux=NULL,check=FALSE,zfun,eps=0.01)

sbmodelnames(m=1:3,one.sided=TRUE,two.sided=FALSE,rev.sided=FALSE,poly,sing,poa,pob,sia,sib,sphe)

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.
lambda a numeric of specifying the type of p-values; Bayesian (lambda=0) Frequentist (lambda=1).
aux auxiliary parameter. Currently not used.
check logical for boundary check.
zfun z-value function with (s,beta) as parameters.
eps delta for numerical computation of derivatives.
m numeric vector to specify the numbers of parameters.
one.sided logical to include poly and sing models.
two.sided logical to include poa and sia models.
rev.sided logical to include pob and sib models.
poly maximum number of parameters in poly models.
sing maximum number of parameters in sing models.
sphe maximum number of parameters in sphe models.
poa maximum number of parameters in poa models.
pob maximum number of parameters in pob models.
sia maximum number of parameters in sia models.
sib maximum number of parameters in sib models.

Details

For k=1, the sbpsi functions return their psi function values at σ^2=σ_0^2. Currently, four 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}

for m>=1. sbpsi.sing defines the singular model;

psi(σ^2 | β) = β_0 + sum_{j=1}^{m-2} frac{β_j σ^{2j}}{1 + β_{m-1}(σ-1)}

for m>=3 and 0<=β_{m-1}<=1. sbpsi.sphe defines the spherical model; currently the number of parameters must be $m=3$. sbpsi.generic is to calculate psi value and extrapolation from a given z-function.

For k>1, the 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;

q_k = 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. In the summary.scaleboot, the AU p-values are defined by p_k = 1-Phi(q_k) 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.foo and sbini.foo functions for model foo. 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, 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 0.3-2 Index]