summary.scaleboot {scaleboot}R Documentation

P-value Calculation for Multiscale Bootstrap

Description

summary method for class "scaleboot" and "scalebootv".

Usage


## S3 method for class 'scaleboot':
summary(object,models=names(object$fi),k=1:3,s=1,sp=-1,...)

## S3 method for class 'scalebootv':
summary(object,models=attr(object,"models"),k=1:3,...)

Arguments

object an object used to select a method.
models character vector of model names. If numeric, names(object$fi)[models] is used for each "scaleboot" object.
k numeric vector of k for calculating p-values.
s σ_0^2
sp σ_p^2
... further arguments passed to or from other methods.

Details

For each model, a class of approximately unbiased p-values, indexed by k=1,2,..., is calculaed. The p-values are named as k.1, k.2, ..., where k=1 (k.1) corresponds to the ordinary bootstrap probability, and k=2 (k.2) corresponds to the third-order accurate p-value of Shimodaira (2002). As k value increases, the bias of testing decreases, although the p-value becomes less stable numerically and the monotonicity of rejection regions becomes worse. Typically, k=3 provides a reasonable compromise. sbpval method is available to extract p-values from "summary.scaleboot" object.

The p-value is defined as

hatα_{k,σ_0} = 1 - Phi( 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} ),

where psi(σ^2|β) is the model specification function, σ_0^2 is the evaluation point for the Taylor series, and σ_p^2 is an additional parameter. Typically, we do not change the default values σ_0^2=1 and σ_p^2=-1.

The p-values are justified only for good fitting models. By default, the model which minimizes the AIC value is selected. We can modify the AIC value by sbaic function. We also diagnose the fitting by the plot method.

Value

summary.scaleboot returns an object of class "summary.scaleboot" inheriting from class "scaleboot". It is a list containing all the components of class "scaleboot" and the following components:

pv matrix of p-values of size length(models) * length(k) with elements hatα_{k,σ_0}.
pe matrix of standard errors of p-values.
best a list consisting of components model for the best fitting model name, aic for its AIC value, pv for a vector of p-values, and pe for a vector of standard errors.

Author(s)

Hidetoshi Shimodaira

See Also

sbfit, sbpsi, sbpval, sbaic.

Examples

data(mam15)
## For a single hypothesis
a <- mam15.relltest[["t4"]] # an object of class "scaleboot"
summary(a) # calculate and print p-values (k=1:3)
summary(a,k=1:4) # up to "k.4" p-value.

## For multiple hypotheses
b <- mam15.relltest[1:15] # an object of class "scalebootv"
summary(b) # calculate and print p-values (k=1:3)
summary(b,k=1:4) # up to "k.4" p-value.


[Package scaleboot version 0.1-2 Index]