summary.scaleboot {scaleboot} | R Documentation |
summary
method for class "scaleboot"
and "scalebootv"
.
## S3 method for class 'scaleboot': summary(object,models=names(object$fi),k=3,s=1,sp=-1, type=c("Frequentist","Bayesian"),...) ## S3 method for class 'scalebootv': summary(object,models=attr(object,"models"),k=3,type="Frequentist",...) ## S3 method for class 'summary.scaleboot': print(x,sort.by=c("aic","none"),verbose=FALSE,...) ## S3 method for class 'summary.scalebootv': print(x,select="average",sort.by=NULL,nochisq=TRUE,...)
object |
an object used to select a method. |
models |
character vector of model names. If numeric,
names(object$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 |
type |
If numeric, it is passed to sbpsi functions as
lambda to specify p-value type. If "Frequentist" or
"Bayesian", then equivalent to specifying lambda = 1 or 0,
respectively. |
select |
character of model name (such as "poly.3") or one of "average" and "best". If "average" or "best", then the averaging by Akaike weights or the best model is used, respectively. |
x |
object. |
sort.by |
sort key. |
verbose |
logical. |
nochisq |
logical. |
... |
further arguments passed to and from other methods. |
For each model, a class of approximately unbiased p-values,
indexed by k=1,2,..., is calculaed. The p-values are named
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 the
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. The sbpval
method is available to extract p-values from
the "summary.scaleboot"
object.
The p-value is defined as
p_k = 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 using the sbaic
function. We also diagnose the
fitting by using the plot
method.
summary.scaleboot
returns
an object of the class "summary.scaleboot"
, which is inherited
from the 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 p_k. |
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. |
parex |
a list of components k , s , and sp . |
Hidetoshi Shimodaira
data(mam15) ## For a single hypothesis a <- mam15.relltest[["t4"]] # an object of class "scaleboot" summary(a) # calculate and print p-values (k=3) summary(a,k=2) # calculate and print p-values (k=2) 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=3) summary(b,k=1:4) # up to "k.4" p-value.