Description Usage Arguments Details Value Author(s) See Also Examples
summary
method for class "scaleboot"
and "scalebootv"
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ## S3 method for class 'scaleboot'
summary(object,models=names(object$fi),k=3,sk=k,s=1,sp=-1,
hypothesis=c("auto","null","alternative"),
type=c("Frequentist","Bayesian"),...)
## S3 method for class 'scalebootv'
summary(object,models=attr(object,"models"),k=3,sk=k,
hypothesis="auto",type="Frequentist", select="average",...)
## S3 method for class 'summary.scaleboot'
print(x,sort.by=c("aic","none"),verbose=FALSE,...)
## S3 method for class 'summary.scalebootv'
print(x,...)
|
object |
an object used to select a method. |
models |
character vector of model names. If numeric,
|
k |
numeric vector of k for calculating p-values. |
sk |
numeric vector of k for calculating selective inference p-values. |
s |
σ_0^2 |
sp |
σ_p^2 |
hypothesis |
specifies type of selective infernece.
"null" takes the region as null hypothesis, and "alternative" takes the region as alternative hypothesis.
"auto" determins it by the sign of beta0. The selectice pvalues ( |
type |
If numeric, it is passed to |
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. |
... |
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 - Φ≤ft( ∑_{j=0}^{k-1} \frac{(σ_p^2-σ_0^2)^j}{j!} \frac{d^j ψ(x|β)}{d x^j}\Bigr|_{σ_0^2} \right),
where ψ(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.
Now includes selective inference p-values. The method is described in Terada and Shimodaira (2017; arXiv:1711.00949) "Selective inference for the problem of regions via multiscale bootstrap".
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 |
pe |
matrix of standard errors of p-values. |
spv |
matrix of selective inference p-values of size |
spe |
matrix of standard errors of selective inference p-values. |
betapar |
list array containing (beta0, beta1) and its covariance matrix for each model. They are obtained by linear extrapolation. This will be used for interpreting the fitting in terms of signed distance and curvature. |
best |
a list consisting of components |
average |
a list of results for the average model computed by Akaike weight. |
parex |
a list of components |
Hidetoshi Shimodaira
1 2 3 4 5 6 7 8 9 10 11 | 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.
|
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