plot_squared_sel: Plot the graph of the squared scaled expected length of the...
In ciuupi: Confidence Intervals Utilizing Uncertain Prior Information
View source: R/plot_squared_sel.R
plot_squared_sel R Documentation
Plot the graph of the squared scaled expected length
of the CIUUPI
Description
The input bs.list determines the functions b and s
that specify the confidence interval that utilizes the uncertain
prior information (CIUUPI), for all possible values of \sigma
and observed response vector.
The scaled expected length of the CIUUPI is an even function of
the unknown parameter
\gamma = \tau \big/ \big(\sigma \, v_{\tau}^{1/2} \big).
The R function plot_squared_sel plots the graph of the squared scaled
expected length (i.e. squared SEL)
of the CIUUPI, as a function of |\gamma|.
To provide a stringent
assessment of this squared SEL, we use a grid
seq(0, (d+4), by = 0.01) of values of
\gamma and Gauss Legendre quadrature
with 10 nodes in the relevant integrals. By contrast,
for the computation
of the CIUUPI, implemented in bs_ciuupi, we
use Gauss Legendre quadrature
with 5 nodes in the relevant integrals.
Usage
plot_squared_sel(bs.list)
Arguments
bs.list
A list that includes the following
components.
alpha: the desired minimum coverage is 1 - \alpha.
rho: the known correlation
between \widehat{\theta}
and \widehat{\tau}. This correlation is computed from the
p-vectors
a and c and the n \times p
design matrix X using the formula
\rho=a^{\top}(X^{\top}X)^{-1}c /(v_{\theta} \, v_{\tau})^{1/2}, where
v_{\theta}
=a^{\top}(X^{\top}X)^{-1} a and
v_{\tau}
=c^{\top}(X^{\top}X)^{-1} c.
natural: 1 when the functions b and s are
specified by natural cubic spline interpolation
or 0 if these functions are specified by clamped
cubic spline interpolation
d: the functions b and s are specified by
cubic splines on the interval [-d, d]
n.ints: number of equal-length intervals in [0, d], where
the endpoints of these intervals specify the knots,
belonging to [0, d], of the cubic spline interpolations
that specify the functions b and s. In the description
of bsvec, n.ints is also called q.
bsvec: the (2q-1)-vector
\big(b(h),...,b((q-1)h), s(0),s(h)...,s((q-1)h) \big),
where q=ceiling(d/0.75) and h=d/q.
Value
A plot of the graph of the squared scaled
expected length (i.e. squared SEL)
of the CIUUPI as a function of |\gamma|, where
\gamma denotes the unknown parameter
\tau \big/ \big(\sigma \, v_{\tau}^{1/2} \big).
Examples
plot_squared_sel(bs.list.example)
ciuupi documentation built on June 22, 2024, 11:32 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
View source: R/plot_squared_sel.R
| plot_squared_sel | R Documentation |
Plot the graph of the squared scaled expected length of the CIUUPI
Description
The input bs.list determines the functions b and s
that specify the confidence interval that utilizes the uncertain
prior information (CIUUPI), for all possible values of \sigma
and observed response vector.
The scaled expected length of the CIUUPI is an even function of
the unknown parameter
\gamma = \tau \big/ \big(\sigma \, v_{\tau}^{1/2} \big).
The R function plot_squared_sel plots the graph of the squared scaled
expected length (i.e. squared SEL)
of the CIUUPI, as a function of |\gamma|.
To provide a stringent
assessment of this squared SEL, we use a grid
seq(0, (d+4), by = 0.01) of values of
\gamma and Gauss Legendre quadrature
with 10 nodes in the relevant integrals. By contrast,
for the computation
of the CIUUPI, implemented in bs_ciuupi, we
use Gauss Legendre quadrature
with 5 nodes in the relevant integrals.
Usage
plot_squared_sel(bs.list)
Arguments
bs.list |
A list that includes the following components.
where |
Value
A plot of the graph of the squared scaled
expected length (i.e. squared SEL)
of the CIUUPI as a function of |\gamma|, where
\gamma denotes the unknown parameter
\tau \big/ \big(\sigma \, v_{\tau}^{1/2} \big).
Examples
plot_squared_sel(bs.list.example)
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.