Type: Package
Title: Statistical Tests of Familial Hypotheses
Version: 1.0.7
Description: Provides functionality for testing familial hypotheses. Supports testing centers belonging to the Huber family. Testing is carried out using the Bayesian bootstrap. One- and two-sample tests are supported, as are directional tests. Methods for visualizing output are provided.
URL: https://github.com/ryan-thompson/familial
BugReports: https://github.com/ryan-thompson/familial/issues
License: GPL-3
Encoding: UTF-8
Depends: R (≥ 4.1.0)
Imports: parallel, ggplot2, DepthProc, matrixStats
RoxygenNote: 7.3.2
Suggests: testthat, knitr, rmarkdown, MASS
VignetteBuilder: knitr
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2024-12-10 03:39:42 UTC; ryan
Author: Ryan Thompson ORCID iD [aut, cre]
Maintainer: Ryan Thompson <ryan.thompson-1@uts.edu.au>
Repository: CRAN
Date/Publication: 2024-12-10 04:00:02 UTC

Bayesian bootstrap

Description

Performs a Bayesian bootstrap for a statistic defined via a suitable function.

Usage

bayes.boot(x, fun, nboot = 1000, cluster = NULL, ...)

Arguments

x

a numeric vector to be passed as the first argument to fun

fun

the function to bootstrap; must accept data x and weights w (in that order), and return a data frame

nboot

the number of bootstraps to perform

cluster

an optional cluster for running bootstraps in parallel; must be set up using parallel::makeCluster

...

any other arguments for fun

Value

An object of class bayes.boot; a data frame with the following columns:

boot.id

the bootstrap iteration index

...

any columns returned by fun

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Examples

set.seed(123)

boot <- bayes.boot(MASS::galaxies, fun = fit.family, nboot = 100)
head(boot)

Center test

Description

Performs a one- or two-sample test for a family of centers.

Usage

center.test(
  x,
  y = NULL,
  family = "huber",
  alternative = c("two.sided", "less", "greater"),
  mu = 0,
  paired = FALSE,
  nboot = 1000,
  loss = NULL,
  cluster = NULL,
  ...
)

Arguments

x

a numeric vector of data

y

an optional numeric vector of data

family

the family of centers; currently only allows 'huber' for Huber family

alternative

the form of the alternative hypothesis; must be one of 'two.sided' (default), 'greater', or 'less'

mu

the null value of the center for a one-sample test, or the null value of the center of differences for a paired two-sample test, or the null value of the difference of centers for an independent two-sample test; can be an interval

paired

a logical indicating whether to treat x and y as paired

nboot

the number of bootstraps to perform

loss

an optional c×2 matrix of losses incurred from an incorrect decision, where c is the number of candidate choices (typically c=3: H0, H1, or indeterminate)

cluster

an optional cluster for running bootstraps in parallel; must be set up using parallel::makeCluster

...

any other arguments

Details

Uses the Bayesian bootstrap to compute posterior probabilities for the hypotheses \mathrm{H}_0:\mu(\lambda)=\mu_0 for some \lambda\in\Lambda vs. \mathrm{H}_1:\mu(\lambda)\neq\mu_0 for all \lambda\in\Lambda, where \{\mu(\lambda):\lambda\in\Lambda\} is a family of centers.
The default loss matrix results in a decision whenever the posterior probability for one of the hypotheses is greater than 0.95 and otherwise is indeterminate.

Value

An object of class center.test; a list with the following components:

expected.loss

the expected loss, calculated by post-multiplying loss with prob

decision

the optimal decision given the expected loss

loss

the loss matrix

prob

the estimated posterior probabilities of the null and alternative

boot

the bootstrap output from bayes.boot

x

the x that was supplied

y

the y that was supplied

mu

the mu that was supplied

family

the family that was supplied

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

References

Thompson, R., Forbes, C. S., MacEachern, S. N., and Peruggia, M. (2024). 'Familial inference: Tests for hypotheses on a family of centres'. Biometrika 111.3, pp. 1029–1045.

Examples

set.seed(123)

test <- center.test(MASS::galaxies, mu = 21000, nboot = 100)
print(test)
plot(test)

cl <- parallel::makeCluster(2)
test <- center.test(MASS::galaxies, mu = 21000, nboot = 100, cluster = cl)
parallel::stopCluster(cl)
print(test)

Fit family

Description

Fits a family of centers.

Usage

fit.family(
  x,
  w = rep(1, length(x)),
  family = "huber",
  spread.fun = weighted.mad,
  eps = .Machine$double.eps
)

Arguments

x

a numeric vector of data

w

a numeric vector of weights

family

the location family; currently only allows 'huber' for Huber family

spread.fun

a function used for the spread of x; must accept data x and weights w (in that order), and return a numeric

eps

a numerical tolerance parameter

Value

An object of class fit.family; a data frame with the following columns:

mu

the fitted values

lambda

the thresholding parameter

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Examples

fit <- fit.family(MASS::galaxies)
plot(fit)

Plot function for center.test object

Description

Plot the posterior distribution for the family of centers using a functional box plot.

Usage

## S3 method for class 'center.test'
plot(x, band = c(0.5, 0.75, 0.95), ninterp = 25, ...)

Arguments

x

an object of class center.test

band

a vector of band limits for the functional box plot

ninterp

the number of interpolation points for the functional box plot; more points lead to finer resolution of the plot at the expense of additional computation

...

any other arguments

Value

A plot of the posterior distribution.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Plot function for fit.family object

Description

Plot a fitted family.

Usage

## S3 method for class 'fit.family'
plot(x, y = NULL, ...)

Arguments

x

an object of class fit.family

y

an object of class fit.family

...

any other arguments

Value

A plot of the fitted family.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Print function for center.test object

Description

Print objects of class center.test.

Usage

## S3 method for class 'center.test'
print(x, ...)

Arguments

x

an object of class center.test

...

any other arguments

Value

The argument x.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Uniform Dirichlet distribution

Description

Random number generation for the uniform Dirichlet distribution (having all concentration parameters set to one).

Usage

rudirichlet(n, d)

Arguments

n

the number of observations

d

the number of dimensions

Value

A matrix; each row is a random draw and each column is a dimension.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Weighted statistics

Description

Assorted weighted statistics unavailable in base R.

Usage

weighted.median(x, w)

weighted.mad(x, w)

Arguments

x

a numeric vector of data

w

a numeric vector of weights

Value

A length-one numeric vector.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>