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familial

Overview

An R package for familial inference. Briefly, this package provides tests for hypotheses of the form

[ \mathrm{H}_0:\mu(\lambda)=\mu_0\text{ for some }\lambda\in\Lambda\quad\text{vs.}\quad\mathrm{H}_1:\mu(\lambda)\neq\mu_0\text{ for all }\lambda\in\Lambda,](https://latex.codecogs.com/png.image?%5Cdpi%7B110%7D&space;%5Cbg_white&space;%0A%5Cmathrm%7BH%7D_0%3A%5Cmu%28%5Clambda%29%3D%5Cmu_0%5Ctext%7B%20for%20some%20%7D%5Clambda%5Cin%5CLambda%5Cquad%5Ctext%7Bvs.%7D%5Cquad%5Cmathrm%7BH%7D_1%3A%5Cmu%28%5Clambda%29%5Cneq%5Cmu_0%5Ctext%7B%20for%20all%20%7D%5Clambda%5Cin%5CLambda%2C%0A ” _0:()=_0_1:()_0, “)

where $\{\mu(\lambda):\lambda\in\Lambda\}$ is a family of centers, e.g., that induced by the Huber loss function with parameter $\lambda$ . In contrast to classic statistical tests such as the $t$ or sign tests for the mean or median, familial tests do not depend on a single (sometimes arbitrarily chosen) center.

Presently, familial supports tests of the Huber family of centers, which includes the mean and median. Testing is carried out using a Bayesian approach whereby the posterior probabilities of the competing hypotheses $\mathrm{H}_0$ and $\mathrm{H}_1$ are from the Bayesian bootstrap. One- and two-sample tests are supported, as are directional tests. Methods for visualizing output are provided.

Installation

To install the latest stable version from CRAN, run the following code:

install.packages('familial')

To install the latest development version from GitHub, run the following code:

devtools::install_github('ryan-thompson/familial')

Usage

The center.test() function performs a test of centers, with the default being the Huber family of centers.

library(familial)
set.seed(1)

# One-sample test with point null
x <- MASS::galaxies
center.test(x, mu = 21000)

## -----------------------------------------------
## familial test of centers with huber family
## -----------------------------------------------
## mu = 21000 
## posterior probabilities: 
##    H0    H1 
## 0.542 0.458 
## optimal decision: indeterminate

# One-sample test with interval null
center.test(x, mu = c(20500, 21500))

## -----------------------------------------------
## familial test of centers with huber family
## -----------------------------------------------
## mu = 20500 21500 
## posterior probabilities: 
##    H0    H1 
## 0.959 0.041 
## optimal decision: H0

# Two-sample test
x <- MASS::cabbages[MASS::cabbages$Cult == 'c39', 'HeadWt']
y <- MASS::cabbages[MASS::cabbages$Cult == 'c52', 'HeadWt']
center.test(x, y)

## -----------------------------------------------
## familial test of centers with huber family
## -----------------------------------------------
## mu = 0 
## posterior probabilities: 
##    H0    H1 
## 0.008 0.992 
## optimal decision: H1

# Two-sample paired directional test
x <- MASS::anorexia[MASS::anorexia$Treat == 'FT', 'Postwt']
y <- MASS::anorexia[MASS::anorexia$Treat == 'FT', 'Prewt']
center.test(x, y, paired = T, alternative = 'greater')

## -----------------------------------------------
## familial test of centers with huber family
## -----------------------------------------------
## mu = 0 
## posterior probabilities: 
##    H0    H1 
## 0.006 0.994 
## optimal decision: H1

Documentation

See the package vignette or reference manual.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.