# reverseR:
Linear Regression Stability to Significance Reversal
(`R`

-package)

## Overview

In biomedical literature, the most widely employed statistical
procedure to analyze and visualize the association between two variables
is linear regression. Data points that exert influence on the fit and
its parameters are routinely, but not as often as required, identified
by established influence measures and their corresponding cut-off
values. In this `R`

package, we specifically address the
presence of influential data points that directly impact the statistical
inference of the models, which none of the established measures detect,
such as

*leverage*

*dffits*

*dfbeta(s)*

*covratio*

*Cook’s distance*

*studentized residuals*

*Hadi’s measure*

We call these data points **“reversers”**.
`reverseR`

tests linear regressions for significance reversal
through leave-one(multiple)-out and checking if \(\alpha \in [p_{\beta1}, p_{\beta1(i)}]\),
where \(p_{\beta1}\) is the
*p*-value of the regression’s slope and \(p_{\beta1(i)}\) is the *p*-value
with the *i*-th point deleted. This paradigm is along the lines
of the living-in-oblivion measure *dfstat* or *dfstud*
(Belsley, Kuh & Welsch, Regression diagnostics: Identifying
influential data and sources of collinearity, 2004) that checks the
impact of each response value on statistical inference.

## Repo Contents

- R:
`R`

package code.
- man: package manuals for the different
functions.

## Hardware Requirements

The `reverseR`

package requires only a standard computer
with enough RAM to support the operations defined by a user. For minimal
performance, this will be a computer with about 4 GB of RAM. For optimal
performance, we recommend a computer with the following specs: RAM: 16+
GB; CPU: 4+ Cores, 3.3+ GHz/Core.

## Software Requirements

`R`

version greater than 3.5.0 for Linux Ubuntu 16,
Windows 7, 8, 10 or Mac.

Several CRAN packages may be needed.

## Runtimes

Runtimes vary for the different functions:

*lmInfl* for “reverser” analysis: ~ 1-5 sec.

*lmMult* for multiple leave-out analysis: ~ 5-30 sec.

*simInfl* for Monte Carlo simulation: 5-600 sec.

## Package dependencies

Users should install the following packages prior to installing
`reverseR`

, from an `R`

terminal:

`install.packages(c("markdown", "knitr"))`

## Installation Guide

From an `R`

session, type:

```
if (!'devtools' %in% installed.packages()) install.packages(devtools)
devtools::install_github("anspiess/reverseR")
source("https://install-github.me/anspiess/reverseR")
```