bootLM: Nonparametric/Parametric bootstrap linear model

In reverseR: Linear Regression Stability to Significance Reversal

Nonparametric/Parametric bootstrap linear model

Description

Nonparametric and parametric bootstrap (sampling cases, residuals or distributions with replacement) method for parameter estimation and confidence interval of a linear model.

Usage

bootLM(model, type = c("cases", "residuals", "residuals2", "parametric"), 
       R = 10000, alpha = 0.05, ret.models = FALSE) 

Arguments

model	an lm model.
type	what to bootstrap. See "Details".
R	number of bootstrap samples.
alpha	the \alpha-level to use as the threshold border.
ret.models	logical. If TRUE, the R models are returned as a list.

Details

If type = "cases", for all (x_i, y_i) datapoints, linear models are created by sampling R times - with replacement - from n \in \{1 \ldots N\} and building models Y_n = X_n\beta + \varepsilon. This is also known as the .632-bootstrap, because the samples will, on average, contain 1 - e^{-1} = 0.632 unique elements. If type = "residuals", for all residuals (r_i = y_i - \hat{y}_i), linear models are created by sampling R times - with replacement - from n \in (1 \ldots N) and building models \hat{Y}_i + r_n = X_i\beta + \varepsilon. If type = "residuals2" is selected, scaled and centered residuals r_n = \frac{r_i}{\sqrt{1 - h_{ii}}} - \bar{r} according to Davison & Hinkley are used. In the "parametric" bootstrap, n values drawn from a normal distribution j_n \in \mathcal{N}(0, \sigma), where \sigma = \sqrt{\frac{\sum(r_i)^2}{n - p}}, are added to the fitted values, and linear models are created \hat{Y}_i + j_n = X_i\beta + \varepsilon. Parameter estimates are obtained from each sampling, from which the average \overline{P_{n}} and standard error \hat{\sigma} is calculated as well as a quantile based confidence interval. p-values are calculated through inversion of the confidence interval.

Value

A dataframe containing the estimated coefficients, their standard error, lower an upper confidence values and p-values. If ret.models = TRUE a list with all R models is returned.

Author(s)

Andrej-Nikolai Spiess

References

An Introduction to the Bootstrap.
Efron B, Tibshirani R.
Chapman & Hall (1993).

The Bootstrap and Edgeworth Expansion.
Hall P.
Springer, New York (1992).

Modern Statistics with R.
Thulin M.
Eos Chasma Press, Uppsala (2021).

Bootstrap methods and their application.
Davison AC, Hinkley DV.
Cambridge University Press (1997).

Examples

## Example with single influencer (#18) and insignificant model (p = 0.115),
## using case bootstrap.
set.seed(123)
a <- 1:20
b <- 5 + 0.08 * a + rnorm(20, 0, 1)
LM <- lm(b ~ a)
bootLM(LM, R = 100)

## using residuals bootstrap.
bootLM(LM, R = 100, type = "residuals")

reverseR documentation built on Sept. 12, 2024, 7:32 a.m.