jackknife {lmboot}

Delete-1 Jackknife in Linear Models

Description

This function performs the delete-1 jackknife in linear models as described by Quenouille (1956) <doi:10.2307/2332914>. Linear models incorporating categorical and/or quantitative predictor variables with a quantitative response are allowed. The function output creates the jackknife sampling distribution for each coefficient. Estimation is performed via least squares.

Usage

jackknife(formula, data = NULL)

Arguments

formula

input a linear model formula of the form response~predictors as you would in the lm() function. All variables must contain non-missing entries.

data

optionally, input the name of the dataset where variables appearing in the model are stored.

Details

Currently, the user must manipulate the output of the function to conduct hypothesis tests and create confidence intervals for the predictor coefficients. More convenient/streamlined output is expected in future package versions.

Value

bootEstParam

matrix containing the jackknife parameter estimates. Each column corresponds to a coefficient. There are n-1 rows, each corresponding to a jackknife sample.

origEstParam

vector containing the least squares parameter estimates. These are the same as estimates obtained from lm.

Author(s)

Megan Heyman, [e-mail]

References

Quenouille, M. (1956). "Notes on bias in estimation." Biometrika. Vol. 61, pp.1-15

Examples

Seed <- 14
set.seed(Seed)
y <- rnorm(20) #randomly generated response
x <- rnorm(20) #randomly generated predictor
JackObj <- jackknife(y~x) #perform the jackknife

#plot the sampling distribution of the slope coefficient
hist(JackObj$bootEstParam[,2], main="Jackknife Sampling Distn.",
     xlab="Slope Estimate") 

#jackknife 95% CI for slope parameter (percentile method)
quantile(JackObj$bootEstParam[,2], probs=c(.025, .975))