Bootstrap Confidence Intervals for Eigenvalue Statistics

Computes bootstrap confidence intervals for statistics based on eigenvalues of grouped covariance matrices. This is intended for use with plot.boxM() to provide confidence intervals for measures beyond the default "logDet".

This is a convenience wrapper that extracts the necessary information from a boxM object, but still requires the original data and grouping variable since these are not stored in the boxM object.

Usage

eigstatCI(
  Y,
  group,
  which = c("product", "sum", "precision", "max"),
  R = 1000,
  conf = 0.95,
  type = c("perc", "bca", "norm", "basic"),
  parallel = FALSE,
  ncpus = 2,
  seed = NULL,
  ...
)

eigstatCI_boxM(boxm, Y, group, ...)

Arguments

Y

Original data matrix used in boxM()

group

Original grouping variable used in boxM()

which

The eigenvalue-based statistic to compute. One of:

product: Product of eigenvalues (= determinant)
sum: Sum of eigenvalues (= trace)
precision: Harmonic mean of eigenvalues
max: Maximum eigenvalue

R

Number of bootstrap replicates. Default is 1000.

conf

Confidence level for intervals (0 < conf < 1). Default is 0.95.

type

Type of bootstrap confidence interval. Options:

perc: Percentile method (default, most robust)
bca: Bias-corrected and accelerated
norm: Normal approximation
basic: Basic bootstrap

parallel

Logical or character string. If TRUE, use parallel processing via the boot package. Can also be "multicore" or "snow". Default is FALSE.

ncpus

Number of CPUs to use if parallel=TRUE. Default is 2.

seed

Random seed for reproducibility. If NULL, no seed is set.

...

Additional arguments passed to eigstatCI()

boxm

A "boxM" object from boxM()

Value

A data frame with one row for each group plus the pooled data. Columns include:

group: Group name (factor level)
statistic: Observed value of the statistic
lower: Lower confidence limit
upper: Upper confidence limit
bias: Bootstrap estimate of bias (if available)
se: Bootstrap standard error (if available)

A data frame with bootstrap confidence intervals

Details

For each group (and the pooled data), this function performs nonparametric bootstrap resampling to estimate the sampling distribution of the specified eigenvalue-based statistic. Confidence intervals are computed using the percentile method or bias-corrected and accelerated (BCa) method.

Unlike logdetCI() which uses analytic approximations based on asymptotic theory, this function makes no distributional assumptions and can handle small to moderate sample sizes, though computational cost increases with the number of bootstrap replicates.

References

Efron, B., & Tibshirani, R. J. (1994). An Introduction to the Bootstrap. CRC Press.

Author

Michael Friendly

Examples

if (FALSE) { # \dontrun{
library(boot)
data(iris)

# Bootstrap CI for product of eigenvalues
CI_prod <- eigstatCI(iris[,1:4], iris$Species, which="product", R=500)
CI_prod

# Bootstrap CI for sum of eigenvalues (= trace)
CI_sum <- eigstatCI(iris[,1:4], iris$Species, which="sum", R=500)
CI_sum

# Use with parallel processing for speed
CI_max <- eigstatCI(iris[,1:4], iris$Species, which="max",
                    R=1000, parallel=TRUE, ncpus=4)
} # }

if (FALSE) { # \dontrun{
library(boot)
data(iris)

# Fit boxM
res <- boxM(iris[,1:4], iris$Species)

# Get bootstrap CIs (must provide original data again)
CI <- eigstatCI_boxM(res, Y = iris[,1:4], group = iris$Species,
                     which = "sum", R = 500)
} # }