Question . How can I use boostrap to obtain confidence intervals for collecting statistics calculated on the eigenvalues of covariance matrices, separately for each group (factor level) in the data frame?
Problem : I can’t fully work out the data. I must contain these results that are suitable for the function boot, or a way to “match” the load by groups and get confidence intervals in a form suitable for construction.
Context : The package heplots boxMcomputes the Box M test for equality of covariance matrices. There is a plot method that gives a useful graph of the logarithmic determinants that go into this quiz. Confidence intervals on this graph are based on an approximation of the asymptotic theory.
> library(heplots)
> iris.boxm <- boxM(iris[, 1:4], iris[, "Species"])
> iris.boxm
Box M-test for Homogeneity of Covariance Matrices
data: iris[, 1:4]
Chi-Sq (approx.) = 140.94, df = 20, p-value < 2.2e-16
> plot(iris.boxm, gplabel="Species")
The plot method can also display other eigenvalue functions, but in this case, confidence intervals are available.
op <- par(mfrow=c(2,2), mar=c(5,4,1,1))
plot(iris.boxm, gplabel="Species", which="product")
plot(iris.boxm, gplabel="Species", which="sum")
plot(iris.boxm, gplabel="Species", which="precision")
plot(iris.boxm, gplabel="Species", which="max")
par(op)
Thus, I would like to be able to calculate these CIs using boostrap and display them on the respective graphs.
What I tried :
Below are the functions that increase these statistics, but the sample, not taking into account the group ( Species).
cov_stat_fun <- function(data, indices,
stats=c("logdet", "prod", "sum", "precision", "max")
) {
dat <- data[indices,]
cov <- cov(dat, use="complete.obs")
eigs <- eigen(cov)$values
res <- c(
"logdet" = log(det(cov)),
"prod" = prod(eigs),
"sum" = sum(eigs),
"precision" = 1/ sum(1/eigs),
"max" = max(eigs)
)
}
boot_cov_stat <- function(data, R=500, ...) {
boot(data, cov_stat_fun, R=R, ...)
}
, ( )
> iris.boot <- boot_cov_stat(iris[,1:4])
>
> iris.ci <- boot.ci(iris.boot)
> iris.ci
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 500 bootstrap replicates
CALL :
boot.ci(boot.out = iris.boot)
Intervals :
Level Normal Basic Studentized
95% (-6.622, -5.702 ) (-6.593, -5.653 ) (-6.542, -5.438 )
Level Percentile BCa
95% (-6.865, -5.926 ) (-6.613, -5.678 )
Calculations and Intervals on Original Scale
Some BCa intervals may be unstable
>
, , , . - ?
# calculate covariance matrices by group and pooled
covs <- function(Y, group) {
Y <- as.matrix(Y)
gname <- deparse(substitute(group))
if (!is.factor(group)) group <- as.factor(as.character(group))
valid <- complete.cases(Y, group)
if (nrow(Y) > sum(valid))
warning(paste(nrow(Y) - sum(valid)), " cases with missing data have been removed.")
Y <- Y[valid,]
group <- group[valid]
nlev <- nlevels(group)
lev <- levels(group)
mats <- aux <- list()
for(i in 1:nlev) {
mats[[i]] <- cov(Y[group == lev[i], ])
}
names(mats) <- lev
pooled <- cov(Y)
c(mats, "pooled"=pooled)
}
Edit:
-, , Bootstrap , , strata boot(), . [Ah: strata , .]
, , Species.
> iris.boot.strat <- boot_cov_stat(iris[,1:4], strata=iris$Species)
>
> boot.ci(iris.boot.strat, conf=0.95, type=c("basic", "bca"))
BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 500 bootstrap replicates
CALL :
boot.ci(boot.out = iris.boot.strat, conf = 0.95, type = c("basic",
"bca"))
Intervals :
Level Basic BCa
95% (-6.587, -5.743 ) (-6.559, -5.841 )
Calculations and Intervals on Original Scale
Some BCa intervals may be unstable
>