Plot for Box's M test and generalizations

This function creates a simple dot chart showing the contributions (log determinants) of the various groups to Box's M test for equality of covariance matrices. An important virtue of these plots is that they can show how the groups differ from each other, and from the pooled covariance matrix using a scalar like \(ln | S |\). In this way, they can suggest more specific questions or hypotheses regarding the equality of covariance matrices, analogous to the use of contrasts and linear hypotheses for testing differences among group mean vectors.

Because Box's M test is based on a specific function (log determinant) of the covariance matrices in the groups compared to the pooled covariance matrix, this function also also allow plots of other measures based on the eigenvalues of these covariance matrices.

Confidence intervals are only available for the default Box M test, using which="logDet".

Usage

# S3 method for class 'boxM'
plot(
  x,
  gplabel = NULL,
  which = c("logDet", "product", "sum", "precision", "max"),
  log = which == "product",
  pch = c(16, 15),
  cex = c(2, 2.5),
  col = c("blue", "red"),
  rev = FALSE,
  xlim,
  conf = 0.95,
  method = 1,
  bias.adj = TRUE,
  lwd = 2,
  ...
)

Arguments

x: A "boxM" object resulting from boxM
gplabel: character string used to label the group factor.
which: Measure to be plotted. The default, "logDet", is the standard plot. Other values are: "product", "sum", "precision" and "max"
log: logical; if TRUE, the log of the measure is plotted. The default, which=="product", produces a plot equivalent to the plot of "logDet".
pch: a vector of two point symbols to use for the individual groups and the pooled data, respectively
cex: character size of point symbols, a vector of length two for groups and pooled data, respectively
col: colors for point symbols, a vector of length two for the groups and the pooled data
rev: logical; if TRUE, the order of the groups is reversed on the vertical axis.
xlim: x limits for the plot
conf: coverage for approximate confidence intervals, 0 <= conf < 1 ; use conf=0 to suppress these
method: confidence interval method; see logdetCI
bias.adj: confidence interval bias adjustment; see logdetCI
lwd: line width for confidence interval
...: Arguments passed down to dotchart.

References

Friendly, M., & Sigal, M. (2018). Visualizing Tests for Equality of Covariance Matrices. The American Statistician, 72(4); doi:10.1080/00031305.2018.1497537 . Online: https://www.datavis.ca/papers/EqCov-TAS.pdf.

Author

Michael Friendly

Examples


# Iris data
res <- boxM(iris[, 1:4], iris[, "Species"])
plot(res, gplabel="Species")


# Skulls data
skulls.mod <- lm(cbind(mb, bh, bl, nh) ~ epoch, data=Skulls)
skulls.boxm <- boxM(skulls.mod)
plot(skulls.boxm, gplabel="Epoch")

plot(skulls.boxm, gplabel="Epoch", bias.adj=FALSE)


# other measures
 plot(skulls.boxm, which="product", gplabel="Epoch", xlim=c(10,14))

 plot(skulls.boxm, which="sum", gplabel="Epoch")

 plot(skulls.boxm, which="precision", gplabel="Epoch")

 plot(skulls.boxm, which="max", gplabel="Epoch")