corrPlot: Function to Visualize Correlations Between Model Matrix...

In DoE.base: Full Factorials, Orthogonal Arrays and Base Utilities for DoE Packages

Function to Visualize Correlations Between Model Matrix Columns for an Experimental Design

Description

Function corrplot plots absolute or squared values of correlations between model matrix columns of main effects up to three-factor interactions for factorial designs.

Usage

corrPlot(design, scale = "corr", recode = TRUE, cor.out = TRUE, mm.out=FALSE,  
    main.only = TRUE, three = FALSE, run.order=FALSE,
    frml=as.formula(ifelse(three, ifelse(run.order, "~ run.no + .^3", "~ .^3"), 
                                   ifelse(run.order, "~ run.no + .^2", "~ .^2"))),
    pal = NULL, col.grid = "black", col.small = "grey", lwd.grid = 1.5, lwd.small = 0.5, 
    lty.grid = 1, lty.small = 3, cex.y = 1, cex.x = 0.7, x.grid = NULL,
    main = ifelse(scale == "corr", "Plot of absolute correlations", ifelse(scale == "R2",
         "Plot of squared correlations", 
         "Plot of absolute correlations of coefficient estimates")), 
    split = 0, ask = (split > 0), ...)

Arguments

design	a class design object, or an object that can be made into that class by function data2design
scale	"corr" for absolute correlation of model matrix columns (default), "R2" for squared correlation of model matrix columns, "corr.est" for absolute correlation of coefficient estimates; "corr.est" works for model matrices with full column rank only
recode	logical indicating whether or not to recode each column into normalized orthogonal coding with function contr.XuWu
cor.out	logical; if TRUE (default), the correlation matrix is invisibly returned
mm.out	logical; if TRUE (default: FALSE), the correlation matrix is invisibly returned, with the model matrix attached to it as an attribute
main.only	logical; if TRUE (default), only correlations with main effects columns are visualized, otherwise also those with two-factor interactions
three	logical; if FALSE (default), only two-factor interactions are included, otherwise also three-factor interactions
run.order	logical; if TRUE, the linear run order effect is included into the plot, and main effects are shown on the horizontal axis; used in conjunction with function rerandomize.design, this option can help to find a suitable random order with reasonably low correlation to the effects of interest.
frml	the model formula; useful, if absolute correlation for the coefficient estimates are desired in a situation where a full model has a rank deficiency; for requirements on the formula, see the Details section.
pal	NULL (default), or a color palette. If NULL, the color palette depends on whether or not package RColorBrewer is available: if so, the Blues palette with nine shades is used; otherwise, a 10 level palette of heat colors augmented with white is used. The number of colors in pal determines the number of bins for plotting.
col.grid	color of the main grid lines
col.small	color of the small grid lines
lwd.grid	width of the main grid lines
lwd.small	with of the small grid lines
lty.grid	line type of the main grid lines
lty.small	line type of the small grid lines
cex.y	size of tick mark labels on vertical axis
cex.x	size of tick mark labels on horizontal axis
x.grid	vector of numerical positions for thicker vertical grid lines (default: NULL for none)
main	title
split	an integer number (default: 0, no split) of columns after which to split the horizontal axis; if this number is nonzero and smaller than the number of columns to display, several plots are created; note: the color legend needs attention, since it may differ between the different plots, depending on the plot's range of values
ask	logical; if yes (default in case of splitting, otherwise not), the user is asked to confirm creation of each new plot
...	additional arguments to function levelplot

Details

The function can be used for visualizing confounding within an experimental design. It is strongly recommended to apply it to designs with columns coded in normalized orthogonal coding (contr.XuWu, contr.XuWuPoly, if applicable also contr.FrF2). Nevertheless, for factors with more than two levels, the picture shown depends on the choice of normalized orthogonal coding (see examples). Option recode=FALSE is there to allow to keep a suitably-chosen normalized orthogonal coding for each factor.

The function shows the absolute correlation or squared correlation between model matrix columns, or, on request and if possible, the absolute correlation between estimated coefficients (other than the intercept). In case the latter cannot be obtained for the full model, a model formula can be specified with option frml. Note that it is implicitly assumed that all main effects are included in the model formula, and for main.only=FALSE also all two-factor interactions.

For resolution III and higher designs, the vertical axis shows the main effects (and, if main.only=FALSE, also the two-factor interactions), the horizontal axis shows the two-factor interactions (and, if three=TRUE, also the three-factor interactions). For resolution II designs, the horizontal axis additionally shows the main effect columns (since they are correlated with other main effect columns). For resolution VI and higher designs, the function stops with an error. For resolution V designs, the function shows correlations between two-factor interactions on the vertical axis and three-factor interactions on the horizontal axis, if both are activated. The most interesting cases are designs of resolution up to IV.

The diagonal of the correlation matrix is set to NA before plotting, in order to be able to better see differences in case there are only relatively low correlations.

With scale="R2", and using normalized orthogonal coding, some sums of matrix entries coincide with contributions to generalized word counts (resolution II: main effects with main effects; resolution III: main effects with two-factor interactions; resolution IV: main effects with three-factor interactions; see Groemping and Xu (2014) for the background of this result and Groemping (2017).

Value

The entire matrix of absolute correlations is output invisibly.

Author(s)

Ulrike Groemping, Berliner Hochschule fuer Technik

References

Groemping, U. (2017). Frequency Tables for the coding invariant quality assessment of factorial designs. IISE Transactions 49(5), 505–517.

Groemping, U. and Xu, H. (2014). Generalized resolution for orthogonal arrays. The Annals of Statistics 42, 918–939.

The function works similarly to colormap in package daewr (but offers significantly more choices). That package accompanies the following book:

Lawson, J. (2013). Design and Analysis of Experiments with R. CRC, Boca Raton.

See Also

See Also as levelplot, ~~~

Examples

## this is with the default contr.XuWu recoding
mat <- corrPlot(VSGFS)
round(mat, 2)

## NOT RECOMMENDED: force-keep non-normalized coding
corrPlot(VSGFS, recode=FALSE)  # not useful!

## custom normalized orthogonal coding
## that has correlations more concentrated on fewer columns
plan <- change.contr(VSGFS, "contr.XuWuPoly")
contrasts(plan$CDs) <- contr.FrF2(4)
corrPlot(plan, recode=FALSE)  # that is the purpose of recode=FALSE

corrPlot(VSGFS, main.only=FALSE, three=TRUE, cex.x=0.5, cex.y=0.5, split=100)

DoE.base documentation built on Nov. 15, 2023, 1:06 a.m.