copula (version 0.999-13)

pairsRosenblatt: Plots for Graphical GOF Test via Pairwise Rosenblatt Transforms

Description

pairsColList() creates a list containing information about colors for a given matrix of (approximate aka pseudo) p-values. These colors are used in pairsRosenblatt() for visualizing a graphical goodness-of-fit test based on pairwise Rosenblatt transformed data.

Usage

pairsRosenblatt(cu.u, pvalueMat=pviTest(pairwiseIndepTest(cu.u)),
                method = c("scatter", "QQchisq", "QQgamma",
                           "PPchisq", "PPgamma", "none"),
                g1, g2, col = "B&W.contrast",
                colList = pairsColList(pvalueMat, col=col),
                main=NULL,
                sub = gpviString(pvalueMat, name = "pp-values"),
		panel = NULL, do.qqline = TRUE,
                keyOpt = list(title="pp-value", rug.at=pvalueMat), ...)
pairsColList(P, pdiv = c(1e-04, 0.001, 0.01, 0.05, 0.1, 0.5),
             signif.P = 0.05, pmin0 = 1e-05, bucketCols = NULL,
             fgColMat = NULL, bgColMat = NULL, col = "B&W.contrast",
             BWcutoff = 170,
             bg.col = c("ETHCL", "zurich", "zurich.by.fog", "baby",
                        "heat", "greenish"),
             bg.ncol.gap = floor(length(pdiv)/3),
             bg.col.bottom = NULL, bg.col.top = NULL, ...)

Arguments

cu.u

$(n,d,d)$-array of pairwise Rosenblatt-transformed observations as returned by pairwiseCcop().

pvalueMat

$(d,d)$-matrix of p-values (or pp-values).

method

character indicating the plot method to be used. Currently possible are: [object Object],[object Object],[object Object],[object Object],[object Object],[object Object] Note: These methods mer

g1

function from $[0,1]^n\to[0,1]^n$ applied to "x" for plotting in one panel.

g2

function from $[0,1]^{n\times 2}\to[0,1]^n$ applied to "y" for plotting in one panel.

colList

list of colors and information as returned by pairsColList().

main

title.

sub

sub-title with a smart default containing a global (p)p-value.

panel

a panel function as for pairs, or, by default, NULL, where the panel is set as points or points $+$

do.qqline

if method = "QQ....", specify if the plot panels should also draw a qqline().

keyOpt

argument passed to .pairsCond() for options for the key.

...

additional arguments passed to .pairsCond() (for pairsRosenblatt()) and to heat_hcl() (for pairsColList; used to generate the color palette), see Detail

P

$d \times d$ matrix of p-values.

pdiv

numeric vector of strictly increasing p-values in (0,1) that determine the buckets for the background colors of .pairsCond() which creates the pairs-like goodness-of-fit plot

signif.P

significance level (must be an element of pdiv).

pmin0

a numeric indicating the lower endpoint of the p-value buckets if pmin is zero. If set to 0, the lowest value of the p-value buckets will also be 0.

Note that pmin0 s

bucketCols

vector of length as pdiv containing the colors for the buckets. If not specified, either bg.col.bottom and bg.col.top are used (if provided) or bg.co

fgColMat

$(d,d)$-matrix with foreground colors (the default will be black if the background color is bright and white if it is dark; see also BWcutoff).

bgColMat

$(d,d)$-matrix of background colors; do not change this unless you know what you are doing.

col

foreground color (defaults to "B&W.contrast" which switches black/white according to BWcutoff), passed to .pairsCond(). If colList is not specified, this color is u

BWcutoff

number in (0, 255) for switching foreground color if col="B&W.contrast".

bg.col

color scheme for the background colors.

bg.ncol.gap

number of colors left out as "gap" for color buckets below/above signif.P (to make significance/non-significance more visible).

bg.col.bottom

vector of length 3 containing a HCL color specification. If bg.col.bottom is provided and bucketCols is not, bg.col.bottom is used as the color for the buck

bg.col.top

vector of length 3 containing a HCL color specification. If bg.col.top is provided and bucketCols is not, bg.col.top is used as the color for the bucket of

Value

• [object Object],[object Object]

Details

Extra arguments of pairsRosenblatt() are passed to .pairsCond(), these notably may include key, true by default, which draws a color key for the colors used as panel background encoding (pseudo) p-values.

pairsColList() is basically an auxiliary function to specify the colors used in the graphical goodness-of-fit test as conducted by pairsRosenblatt(). The latter is described in detail in Hofert and Mächler{Maechler} (2013). See also demo(gof_graph).

References

Hofert, M. and Mächler{Maechler}, M. (2013) A graphical goodness-of-fit test for dependence models in higher dimensions; Journal of Computational and Graphical Statistics, 23(3), 700--716.

See Also

pairwiseCcop for the tools behind the scenes. demo(gof_graph) for examples.

Examples

## 2-dim example {d = 2} ===============
##
## "t" Copula with 22. degrees of freedom; and (pairwise) tau = 0.5
nu <- 2.2 # degrees of freedom
## Define the multivariate distribution
tCop <- ellipCopula("t", param=iTau(ellipCopula("t", df=nu), tau = 0.5),
                    dim=2, df=nu)
set.seed(19)
X <- qexp(rCopula(n = 400, tCop))

## H0 (wrongly): a Normal copula, with correct tau
copH0 <- ellipCopula("normal", param=iTau(ellipCopula("normal"), tau = 0.5))

## create array of pairwise copH0-transformed data columns
cu.u <- pairwiseCcop(pobs(X), copH0)

## compute pairwise matrix of p-values and corresponding colors
pwIT <- pairwiseIndepTest(cu.u, N=200) # (d,d)-matrix of test results

round(pmat <- pviTest(pwIT), 3) # pick out p-values
## .286 and .077
pairsRosenblatt(cu.u, pvalueMat= pmat)



### A shortened version of   demo(gof_graph) -------------------------------

N <- 32 ## too small, for "testing"; realistically, use a larger one:
if(FALSE)
N <- 100

## 5d Gumbel copula ##########

n <- 250 # sample size
d <- 5 # dimension
family <- "Gumbel" # copula family
tau <- 0.5
set.seed(17)
## define and sample the copula (= H0 copula), build pseudo-observations
cop <- getAcop(family)
th <- cop@iTau(tau) # correct parameter value
copH0 <- onacopulaL(family, list(th, 1:d)) # define H0 copula
U. <- pobs(rCopula(n, cop=copH0))

## create array of pairwise copH0-transformed data columns
cu.u <- pairwiseCcop(U., copH0)

## compute pairwise matrix of p-values and corresponding colors
pwIT <- pairwiseIndepTest(cu.u, N=N, verbose=interactive()) # (d,d)-matrix of test results
round(pmat <- pviTest(pwIT), 3) # pick out p-values
## Here (with seed=1):  no significant ones, smallest = 0.0603

## Plots ---------------------

## plain (too large plot symbols here)
pairsRosenblatt(cu.u, pvalueMat=pmat, pch=".")

## with title, no subtitle
pwRoto <- "Pairwise Rosenblatt transformed observations"
pairsRosenblatt(cu.u, pvalueMat=pmat, pch=".", main=pwRoto, sub=NULL)

## two-line title including expressions, and centered
title <- list(paste(pwRoto, "to test"),
              substitute(italic(H[0]:C~~bold("is Gumbel with"~~tau==tau.)),
                         list(tau.=tau)))
line.main <- c(4, 1.4)
pairsRosenblatt(cu.u, pvalueMat=pmat, pch=".",
                main=title, line.main=line.main, main.centered=TRUE)

## Q-Q plots -- can, in general, better detect outliers
pairsRosenblatt(cu.u, pvalueMat=pmat, method="QQchisq", cex=0.2)