selm fitsDiagnostic plots for objects of class selm
and mselm generated by a call to function selm
# S4 method for selm
plot(x, param.type="CP", which = c(1:4), caption,
panel = if (add.smooth) panel.smooth else points, main = "",
ask = prod(par("mfcol")) < length(which) && dev.interactive(), ...,
id.n = 3, labels.id = names(x@residuals.dp),
cex.id = 0.75, identline = TRUE, add.smooth = getOption("add.smooth"),
label.pos = c(4, 2), cex.caption = 1) # S4 method for mselm
plot(x, param.type="CP", which, caption,
panel = if (add.smooth) panel.smooth else points, main = "",
ask = prod(par("mfcol")) < length(which) && dev.interactive(), ...,
id.n = 3, labels.id = names(x@residuals.dp),
cex.id = 0.75, identline = TRUE, add.smooth = getOption("add.smooth"),
label.pos = c(4, 2), cex.caption = 1)
an object of class selm or mselm.
a character string which selects the type of residuals
to be used for some of of the plots;
possible values are: "CP" (default), "DP",
"pseudo-CP". The various type of residuals only differ by an
additive term; see ‘Details’ for more information.
if a subset of the plots is required, specify a subset of
1:4; see ‘Details’ for a description of the plots.
a vector of character strings with captions to appear above the plots.
panel function. The useful alternative to points,
panel.smooth can be chosen by add.smooth = TRUE.
title to each plot, in addition to the above caption.
logical; if TRUE, the user is asked before each plot.
other parameters to be passed through to plotting functions.
number of points to be labelled in each plot, starting with the most extreme.
vector of labels, from which the labels for extreme points
will be chosen. NULL uses observation numbers..
magnification of point labels.
logical indicating if an identity line should be added to
QQ-plot and PP-plot (default: TRUE).
logical indicating if a smoother should be added to most
plots; see also panel above.
positioning of labels, for the left half and right half of the graph respectively, for plots 1-3.
controls the size of caption.
Healy-type graphical diagnostics, in the form of QQ- and PP-plots, for the multivariate normal distribution have been extended to the skew-normal distribution by Azzalini and Capitanio (1999, section 6.1), and subsequently to the skew-\(t\) distribution in Azzalini and Capitanio (2003). A brief explanation in the univariate SN case is provided in Section 3.1.1 of Azzalini and Capitanio (2014); see also Section 3.1.6. For the univariate ST case, see p.102 and p.111 of the monograph. The multivariate case is discussed in Section 5.2.1 as for the SN distribution, in Section 6.2.6 as for the ST distribution.
Adelchi Azzalini
The meaning of param.type is described in
dp2cp. However, for these plot only the first parameter
component is relevant, which affects the location of the residuals; the other
components are not computed. Moreover, for QQ-plot and
PP-plot, DP-residuals are used irrespectively of
param.type; see Section ‘Background’.
Values which=1 and which=2 have a
different effect for object of class "selm" and class "mselm".
In the univariate case, which=1 plots the residual values versus the
fitted values if p>1, where p denotes the number of covariates
including the constant; if p=1, a boxplot of the response is produced.
Value which=2 produces an histogram of the residuals with superimposed
the fitted curve, when p>1; if p=1, a similar plot is generated
using the response variable instead of the residuals. Default value for
which is 1:4.
In the multivariate case, which=1 is feasible only if p=1 and it
displays the data scatter with superimposed the fitted distribution. Value
which=2 produces a similar plot but for residuals instead of
data. Default value for codewhich is 2:4 if p>1, otherwise
c(1,3,4).
Value which=3 produces a QQ-plot, both in the univariate and in the
multivariate case; the difference is that the squares of normalized residuals
and suitably defined Mahalanobis distances, respectively, are used in the two
cases. Similarly, which=4 produces a PP-plot, working in a similar
fashion.
Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew normal distribution. J.Roy.Statist.Soc. B 61, 579-602. Full-length version available at https://arXiv.org/abs/0911.2093
Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J.Roy. Statist. Soc. B 65, 367-389. Full-length version available at https://arXiv.org/abs/0911.2342
Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.
selm, dp2cp
data(wines)
#
m10 <- selm(flavanoids ~ 1, family="SN", data=wines, subset=(wine=="Barolo"))
plot(m10)
plot(m10, which=c(1,3)) # fig 3.1 and 3.2(a) of Azzalini and Capitanio (2014)
#
m18 <- selm(acidity ~ sugar + nonflavanoids + wine, family="SN", data=wines)
plot(m18)
plot(m18, param.type="DP")
#
m28 <- selm(cbind(acidity, alcohol) ~ sugar + nonflavanoids + wine,
family="SN", data=wines)
plot(m28, col=4)
#
data(ais)
m30 <- selm(cbind(RCC, Hg, Fe) ~ 1, family="SN", data=ais)
plot(m30, col=2, which=2)
# multiple plots on the same sheet
par(mfcol=c(2,2))
plot(m30, which=1:3)
par(mfcol=c(1,1))
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