Diagnostic plots for selm fits

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Description

Diagnostic plots for objects of class selm and mselm generated by a call to function selm

Usage

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  ## S4 method for signature '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 signature '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)

Arguments

x

an object of class selm or mselm.

param.type

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.

which

if a subset of the plots is required, specify a subset of 1:4; see ‘Details’ for a description of the plots.

caption

a vector of character strings with captions to appear above the plots.

panel

panel function. The useful alternative to points, panel.smooth can be chosen by add.smooth = TRUE.

main

title to each plot, in addition to the above caption.

ask

logical; if TRUE, the user is asked before each plot.

...

other parameters to be passed through to plotting functions.

id.n

number of points to be labelled in each plot, starting with the most extreme.

labels.id

vector of labels, from which the labels for extreme points will be chosen. NULL uses observation numbers..

cex.id

magnification of point labels.

identline

logical indicating if an identity line should be added to QQ-plot and PP-plot (default: TRUE).

add.smooth

logical indicating if a smoother should be added to most plots; see also panel above.

label.pos

positioning of labels, for the left half and right half of the graph respectively, for plots 1-3.

cex.caption

controls the size of caption.

Details

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.

Background

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.

Author(s)

Adelchi Azzalini

References

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 http://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 http://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.

See Also

selm, dp2cp

Examples

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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)

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