dtop {gamlss}

Detrended transformed Owen's plot

Description

Provides single or multiple detrended transformed Owen's plot, Owen (1995), for a GAMLSS fitted objects or any other fitted object which has the method resid(). This is a diagnostic tool for checking whether the normalised quantile residuals are coming from a normal distribution or not. This could be true if the horizontal line is within the confidence intervals.

Usage

dtop(object = NULL, xvar = NULL, resid = NULL,
      type = c("Owen", "JW"), 
      conf.level = c("95", "99"), n.inter = 4, 
      xcut.points = NULL, overlap = 0, 
      show.given = TRUE, cex = 1, pch = 21, 
      line = TRUE, ...)

Arguments

object

a GAMLSS fitted object or any other fitted object which has the method resid().

xvar

the explanatory variable against which the detrended Owen's plots will be plotted

resid

if the object is not specified the residual vector can be given here

type

whether to use Owen (1995) or Jager and Wellner (2004) approximate formula

conf.level

95 (default) or 99 percent confidence interval for the plots

n.inter

he number of intervals in which the explanatory variable xvar will be cut

xcut.points

the x-axis cut off points e.g. c(20,30). If xcut.points=NULL then the n.inter argument is activated

overlap

how much overlapping in the xvar intervals. Default value is overlap=0 for non overlapping intervals

show.given

whether to show the x-variable intervals in the top of the graph, default is show.given=TRUE

cex

the cex plotting parameter with default cex=1

pch

the pch plotting parameter with default pch=21

line

whether the detrended empirical cdf should be plotted or not

...

for extra arguments

Details

If the xvar argument is not specified then a single detrended Owen's plot is used, see Owen (1995). In this case the plot is a detrended nonparametric likelihood confidence band for a distribution function. That is, if the horizontal lines lies within the confidence band then the normalised residuals could have come from a Normal distribution and consequently the assumed response variable distribution is reasonable. If the xvar is specified then we have as many plots as n.iter. In this case the x-variable is cut into n.iter intervals with an equal number observations and detrended Owen's plots for each interval are plotted. This is a way of highlighting failures of the model within different ranges of the explanatory variable.

Value

A plot is returned.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Vlassios Voudouris

References

Jager, L. and Wellner, J. A (2004) A new goodness of fit test: the reversed Berk-Jones statistic, University of Washington, Department of Statistics, Technical report 443.

Owen A. B. (1995) Nonparametric Confidence Bands for a Distribution Function. Journal of the American Statistical Association Vol. 90, No 430, pp. 516-521.

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, 1-38.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, https://www.jstatsoft.org/v23/i07/.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

(see also https://www.gamlss.com/).

See Also

wp

Examples

data(abdom)
a<-gamlss(y~pb(x),sigma.fo=~pb(x,1),family=LO,data=abdom)
dtop(a)
dtop(a, xvar=abdom$x)
rm(a)