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.

```
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, ...)
```

A plot is returned.

- 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

Mikis Stasinopoulos, Bob Rigby and Vlassios Voudouris

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.

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/).

`wp`

```
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)
```

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