R: Detrended transformed Owen's plot

dtop {gamlss} | R Documentation

## 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, http://www.stat.washington.edu/www/research/reports/2004/tr443.pdf.

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.

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, http://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 http://www.gamlss.org/).

### 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)

[Package gamlss version 5.0-2 Index]