This function plots worm plots, van Buuren and Fredriks M. (2001), or QQ-plots of the normalized randomized quantile residuals (Dunn and Smyth, 1996) for a model using a discrete GAMLSS family distribution.

```
rqres.plot(obj = NULL, howmany = 6, plot.type = c("few", "all"),
type = c("wp", "QQ"), xlim = NULL, ylim = NULL, ...)
get.rqres(obj = NULL, howmany = 10, order = FALSE)
```

If `save`

it is TRUE then the vector of the median residuals is saved.

- obj
a fitted GAMLSS model object from a "discrete" type of family

- howmany
The number randomise quantile residuals required i.e.

`howmany=6`

- plot.type
whether to plot few of the randomised quantile residual realisations,

`"few"`

in a separate plots (there must be less than 8) or all`"all"`

in one plot (with their median)- type
whether to plot worm plots

`"wp"`

or QQ plots`"QQ"`

with default worm plots- xlim
setting manually the

`xlim`

of the graph- ylim
setting manually the

`ylim`

of the graph- order
whether to order the ealization of randomised quantile residuals

- ...
for extra arguments to be passed to

`wp()`

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk

For discrete family distributions, the `gamlss()`

function saves on exit one realization of randomized quantile residuals which
can be plotted using the generic function `plot`

which calls the `plot.gamlss`

. Looking at only one realization can be misleading, so the
current function creates QQ-plots for several
realizations. The function allows up to 10 QQ-plots to be plotted. Occasionally one wishes to create a lot of realizations
and then take a median of them (separately for each ordered value) to create a single median realization. The option `all`

in combinations
with the option `howmany`

creates a
QQ-plot of the medians of the normalized randomized quantile residuals. These 'median' randomized quantile residuals can be saved using the option
(`save=TRUE`

).

Dunn, P. K. and Smyth, G. K. (1996) Randomised quantile residuals,
*J. Comput. Graph. Statist.*, **5**, 236--244

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),
*Appl. Statist.*, **54**, part 3, pp 507-554.

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/).

van Buuren and Fredriks M. (2001) Worm plot: simple diagnostic device for modelling growth reference curves.
*Statistics in Medicine*, **20**, 1259--1277

`plot.gamlss`

, `gamlss`

```
data(aids) # fitting a model from a discrete distribution
h<-gamlss(y~pb(x)+qrt, family=NBI, data=aids) #
plot(h)
# plot qq- plots from 6 realization of the randomized quantile residuals
rqres.plot(h)
# a worm-plot of the medians from 10 realizations
rqres.plot(h,howmany=40,plot="all") #
```

Run the code above in your browser using DataLab