This function calculates and prints the Q-statistics (or Z-statistics) which are useful to test normality of the residuals within a range of an independent variable, for example age in centile estimation, see Royston and Wright (2000).

```
Q.stats(obj = NULL, xvar = NULL, resid = NULL, xcut.points = NULL, n.inter = 10,
zvals = TRUE, save = TRUE, plot = TRUE, digits.xvar = getOption("digits"),
...)
```

A table containing the Q-statistics or Z-statistics. If `plot=TRUE`

it produces also an graphical representation of the table.

- obj
a GAMLSS object

- xvar
a unique explanatory variable

- resid
quantile or standardised residuals can be given here instead of a GAMLSS object in

`obj`

. In this case the function behaves differently (see details below)- xcut.points
the x-axis cut off points e.g.

`c(20,30)`

. If`xcut.points=NULL`

then the`n.inter`

argument is activated- n.inter
if

`xcut.points=NULL`

this argument gives the number of intervals in which the x-variable will be split, with default 10- zvals
if

`TRUE`

the output matrix contains the individual Z-statistics rather that the Q statistics- save
whether to save the Q-statistics or not with default equal to

`TRUE`

. In this case the functions produce a matrix giving individual Q (or z) statistics and the final aggregate Q's- plot
whether to plot a visual version of the Q statistics (default is TRUE)

- digits.xvar
to control the number of digits of the

`xvar`

in the plot- ...
for extra arguments

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby with contributions from Elaine Borghie

Note that the function `Q.stats`

behaves differently depending whether the `obj`

or the `resid`

argument is set. The `obj`

argument produces the Q-statistics (or Z-statistics) table appropriate for centile estimation (therefore it expect a reasonable large number of observations). The argument `resid`

allows any model residuals, (not necessary GAMLSS), suitable standardised and is appropriate for any size of data. The resulting table contains only the individuals Z-statistics.

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.

Royston P. and Wright E. M. (2000) Goodness of fit statistics for the age-specific reference intervals.
*Statistics in Medicine*, 19, pp 2943-2962.

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/).

`gamlss`

, `centiles.split`

, `wp`

```
data(abdom)
h<-gamlss(y~pb(x), sigma.formula=~pb(x), family=BCT, data=abdom)
Q.stats(h,xvar=abdom$x,n.inter=8)
Q.stats(h,xvar=abdom$x,n.inter=8,zvals=FALSE)
Q.stats(resid=resid(h), xvar=abdom$x, n.inter=5)
rm(h)
```

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