R: A function to calculate the Q-statistics

Q.stats {gamlss} | R Documentation

## A function to calculate the Q-statistics

### Description

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).

### Usage

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

### Arguments

`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 diffently (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

### Details

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.

### Value

A table containing the Q-statistics or Z-statistics. If `plot=TRUE` it produces also an graphical represenation of the table.

### Author(s)

Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby with contributions from Elaine Borghie

### References

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.

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

`gamlss`, `centiles.split`, `wp`

### Examples

    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)

[Package gamlss version 5.0-2 Index]