gamlss (version 4.3-4)

Q.stats: 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

Value

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

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.

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. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

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.

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)