Q.stats: A function to calculate the Q-statistics

In gamlss: Generalized Additive Models for Location Scale and Shape

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 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

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 representation of the table.

Author(s)

Mikis Stasinopoulos, 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.

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/).

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)

gamlss documentation built on May 29, 2024, 6:08 a.m.