resid_dtop: Detrended Transformed Owen's Plot and ECDF for the residuals

Description

The function resid_dtop() provides single de-trended transformed Owen's plot, Owen (1995), for a GAMLSS fitted objects or any other residual vector (suitable standardised). This is a diagnostic tool for checking whether the normalised quantile residuals are coming from a normal distribution or not. This could be true if the horizontal line is within the confidence intervals.

The function resid_ecdf() provides the empirical cumulative distribution function of the residuals.

The function y_ecdf() provides the empirical cumulative distribution function of any numerical vector y.

Usage

resid_dtop(obj, resid, type = c("Owen", "JW"), conf.level = c("95", "99"),
           value = 2, points.col = "steelblue4",
           check_overlap = TRUE,  title, ylim, ...)
           
resid_ecdf(obj, resid, type = c("Owen", "JW"), conf.level = c("95", "99"), 
           value = 2, points.col = "steelblue4", 
           check_overlap = TRUE,  show.outliers = TRUE, title, ...)
           
y_ecdf(y, type = c("Owen", "JW"), conf.level = c("95", "99"), value = 2, 
           points.col = "steelblue4", check_overlap = TRUE, 
           show.outliers = FALSE, from, to, title, ...)

Value

A ggplot is generated

Arguments

obj: A GAMLSS fitted model
resid: if the object is not specified the residual vector can be given here
y: a numeric vector
type: whether to use Owen (1995) or Jager and Wellner (2004) approximate formula
conf.level: 95% (default) or 99% percent confidence interval for the plots
value: cut of point for large residuals
points.col: the colour of the points in the plot
check_overlap: to check for overlap when plotting the observation numbers
title: required title
show.outliers: whether to shoe the number of an outlier obsrvation
ylim: if the y limit should be different from the default max(y)+.1
from: where to start the ecdf
to: where to finish the ecdf
...: further arguments

Author

Mikis Stasinopoulos, Bob Rigby and Fernanda de Bastiani

References

Jager, L. and Wellner, J. A (2004) A new goodness of fit test: the reversed Berk-Jones statistic, University of Washington, Department of Statistics, Technical report 443.

Owen A. B. (1995) Nonparametric Confidence Bands for a Distribution Function. Journal of the American Statistical Association Vol. 90, No 430, pp. 516-521.

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, 1-38.

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.

Stasinopoulos, M.D., Kneib, T., Klein, N., Mayr, A. and Heller, G.Z., (2024). Generalized Additive Models for Location, Scale and Shape: A Distributional Regression Approach, with Applications (Vol. 56). Cambridge University Press.

(see also https://www.gamlss.com/).

Examples

Run this code

library(ggplot2)
data(abdom)
a<-gamlss(y~pb(x),sigma.fo=~pb(x,1),family=LO,data=abdom)
resid_dtop(a)
resid_ecdf(a)+ stat_function(fun = pNO, args=list(mu=0, sigma=1)) 
# create a gamma distributed random variable
y <- rGA(1000, mu=3, sigma=1)
gp<- y_ecdf(y)
gp + stat_function(fun = pGA, args=list(mu=3, sigma=1))

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