centile_bucket: Centile bucket plot

In gamlss.ggplots: Plotting Functions for Generalized Additive Model for Location Scale and Shape

Centile bucket plot

Description

A bucket plot is a graphical way to check the skewness and kurtosis of a continuous variable or the residuals of a fitted GAMLSS model. It plots the centile skewness (tail or central) and transformed centile kurtosis of the variable (or residuals) together with a cloud of points obtained using a non-parametric bootstrap from the original variable (or residuals). It also provides a graphical way of performing a Monte Carlo simulation test on whether the centile skewness and transformed centile kurtosis of the variable of interest are simultaneously equal to zero.

There are two function here:

i) cenlile_bucket() for a single bucket plot. Note that model_cent_bucket() and centile_bucket() are synonymous.

ii) centile_bucket_wrap() for multiple bucket plots cut according to terms in the model.

Usage

centile_bucket(x, ..., type = c("tail", "central"), weights = NULL, 
       no_bootstrap = 99, col_bootstrap = hcl.colors(length.obj, 
       palette = "Set 2"), alpha_bootstrap = 1, text_to_show = NULL, 
       cex_text = 5, col_text = "black", colour_bucket = FALSE, 
       line_width = 0.5, sim_test = FALSE, no_sim_test = 1000, 
       col_sim_test = gray(0.7), alpha_sim_test = 0.1, seed_test = 1234)

model_cent_bucket(x, ..., type = c("tail", "central"), weights = NULL, 
       no_bootstrap = 99, col_bootstrap = hcl.colors(length.obj, 
       palette = "Set 2"), alpha_bootstrap = 1, text_to_show = NULL, 
       cex_text = 5, col_text = "black", colour_bucket = FALSE, 
       line_width = 0.5, sim_test = FALSE, no_sim_test = 1000, 
       col_sim_test = gray(0.7), alpha_sim_test = 0.1, seed_test = 1234)


centile_bucket_wrap(x, ..., type = c("tail", "central"), weights = NULL, 
      xvar = NULL, n_inter = 4, no_bootstrap = 99, 
      col_bootstrap = hcl.colors(length.obj, palette = "Set 2"), 
      alpha_bootstrap = 1, text_to_show = NULL, check_overlap_text = FALSE, 
      cex_text = 5, col_text = "black", colour_bucket = FALSE, 
      line_width = 0.5, sim_test = FALSE, no_sim_test = 1000, 
      col_sim_test = gray(0.7), alpha_sim_test = 0.1, seed_test = 1234)       
       

Arguments

x	x should be a continuous vector of a GAMLSS fitted model.
...	for more that one continuous vectors or fitted models
type	whether "tail" of "central" skewness and kurtosis
weights	if priors weights are needed
no_bootstrap	the number of bootstrap samples for the cloud around the point of skewness and kurtosis.
col_bootstrap	The colour of the bootstrap samples
alpha_bootstrap	The transparency parameter of the bootstrap samples.
text_to_show	what text to show in the plots, default the names of vectors or models
cex_text	the character size of the text
col_text	the colour of the text
colour_bucket	whether colour or gray lines in the bucket
line_width	the line width
sim_test	whether to Monde Carlo simulation is needed to check the null hypothesis that there is no centile skewness and transformed centile kurtosis in the sample.
no_sim_test	The number of simulation for the test
col_sim_test	the colour used for displaying the Monde Carlo test values
alpha_sim_test	The transparency parameter of the Monde Carlo samples.
seed_test	A seed value for the Monde Carlo simulation.
xvar	the x term
n_inter	how many intervals needed
check_overlap_text	whether to check overlapping text

Details

More details about centile bucket plots is given in De Bastiani et al. (2022)

Value

A plot displaying the centile skewness and transformed centile kurtosis of the sample or residual of a model.

Note

The bucket plot provides an additional residual diagnostic tool that can be used for fitted model checking, alongside other diagnostic tools, for example worm plots, and Q (and Z) statistics.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

De Bastiani, F., Stasinopoulos, D. M., Rigby, R. A., Heller, G. Z., and Lucas A. (2022) Bucket Plot: A Visual Tool for Skewness and Kurtosis Comparisons. To be published.

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.

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1201/9780429298547")} 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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v023.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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1201/b21973")}

Stasinopoulos, M. D., Rigby, R. A., and De Bastiani F., (2018) GAMLSS: a distributional regression approach, Statistical Modelling, Vol. 18, pp, 248-273, SAGE Publications Sage India: New Delhi, India.

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/).

See Also

wp, Q.stats

Examples

m1 <- gamlss(R~pb(Fl)+pb(A), data=rent, family=GA)
centile_bucket(m1)

centile_bucket_wrap(m1, xvar=rent$A)

gamlss.ggplots documentation built on May 29, 2024, 1:34 a.m.