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.
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)
A plot displaying the centile skewness and transformed centile kurtosis of the sample or residual of a model.
x should be a continuous vector of a GAMLSS fitted model.
for more that one continuous vectors or fitted models
whether "tail" of "central" skewness and kurtosis
if priors weights are needed
the number of bootstrap samples for the cloud around the point of skewness and kurtosis.
The colour of the bootstrap samples
The transparency parameter of the bootstrap samples.
what text to show in the plots, default the names of vectors or models
the character size of the text
the colour of the text
whether colour or gray lines in the bucket
the line width
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.
The number of simulation for the test
the colour used for displaying the Monde Carlo test values
The transparency parameter of the Monde Carlo samples.
A seed value for the Monde Carlo simulation.
the x term
how many intervals needed
whether to check overlapping text
Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani
More details about centile bucket plots is given in De Bastiani et al. (2022)
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. 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, 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. 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/).
wp, Q.stats
m1 <- gamlss(R~pb(Fl)+pb(A), data=rent, family=GA)
centile_bucket(m1)
# \donttest{
centile_bucket_wrap(m1, xvar=rent$A)
# }
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