moment_bucket {gamlss.ggplots}

Moment 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 transformed moment skewness and transformed moment 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 the Jarque-Bera test (JarqueandBera,1980).

There are two function here:

i) moment_bucket() for a single bucket plot. Note that model_mom_bucket() and moment_bucket() are synonymous.

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

Usage

moment_bucket(x, ..., 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, col_JB_test = gray(.7), alpha_JB_test = .1)
           
model_mom_bucket(x, ..., 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, col_JB_test = gray(.7), alpha_JB_test = .1)           
           
moment_bucket_wrap(x, ..., 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,
          col_JB_test = gray(.7), alpha_JB_test = .1)           
           

Arguments

x

x should be a continuous vector of a GAMLSS fitted model.

...

this for more that one continuous vectors or fitted models

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 ot 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

xvar

the x term

n_inter

how many intervals needed

check_overlap_text

whether to check overlapping text

col_JB_test

the colour for the Jarque-Bera test

alpha_JB_test

the transparency constant for the Jarque-Bera test

Value

A plot displaying the transformed moment skewness and transformed moment 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. 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, 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. 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)
moment_bucket(m1)
moment_bucket_wrap(m1, xvar=rent$A)