Package 'gamlss.ggplots'

Plotting Functions for Generalized Additive Model for Location Scale and Shape

Description

Functions for plotting Generalized Additive Models for Location Scale and Shape from the 'gamlss' package, Stasinopoulos and Rigby (2007) <doi:10.18637/jss.v023.i07>, using the graphical methods from 'ggplot2'.

Details

The DESCRIPTION file:

Package:	gamlss.ggplots
Title:	Plotting Functions for Generalized Additive Model for Location Scale and Shape
Version:	2.1-15
Date:	2024-05-31
Authors@R:	c(person("Mikis", "Stasinopoulos", role = c("aut", "cre", "cph"), email = "[email protected]", comment = c(ORCID = "0000-0003-2407-5704")), person("Robert", "Rigby", role = "aut", email = "[email protected]", comment = c(ORCID = "0000-0003-3853-1707")), person("Fernanda", "De Bastiani", role = "aut", email = "[email protected]", comment = c(ORCID = "0000-0001-8532-639X")), person("Julian", "Merder", role = "ctb") )
Description:	Functions for plotting Generalized Additive Models for Location Scale and Shape from the 'gamlss' package, Stasinopoulos and Rigby (2007) <doi:10.18637/jss.v023.i07>, using the graphical methods from 'ggplot2'.
License:	GPL-2 | GPL-3
URL:	https://www.gamlss.com/
BugReports:	https://github.com/gamlss-dev/gamlss.ggplots/issues
Depends:	R (>= 3.5.0), gamlss.dist, gamlss (>= 4.3.3), gamlss.foreach
Imports:	methods, ggridges, ellipse, gamlss.inf, foreach, mgcv, ggplot2, yaImpute, gamlss2
Suggests:	glmnet, reshape2, igraph, networkD3, grid, gridExtra
Additional_repositories:	https://gamlss-dev.R-universe.dev
LazyLoad:	yes
Repository:	https://gamlss-dev.r-universe.dev
RemoteUrl:	https://github.com/gamlss-dev/gamlss.ggplots
RemoteRef:	HEAD
RemoteSha:	10ff8ea0cef7512617318a25fdb5e4416d4d7b38
Author:	Mikis Stasinopoulos [aut, cre, cph] (<https://orcid.org/0000-0003-2407-5704>), Robert Rigby [aut] (<https://orcid.org/0000-0003-3853-1707>), Fernanda De Bastiani [aut] (<https://orcid.org/0000-0001-8532-639X>), Julian Merder [ctb]
Maintainer:	Mikis Stasinopoulos <[email protected]>

Index of help topics:

ACE                     Alternating Conditional Expectations
boot_coef               Plotting Bootstrap Coefficients
centile_bucket          Centile bucket plot
family_pdf              Plotting Probabilities Density Functions
                        (pdf's) for GAMLSS
fit_PB                  P-spline smoother
fitted_cdf              Plotting Cumulative Distribution Functions
                        (cdf's) for GAMLSS,
fitted_centiles         Plotting centile (growth) curves
fitted_devianceIncr     Plotting the deviance increment of GAMLSS
fitted_leverage         Plot of the linear leverage of a GAMLSS model
fitted_terms            Plotting fitted additive terms
gamlss.ggplots-package
                        Plotting Functions for Generalized Additive
                        Model for Location Scale and Shape
histSmo_plot            Supporting histSmo()
model_GAIC              Plotting GAIC for GAMLSS models
model_pca               Plotting residuals using PCA
moment_bucket           Moment bucket plot
moment_gray_half        Functions to create the background for the
                        bucket plots
pcr_coef_path           Plotting the fitted path of a PCR model.
pe_param                Partial Effect of a term on the parameters and
                        predictors
pe_pdf                  Partial Effect of a term on the response
                        distribution
prof_term               Plotting the profile deviance of one fitted
                        term
resid_density           Density of the residuals in a GAMLLSS model
resid_dtop              Detrended Transformed Owen's Plot and ECDF for
                        the residuals
resid_index             A residual plots
resid_qqplot            QQ-plot of the residuals of a GAMLSS model
resid_symmetry          Symmetry plots
resid_wp                Worm plot using ggplot2
resp_mu                 Plotting the response against quantities of the
                        fitted model
y_hist                  Histogram and density plot.

The following convention has been used to name the functions:

fitted_NAME: plots concerning fitted values from a single fitted model

resid_NAME: plots concerning residuals from a single fitted model

predict_NAME: plots concerning prediction values from a single fitted model usually having newdata option.

model_NAME: plots concerning different fitted models

where NAME refer to different characteristics.

Author(s)

Mikis Stasinopoulos [aut, cre, cph] (<https://orcid.org/0000-0003-2407-5704>), Robert Rigby [aut] (<https://orcid.org/0000-0003-3853-1707>), Fernanda De Bastiani [aut] (<https://orcid.org/0000-0001-8532-639X>), Julian Merder [ctb]

Maintainer: Mikis Stasinopoulos <[email protected]>

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.

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

gamlss, gamlss.family

Examples

library(gamlss)
m1 <- gamlss(y~pb(x), data=abdom)
resid_index(m1)

---

Alternating Conditional Expectations

Description

The function ACE() uses the alternating conditional expectations algorithm to find a transformations of y and x that maximise the proportion of variation in y explained by x. It is a less general function than the ace() function of the package 'acepack' in that it takes only one explanatory variable. The function ACE() is used by the function mcor() to calculate the maximal correlation between x and y.

Usage

ACE(x, y, weights, data = NULL, con_crit = 0.001, 
    fit.method = c("loess", "P-splines"), nseg = 10, 
    max.df = 6, ...)
    
mcor(x, y, data = NULL,  fit.method = c("loess", "P-splines"),  
        nseg = 10, max.df = 6,  ...)

Arguments

x	the unique x-variables
y	the y-variable
weights	prior weights
data	a data frame for y, x and weights
con_crit	the convergence criterio of the algorithm
fit.method	the method use to fit the smooth functions $t_1()$ and $t_2()$
nseg	the number of knots
max.df	the maximum od df allowed
...	arguments to pass to the fitted functions fir_PB or loess()

Details

The function ACE is a simplified version of the function ace() of the package agepack.

Value

A fitted ACE model with methods print.ACE() and plot.ACE()

Author(s)

Mikis Stasinopoulos

References

Eilers, P. H. C. and Marx, B. D. (1996). Flexible smoothing with B-splines and penalties (with comments and rejoinder). Statist. Sci, 11, 89-121.

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. 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/).

See Also

fit_PB

Examples

data(rent)
ACE(Fl, R, data=rent)
pp <- ACE(Fl, R, data=rent)
pp
plot(pp)
mcor(Fl, R, data=rent)

---

Plotting Bootstrap Coefficients

Description

The function boot_coef() plots in one or multiple pages the results from a boostrap generated by the function BayesianBoot(), NonParamatricBoot or nonpar_boot().

The function boot_coef_one() plots a single parameter.

Usage

boot_coef(x, terms = NULL, hist.col = "black", 
                hist.fill = "white", dens.fill = "#FF6666", 
                alpha = 0.2, nrow = NULL, ncol = NULL, 
                plots.per.page = 9, one.by.one = FALSE, title, ...)
                
boot_coef_one(x, par = 1, rug = TRUE, alpha = 0.2, hist.col = "black", 
                hist.fill = "white", line.col = "gray", 
                dens.fill = "#FF6666", title, ...)

Arguments

x	a Bayesian.boot or NonParametric.boot object
terms	which terms to plot (default NULL means all terms
par	which parameter to plot
hist.col	colour of the border histogram
hist.fill	the colour of the histogram
dens.fill	the colour of the density estimate
alpha	transparity constant
nrow	how namy rows
ncol	how many columns
plots.per.page	the maxiimum plots per page
one.by.one	whether single plots
rug	whether rug is required for boot_coef_one()
line.col	the vertical line colour for boot_coef_one()
title	the title
...	for more argument

Details

The function plots in one ore multiple pages the results from a boostrap simulation

Value

Greates a ggplot object

Author(s)

Mikis Stasinopoulos

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.

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/).

See Also

term.plot

Examples

data(aids)
a <- gamlss(y ~ pb(x) + qrt, data = aids, family = NBI)
registerDoParallel(cores = 2)
B1 <- BayesianBoot(a, B=100)
stopImplicitCluster()
boot_coef(B1)

---

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. 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)
centile_bucket(m1)

centile_bucket_wrap(m1, xvar=rent$A)

---

Plotting Probabilities Density Functions (pdf's) for GAMLSS

Description

The function family_pdf() takes a GAMLSS family distribution and plots different pdf's according to the specified parameters.

The function fitted_pdf() takes a gamlss fitted object and plots the fitted distributions for specified observations.

The function fitted_pdf_data() it does the same as fitted_pdf() but it adds also the observation values as grey vertical lines.

The function predict_pdf() takes a fitted object and test data and plots the predictive pdf's.

Usage

family_pdf(family = NO(), mu = NULL, sigma = NULL, nu = NULL, tau = NULL, 
         title, from = 0, to = 10, no.points = 201,
         alpha = 0.4, col.fill = hcl.colors(lobs, palette = "viridis"), 
         size.seqment = 1.5, plot.point = TRUE, size.point = 1, 
         plot.line = TRUE, size.line = 0.2, ...)
         
fitted_pdf(model, obs, title, from = 0, to = 10, no.points = 201, alpha = 0.4, 
         col.fill = hcl.colors(lobs, palette = "viridis"), 
         size.seqment = 1.5, plot.point = TRUE, size.point = 1, plot.line = TRUE,
         size.line = 0.2, ...)
         
fitted_pdf_data(model, obs, from, to, ...)         
         
predict_pdf(model, newdata, title, from = 0, to = 10, no.points = 201, 
         alpha = 0.4, col.fill = hcl.colors(lobs, palette = "viridis"), 
         size.seqment = 1.5, plot.point = TRUE, size.point = 1, 
         plot.line = TRUE, size.line = 0.2, ...)

Arguments

family	A GAMLSS family
model	A GAMLSS fitted model
obs	observations to plot fitted distributions
newdata	for test data
mu	the mu parameter value(s)
sigma	the sigma parameter value(s)
nu	the nu parameter value(s)
tau	the tau parameter value(s)
title	a diferent title for the default
from	minimum value for the response
to	maximum value for the response
no.points	number of points (relevant for continuous responses)
alpha	trasparency factor
col.fill	the colour pallet default is hcl.colors(lobs, palette="viridis")
size.seqment	for discrete responses the size of the bars
plot.point	for discrete responses whether to put poits on the top of the bars
size.point	for discrete responses
plot.line	for discrete responses whether to joint the bars with lines
size.line	for discrete responses the size of the joining lines
...	for extra argumnets

Details

The functions family_pdf() and fitted_pdf() are ggplot version of the function pdf.plot() used to plot fitted distributions of GAMLSS family at specified observation values. Note that the range of the response has to be specified using the argument from to.

For discrete fitted distributions maybe increase the value of alpha for clearer plot.

For binomial type of data (discrete response with upper limit) the function family_pdf() takes the argument to as the binomial denominator, For fitted model with binomial type responses the function fitted_pdf() takes the binomial denominator form the fitted model and set the argument to to the maximum of those binomial denominators.

Value

Creates a plot

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

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/).

See Also

gamlss, resid_density

Examples

###################################
# function fitted_pdf
# continuous variabe
a1 <- gamlss(y~pb(x),sigma.fo=~pb(x), data=abdom, family=LO)
fitted_pdf(a1, obs=c(10,15,20), from=30, to=100)
# count data
p1 <- gamlss(y~pb(x)+qrt, data=aids, family=NBI)
fitted_pdf(p1, obs=c(10:15), from=25, to=130, alpha=.9)
# binomial type
h<-gamlss(y~ward+loglos+year, sigma.formula=~year+ward, family=BB, data=aep) 
fitted_pdf(h, obs=c(10:15),  alpha=.9)
###################################
# function predict_pdf
predict_pdf(a1, newdata=abdom[10:20, ], from=30, to=100)
# count data
predict_pdf(p1, newdata=aids[10:15, ], from=30, to=150)
# binomial
predict_pdf(h, newdata=aep[10:15, ], from=0, to=20)
###################################
# function family_pdf
# continuous
family_pdf(from=-5,to=5, mu=0, sigma=c(.5,1,2))
# count data 
family_pdf(NBI, to=15, mu=1, sigma=c(.5,1,2), alpha=.9, size.seqment = 3)
# binomial type
family_pdf(BB, to=15, mu=.5, sigma=c(.5,1,2),  alpha=.9, , size.seqment = 3)

---

P-spline smoother

Description

The function fit_PB() fits a P-spline univariate smoother [Eilers and Marx (1996)] to y against the x with prior weights weights.

Usage

fit_PB(x, y, weights, data, xmin, xmax, nseg = 20, 
      lambda = 10, order = 2, degree = 3, max.df = 20, 
      ylim, plot = TRUE, col.ribbon = "pink")

Arguments

x	the explanatory variable
y	the response
weights	possible prior weights (set to one by default)
data	the data frame where x, y and weights are coming from
xmin	the x minimum if different from min(x)
xmax	the x maximum if different from max(x)
nseg	the number of knots
lambda	the smotthing parameter
order	the ordr of the difference
degree	the degree of the piewise polynonmial
max.df	the maximum allowed degress of freedom
ylim	the ylim in the plot
plot	whether to plot the results
col.ribbon	the color in the se of the fitted values

Value

A object Psplines is produced with methods print(), coef() deviance(), fitted(), predict() and resid().

Note

The functionfit_PB() is an engine for getting the maximal correlation between two continuous variables. It can be also used on its own as a smoother.

Author(s)

Mikis Stasinopoulos

References

Eilers, P. H. C. and Marx, B. D. (1996). Flexible smoothing with B-splines and penalties (with comments and rejoinder). Statist. Sci, 11, 89-121.

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.

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., 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

ACE

Examples

data(abdom)
m1 <- fit_PB(x,y, data=abdom)

---

Plotting Cumulative Distribution Functions (cdf's) for GAMLSS,

Description

The function family_cdf() takes a GAMLSS family distribution and plots different pdf's according to the specified parameters.

The function fitted_cdf() takes a gamlss fitted object and plots the fitted distributions for specified observations.

The function fitted_cdf_data() is similat to fitted_cdf() but also adds the data points as gray vertical lines.

The function predict_pdf() (NOT IMPLEMENTED YET) takes a fitted object and test data and plots the predictive cdf's.

Usage

fitted_cdf(model, obs, title, from = 0, to = 10, no.points = 201, 
          alpha = 1, size.line = 1.2, 
          col.fill = hcl.colors(lobs, palette = "viridis"), 
          size.seqment = 1.5, size.point = 1, 
          plot.line = TRUE, size.line.disc = 0.2, lower.tail = TRUE, ...)

fitted_cdf_data(model, obs, from, to, ...)

predict_cdf(model, newdata, title, from = 0, to = 10, no.points = 201, 
          alpha = 0.4, size.line = 1.2, 
          col.fill = hcl.colors(lobs, palette = "viridis"), 
          size.seqment = 1.5, plot.point = TRUE, size.point = 1, 
          plot.line = TRUE, size.line.disc = 0.2, lower.tail = TRUE, ...)

family_cdf(family = NO(), mu = NULL, sigma = NULL, nu = NULL, 
         tau = NULL, title, from = 0, to = 10, no.points = 201, 
         alpha = 0.4, size.line = 1.2, col.fill = hcl.colors(lobs, 
         palette = "viridis"), size.seqment = 1.5, plot.point = TRUE,  
         size.point = 1, plot.line = TRUE, lower.tail = TRUE, ...)

Arguments

family	A GAMLSS family
model	A GAMLSS fitted model
obs	observations to plot fitted distributions
newdata	for test data
mu	the mu parameter value(s)
sigma	the sigma parameter value(s)
nu	the nu parameter value(s)
tau	the tau parameter value(s)
title	a diferent title for the default
from	minimum value for the response
to	maximum value for the response
no.points	number of points (relevant for continuous responses)
alpha	trasparency factor
col.fill	the colour pallet default is hcl.colors(lobs, palette="viridis")
size.seqment	for discrete responses the size of the bars
plot.point	for discrete responses whether to put poits on the top of the bars
size.point	for discrete responses
plot.line	for discrete responses whether to joint the bars with lines
size.line.disc	for discrete responses the size of the joining lines
size.line	The size of the lines
lower.tail	if TRUE cdf is plotted if FALSE the survival function
...	for extra argumnets

Details

The functions family_cdf(), fitted_cdf(), and predict_cdf() are function to plot cdf's for a gamlss.family, fitted gamlss model or predictive gamlss model, respectively.

For discrete fitted distributions maybe increase the value of alpha for clearer plot.

For binomial type of data (discrete response with upper limit) the function family_cdf() takes the argument to as the binomial denominator, For fitted model with binomial type responses the function fitted_cdf() takes the binomial denominator form the fitted model and set the argument to to the maximum of those binomial denominators.

Value

Creates a plot

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

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/).

See Also

gamlss

Examples

# function fitted_cdf
# continuous variabe
a1 <- gamlss(y~pb(x),sigma.fo=~pb(x), data=abdom, family=LO)
fitted_cdf(a1, obs=c(10,15,20), from=30, to=100)
fitted_cdf(a1, obs=c(10,15,20), from=30, to=100, lower.tail=FALSE)
# count data
p1 <- gamlss(y~pb(x)+qrt, data=aids, family=NBI)
fitted_cdf(p1, obs=c(10:15), from=10, to=130, alpha=.9)
fitted_cdf(p1, obs=c(10:15), from=10, to=130, alpha=.9, lower.tail=FALSE)
# binomial type
h<-gamlss(y~ward+loglos+year, sigma.formula=~year+ward, family=BB, data=aep) 
fitted_cdf(h, obs=c(10:15),  alpha=.9)
fitted_cdf(h, obs=c(10:15),  alpha=.9, lower.tail=FALSE)
###################################
# function predict_pdf
predict_cdf(a1, newdata=abdom[c(10,15,20), ], from=30, to=100)
predict_cdf(a1, newdata=abdom[10:20, ], from=30, to=100, lower.tail=FALSE)
# count data
predict_cdf(p1, newdata=aids[10:15, ], from=10, to=150)
predict_cdf(p1, newdata=aids[10:15, ], from=10, to=150, lower.tail=FALSE)
# binomial
predict_cdf(h, newdata=aep[10:15, ], from=0, to=20)
predict_cdf(h, newdata=aep[10:15, ], from=0, to=20, lower.tail=FALSE)
###################################
# function family_cdf
# continuous
family_cdf(from=-5,to=5, mu=0, sigma=c(.5,1,2))
family_cdf(from=-5,to=5, mu=0, sigma=c(.5,1,2), lower.tail=FALSE)
# count data 
family_cdf(NBI, to=15, mu=1, sigma=c(.5,1,2), alpha=.9, size.seqment = 3)
family_cdf(NBI, to=15, mu=1, sigma=c(.5,1,2), alpha=.9, size.seqment = 3, lower.tail=FALSE)
# binomial type
family_cdf(BB, to=15, mu=.5, sigma=c(.5,1,2),  alpha=.9, , size.seqment = 3)
family_cdf(BB, to=15, mu=.5, sigma=c(.5,1,2),  alpha=.9, , size.seqment = 3, lower.tail=FALSE)

---

Plotting centile (growth) curves

Description

The function fitted_centiles() plots centiles curves for distributions belonging to the GAMLSS family of distributions. The plot is equivalent to the standard plot of gamlss:::centiles() without a legend.

The function fitted_centiles_legend() plots centiles curves for distributions belonging to the GAMLSS family of distributions and it is equivalent to the standard plot of gamlss:::centiles() with a legend. The function is slower than fitted_centiles() since in order to plot the legend the data have to expanded.

The function model_centiles() plots centile curves for more than one model. There is no equivalent plot in the original GAMLSS centile plots but it perform the same function as gamlss:::centiles.com() which compares centiles from different models.

Usage

fitted_centiles(obj, xvar, 
               cent = c(99.4, 98, 90, 75, 50, 25, 10, 2, 0.4), 
               points = TRUE, point.col = "gray", 
               point.size = 1, line.size = 0.8, 
               line.col = hcl.colors(lc, palette = "Dark 2"), 
               line.type = rep(1, length(cent)),
               xlab = NULL, ylab = NULL, title, ...)
               
fitted_centiles_legend(obj, xvar, 
               cent = c(99.4, 98, 90, 75, 50, 25, 10, 2, 0.4),   
               points = TRUE, point.col = "gray", point.size = 1, 
               line.size = 0.8, line.col = hcl.colors(ncent, 
               palette = "Dark 2"), line.type = rep(1, length(cent)),               
               show.legend = TRUE, save.data = FALSE, title, 
               xlab = NULL, ylab = NULL, ...)               

model_centiles(obj, ..., cent = c(97, 90, 75, 50, 25, 10, 3), 
               xvar, xlab = "age", points = TRUE, 
               point.col = gray(0.8), 
               point.size = 0.05, line.size = 0.7, 
               line.col = hcl.colors(ncent,palette = "Dark 2"), 
               ncol = 2, nrow = ceiling(nnames/ncol),  in.one = FALSE,
               title)

Arguments

obj	a fitted gamlss object
xvar	the (unique) explanatory variable
cent	a vector with elements the % centile values for which the centile curves have to be evaluated (note that the order is from the highest to the lowest so legend and the plots are maching)
points	whether to plot the points (TRUE) of the data or not (FALSE)
point.col	the colour of the points
point.size	the zize of the points
line.size	the sized of the centile lines
line.col	the colour of the centile lines
line.type	the type of line (different types of lines for each centile are working with fitted_centiles_legend)
xlab	the label of the x-axis variable
ylab	the label of the resposnse variable
in.one	whether the model_centile plot should be one or multiple
title	the title if need it otherwise a dfault title is pronted
show.legend	whether to show the legend
save.data	whether to save the data.frame of the plot
nrow	the number of rows in the model_centiles() plot
ncol	the number of columns in the model_centiles() plot
...	for extra arguments for fitted_centiles(), and fitted_centiles.legend() and extra models for model_centiles()

Details

Centiles are calculated using the fitted values in obj and xvar must correspond exactly to the predictor in obj to plot correctly.

Value

A plot is created

Warning

This function is appropriate only when one continuous explanatory variable is fitted in the model

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda de Bastiani

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.

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/).

See Also

centiles

Examples

data(abdom)
h<-gamlss(y~pb(x), sigma.formula=~pb(x), family=BCTo, data=abdom) 
h1 <- gamlss(y~pb(x), sigma.formula=~pb(x), family=LO, data=abdom) 
fitted_centiles(h)
fitted_centiles_legend(h)
model_centiles(h, h1)

---

Plotting the deviance increment of GAMLSS

Description

There are two plotting function here:

i) fitted_devianceIncr() plots the fitted model deviance components. This is useful for identifying observations with unusual y-values (given the current fitted distribution).

iii) model_devianceIncr_diff plots the difference of deviance increments from two fitted GAMLSS model. This function is useful if the GAIC and the residuals contradict each other. For example the GAIC is better for model 1 but the residuals look lot better for model 2. This can happens if the two distributions are better suited to fit different parts of the response distribution i.e. one model fits the center better but the other fits the tail better.

Usage

fitted_devianceIncr(obj, plot = TRUE, title, quan.val = 0.99,
         annotate = TRUE, line.col = "steelblue4", 
         point.col = "darkblue", annot.col = "white",
         newdata = NULL)
         

model_devianceIncr_diff(model1, model2, against = "index", 
         tol = 20, data, newdata)

Arguments

obj	a GAMLSS fitted object
plot	whether to create just the plot or save also the values with high deviance increment
title	a tittle if needed it.
quan.val	The quantile values of the deviance increment from which the obsrevrvarion should be identify
annotate	whether to plot the quantile values above in the plot.
line.col	the colour of the line
point.col	the colour of the points
annot.col	the colour of the annotation for the deviance increment plot
model1	The first fitted GAMLSS model
model2	The second fitted GAMLSS model
against	you can plot the deviance increment an index, the response or an x-variable
tol	if the absolute value of deviance increment exceeds the tol the number of the observation is plotted
data	The data if can not be found from model1
newdata	evaluates the function in new data

Details

The functions are diagnostic tools to check unusual observations in the response.

Value

return a plot

Author(s)

Mikis Stasinopulos, Rober Rigby and Fernanda de Bastiani

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.

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/).

See Also

gamlss

Examples

m1 <- gamlss(R~pb(Fl)+pb(A)+H+loc, data=rent, family=GA )
m2 <- gamlss(R~pb(Fl)+pb(A)+H+loc, data=rent, family=NO )
fitted_devianceIncr(m1)
model_devianceIncr_diff(m1,m2, against="Fl")

---

Plot of the linear leverage of a GAMLSS model

Description

This is plot of the "linear" leverage of a GAMLSS fitted model. By linear we mean the leverage (hat-values) we would have obtain in all the explanatory variables for all distribution parameters where put together and used to fit a linear model to the response. The "linear" leverage is them the hat-values obtained by fitting this simple linear model. Hopefully the "linear" leverage can indicate observations with extreme values in the x's. Note that observations with hight linear leverage may not be influential in the GAMLSS fitting especially if the x-variables are fitted using smoothers.

Usage

fitted_leverage(obj, plot = TRUE, title, quan.val = 0.99, 
          annotate = TRUE, line.col = "steelblue4", 
          point.col = "steelblue4", annot.col = "darkred")

Arguments

obj	A GAMLSS fitted model
plot	whether to plot ot not
title	for different title than the default
quan.val	which quantile value of the leverage should be taked to indicate the observation values
annotate	whether to annotate the extreme levarages
line.col	the colour of the lines
point.col	the colout of the points
annot.col	the colour used for annotation

Value

Returns a plot of the linear leverage against index.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

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.

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/).

See Also

gamlss

Examples

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

---

Plotting fitted additive terms

Description

The function fitted_terms() is doing what the function term.plot() is doing for GAMLSS models but it uses ggplot2 package. The function pe_terms() is synonymous to fitted_terms() in the package gamlss.

Usage

fitted_terms(object, 
          what = c("mu", "sigma", "nu", "tau"), 
          parameter = NULL, data = NULL, terms = NULL,
          envir = environment(formula(object)), 
          partial = FALSE, rug = FALSE, rug.sides = "b", 
          rug.col = "gray",  alpha = 0.2, 
          ylim = c("common", "free"), xlabs = NULL, 
          ylabs = NULL, main = NULL, term.col = "darkred", 
          resid.col = "lightblue", resid.alpha = 0.8, 
          resid.size = 1, nrow = NULL, ncol = NULL, 
          plots.per.page = 9, one.by.one = FALSE, 
          surface.gam = FALSE, polys = NULL, 
          polys.scheme = "topo", col.ribbon = "darksalmon",
          col.shaded = "gray", ...)

pe_terms(object, 
          what = c("mu", "sigma", "nu", "tau"), 
          parameter = NULL, data = NULL, terms = NULL,
          envir = environment(formula(object)), 
          partial = FALSE, rug = FALSE, rug.sides = "b", 
          rug.col = "gray",  alpha = 0.2, 
          ylim = c("common", "free"), xlabs = NULL, 
          ylabs = NULL, main = NULL, term.col = "darkred", 
          resid.col = "lightblue", resid.alpha = 0.8, 
          resid.size = 1, nrow = NULL, ncol = NULL, 
          plots.per.page = 9, one.by.one = FALSE, 
          surface.gam = FALSE, polys = NULL, 
          polys.scheme = "topo", col.ribbon = "darksalmon",
          col.shaded = "gray", ...)

Arguments

object	a gamlss fitted model
what	which distribution parameters, i.e. "mu"
parameter	which distribution parameters (equivalent to what)
data	data frame in which variables in object can be found
terms	which terms to plot (default NULL means all terms); a vector passed to lpred(..., type = "terms", terms =*)
envir	environment in which variables in object can be found
partial	logical; should partial residuals be plotted?
rug	add rug plots to the axes
rug.sides	which side the rug "b"=bottom
rug.col	the colour for the rug
alpha	the alpha for the shade
ylim	there are two options here a) "common" and b) "free". The "common"" option plots all figures with the same ylim range and therefore allows the viewer to check the relative contribution of each terms compate to the rest. In the ‘free’ option the limits are computed for each plot seperatly.
xlabs	the x label
ylabs	the y label
main	title NOT WORKING
term.col	the colour of the line for term
resid.col	the colour of the partial residuals
resid.alpha	The alpha for the partial residuals
resid.size	the size of the partial residuals
nrow	the number or rows in a mupliple plot
ncol	the number of rows in a mupliple plot
plots.per.page	the number of plots per page in multiple plots
one.by.one	whether to plot the terms one by one
surface.gam	whether to use surface plot if a ga() term is fitted
polys	for GRMF models
polys.scheme	The polygone information file for MRF models
col.ribbon	he colour of the ribbon
col.shaded	he colour of the shaded area
...	for extra argument

Value

A multiple plot

Author(s)

Mikis Stasinopoulos

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.

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/).

See Also

term.plot

Examples

data(aids)
a <- gamlss(y ~ pb(x) + qrt, data = aids, family = NBI)
fitted_terms(a, pages = 1)

---

Supporting histSmo()

Description

This function helps to plot density estimates created by the histSmo() function.

Usage

histSmo_plot(x, col_fill_bar = gray(0.5), col_bar = "pink", 
        col_line = "darkblue", width_line = 1, title, xlabel)

Arguments

x	a histSmo object
col_fill_bar	The fill colour of the bars
col_bar	the colour of the border of thebars
col_line	the colour of the lines
width_line	the width of the lines
title	title if needed
xlabel	x axis lable if needed.

Details

This function supports histSmo().

Value

A plot

Author(s)

Mikis Stasinopulos, Rober Rigby and Fernanda de Bastiani

References

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/).

See Also

histSmo

Examples

a1 <-histSmo(abdom$y)
gg1 <-histSmo_plot(a1)
gg1

---

Plotting GAIC for GAMLSS models

Description

The function model_GAIC() is similar to the function GAIC.scaled() of the package gamlss. It produces, [for a given set of different fitted models or for a table produced by chooseDist()], the scaled Akaike values (see Burnham and Anderson (2002) section 2.9 for a similar concept of the GAIC weights. The plot of the GAIC's should not be interpreted as posterior probabilities of models given the data but can be used for model selection purpose since they produce a scaled ranking of the model using their relative importance i.e. from the worst to the best model.

The function model_GAIC_lollipop() is almost identical to model_GAIC() but the result is a lollipop plot.

Usage

model_GAIC(object, ..., k = 2, c = FALSE, plot = TRUE, 
       which = 1, diff.dev = 1000, text.to.show = NULL, 
       col = "rosybrown", width = 0.9, horiz = TRUE,
       scale = c("[0,1]","[max,min]"), title)

model_GAIC_lollipop(object, ..., k = 2, c = FALSE, plot = TRUE, 
         which = 1, diff.dev = 1000, text.to.show = NULL, 
         col = "skyblue", col.point = "blue", pch.point = 19, 
         width = 0.9, horiz = TRUE, 
         scale = c("[0,1]", "[max,min]"), order.val = TRUE, title)

Arguments

object	a set of gamlss fitted model(s) or a matrix table produced by chooseDist().
...	it allows several GAMLSS object to be compared using a GAIC
k	the penalty with default k=2
c	whether the corrected AIC, i.e. AICc, should be used, note that it applies only when k=2
plot	whether to plot with default equal TRUE
which	which column of GAIC table to plot
diff.dev	this argument applies only a matrix table produced by chooseDist() and prevents models with a difference in deviance greater than diff.dev from the ‘best’ model to be considered (or plotted).
text.to.show	if NULL, model_GAIC() shows the model names otherwise the character in this list (the length of which should be equal to the length of models)
col	The colour of the bars (or lines. in the lollipop)
col.point	The colour of the points in the lollipop
pch.point	The points character in the lollipop
width	the width of the bars
horiz	whether to plot the bars horizontally (default) or vertically
scale	the scale of the plot, "[0,1]" plots the AIC's from the worst to the best models in a scale from [0,1]. "[max,min]" plots the AIC's from the worst model to the best model but in the original scale of the AIC's
title	if different title is needed
order.val	whether to order the models from the best to the worst

Details

The option allow the AIC to be plotted from worst to best on a $[0,1]$ scale using the formula i.e. $(AIC_w-AIC_m)/(AIC_w-AIC_b))$ where the $AIC_w$ and $AIC_b$ are the worst and best AIC, respectively, and $AIC_m$ is the AIC of the current model. If the option scale is set to[max,min] the difference $(AIC_w-AIC_m)$ is plotted.

Value

It returns a bar plot using package ggplot2.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

Burnham K. P. and Anderson D. R (2002). Model Selection and Multimodel Inference A Practical Information-Theoretic Approach, Second Edition, Springer-Verlag New York, Inc.

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. 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/).

See Also

GAIC.scaled

Examples

data(abdom)
m1 <- gamlss(y~x, family=NO, data=abdom)
m2 <- gamlss(y~x, sigma.fo=~x, family=NO, data=abdom)
m3 <- gamlss(y~pb(x), sigma.fo=~x, family=NO, data=abdom)
m4 <- gamlss(y~pb(x), sigma.fo=~pb(x), family=NO, data=abdom)

model_GAIC(m1,m2, m3, m4)

MT <- chooseDist(m3)
model_GAIC(MT)
model_GAIC(MT, which=2)
model_GAIC_lollipop(m1,m2, m3, m4)

---

Plotting residuals using PCA

Description

The function model_pca() plots several GAMLSS residuals using Principal Component Analysis.

Usage

model_pca(obj, ..., scale = TRUE, arrow_size = 1.5)

Arguments

obj	A gamlss object
...	for extra GAMLSS models
scale	whether to scale the residuals
arrow_size	the arrow sizw in the biplot

Details

The function model_pca() plot a biplot() plot of the residuals from different models. It uses Principal Component Analysis in the residuals of different models and plots the resuls.

Value

A biplot of the first two components is plotted.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

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/).

See Also

gamlss, resid_index

Examples

m1 <- gamlss(y~x, data=abdom)
m2 <- gamlss(y~pb(x), data=abdom)
m3 <- gamlss(y~pb(x), sigma.fo=~pb(x), data=abdom)
model_pca(m1,m2,m3)

---

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)

---

Functions to create the background for the bucket plots

Description

The functions plot the moment transformed skewness and moment transformed kurtosis of five important 4-parameter distributions in GAMLSS.

Usage

moment_gray_half(legend = FALSE)

moment_gray_both(line_width = 1)

moment_colour_half(legend = TRUE)

moment_colour_both(legend = TRUE, line_width = 1)

centile_colour_half(type = c("tail", "central"), legend = TRUE, 
                   line_width = 1)

centile_colour_both(type = c("tail", "central"), legend = TRUE, 
                   line_width = 1)

centile_gray_both(type = c("tail", "central"), legend = TRUE, 
                  line_width = 0.5)

Arguments

legend	whether legend is required
line_width	line width
type	whether to plot ‘tail’ or ‘central’ skewness and kurtosis.

Details

The functions are described in Rigby et al (2019)

Value

A plot is created.

Note

The functions are use by the bucket plot function model_mom_bucket() to create the background of the bucket plots.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda de Bastiani

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.

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., 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

momentSK, centileSK

Examples

moment_gray_half()
moment_gray_both()
moment_colour_half()
moment_colour_both()

centile_colour_both()
centile_gray_both()
centile_colour_half()

---

Plotting the fitted path of a PCR model.

Description

This function is similar to the function plot.PCR() which is used to plot the path of a fitted principal componet regression model, fitted using the function fitPCR() of the package gamlss.foreach.

Usage

pcr_coef_path(x, legend=FALSE, plot=TRUE)

pcr_path(x, parameter = c("mu", "sigma", "nu", "tau"),
          legend = FALSE, plot = TRUE)

Arguments

x	a fitted PCR object (or a fitted GAMLSS object for function pcr_path(
legend	whether legent is needed
plot	whether to plot the path
parameter	which GAMLSS parameter, between "mu", "sigma", "nu", "tau"

Value

A gg-plot.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

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.

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/).

See Also

plot.PCR

Examples

library(gamlss.foreach)
library(glmnet)
library(ggplot2)
data(QuickStartExample)
attach(QuickStartExample)
hist(y, main="(a)")
if (is.null(rownames(x))) 
  colnames(x) <- paste0("X", seq(1:dim(x)[2]))
# fitting
MM<- fitPCR(x,y, k=log(100))
pp<-pcr_coef_path(MM)
pp+ ggplot2::geom_vline(xintercept = MM$pc, colour = "gray") 
# using gamlss
m1 <- gamlss(y~pcr(x=x))
pcr_path(m1)

---

Partial Effect of a term on the parameters and predictors

Description

The function pe_param() is similar to the function getPEF() of the gamlss package. It plot the partial effect that a particular term has one of the parameters of the distribution or its predictor eta. The function pe2_param() is build for partial effects from two terms and it is suitable to display first order interactions.

Usage

pe_param(obj = NULL, term = NULL, data = NULL, n.points = 100, 
               parameter = c("mu", "sigma", "nu", "tau"), 
               type = c("parameter", "eta"), scenario = list(),  
               how = c("median", "last", "fixed"),
               col = "darkblue", linewidth = 1.3, name.obj = NULL,
               rug.plot = TRUE, rug.col = "gray", rug.size = 0.5,  
               data.plot = FALSE, data.col = "lightblue", 
               data.size = 0.1, factor.size = 15,
               data.alpha = 0.9, bins = 30, 
               filled = FALSE, ylim = NULL,
                    title) 

pe_1_param(obj = NULL, term = NULL, data = NULL, n.points = 100,  
                parameter = c("mu", "sigma", "nu", "tau"), 
                type = c("parameter", "eta"),
                how = c("median", "last", "fixed"),
                scale.from = c("mean", "median", "none"),
                scenario = list(), col = "darkblue", linewidth = 1.3,
                name.obj = NULL, data.plot = FALSE, 
                data.col = "lightblue",data.size = 0.1,
                data.alpha = 0.9, rug.plot = TRUE, rug.col = "gray",
                rug.size = 0.5, factor.size = 15,
                ylim = NULL, title) 

pe_2_param(obj = NULL, terms = NULL, data = NULL, n.points = 100, 
                parameter = c("mu", "sigma", "nu", "tau"), 
                type = c("parameter", "eta"),
                how = c("median", "last", "fixed"),
                scenario = list(), col = "darkblue",
                linewidth = 1.3, data.plot = TRUE,
                data.col = "lightblue", data.size = 0.1,
                data.alpha = 0.9,bins = 30, 
                filled = FALSE, name.obj = NULL, title) 

pe_param_grid(model, terms, maxcol = 2, maxrow = 3, ylim=NULL, ...)

Arguments

obj	a GAMLSS fitted object
model	a GAMLSS fitted model
term	the model term we want to investigate can be one i.e. "Fl" or two c("Fl", "A")
terms	a list of model terms for example list(c("Fl","A"), "H", "loc" ))
data	the data frame used otherwise it takes it from the fitted model
n.points	the number of points for the evaluation of the term
parameter	the distribution parameter in which the term is fitted
type	here you specify or the distribution parameter i.e "parameter" or its prediction, "eta"
how	how to set all the other terms in the model
scenario	this can be a list of values for the rest of the terms in the model for the distribution parameter
plot	whether to plot the result
col	the colour of the partial effect of the term
linewidth	the size of the line of partial effect of the term
bins	the number of binds for the contour plot
filled	whether to display the values in the contour
title	the title if different from the default
name.obj	this is a way to pass the name of the object
maxcol	the maximum columns in the grid plot
maxrow	the maximum rowss in the grid plot
data.plot	whether to plot the data
rug.plot	whether to print the rug bellow the figure
rug.size	the size of the rug
rug.col	the colour of the rug
data.col	the color of the data points
data.size	the size of the data points
data.alpha	the trnsparance constant of the data points
factor.size	the size of the symbol if a factor is plotted
ylim	if a common y limit is required
scale.from	whethet to substact from the mean the median or from zero
...	for passing argument from the function pe_param_grid to the function pe_param

Details

The functions pe_param() and pe_param_grid() can be used to help the use the interpretation of a GAMLSS model. The functions pe_param() provides the partial effect of one or two terms of a specified parameter of the distribution while the rest of the terms in the model are set on specific values or scenarios. The function pe_param() calls pe_1param() if the argument terms is one i.e. "Fl" or the function pe_2param() if the terms are two i.e. c("Fl"","A"). The pe_param_grid() plots multiple plots specified by the list used in the term argument.

Similar functions are pe_quantile() and pe_moment().

Value

It is plotting the partial effect or is producing the resulting function

Author(s)

Mikis Stasinopulos, Rober Rigby and Fernanda de Bastiani

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.

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/).

See Also

getPEF

Examples

m1 <- gamlss(R~pb(Fl)+pb(A)+loc+H, data=rent, gamily=GA)
pe_param(m1, "A")
pe_param(m1, c("Fl","A"), filled=TRUE)
pe_param_grid(m1, list(c("Fl","A"), c("H","loc")), filled=TRUE)
# the terms are additive no interaction

---

Partial Effect of a term on the response distribution

Description

The function pe_pdf() plots the partial effect that a specified term has on the distribution of the response.

The function pe_pdf_grid() plot multiple plots on the same page.

Usage

pe_pdf(obj = NULL, term = NULL,  from = NULL, to = NULL,
          y.grid.points = 100, x.grid.points = 10, x.values,
          data = NULL, scale = NULL, how = c("median", "last"), 
          scenario = list(), linewidth = 0.1, horizontal = TRUE, 
          col.fill = hcl.colors(lqq, palette = "viridis"), 
          alpha = 0.6, xlim = NULL, title)
      
pe_pdf_grid(model, terms, maxcol = 2, maxrow = 3, ...)

Arguments

obj, model	A GAMLSS object
term	The model term
terms	The model terms, more than one for pe_pdf_grid().
from	start from
to	end to
y.grid.points	in how many points the pdf should be evaluates
x.grid.points	in how namy points the terms should be plotted
x.values	possible x values
data	The data used for modelling
scale	This is a very importnat value for plotting correctly the fitted distrutions. If the defaul values it is not working please try different values
how	How to fixed the rest of the variables. For continuous oit takes the median fot factor the level with the highest frequency.
scenario	Alternatively scenatio for fixing the values.
linewidth	the size of the pdf line
horizontal	whether to plot the partial pdf on the x-axis and the x on the y-axix or opposite
col.fill	how to fill the pdf body
alpha	the transparency factor
xlim	the limits for plotting x-axis
title	whether to use a different tittle from the default one
maxcol	maximum of colomns in the grid for pe_pdf_grid()
maxrow	maximum of rows on the grid for pe_pdf_grid()
...	extra argument to be passed form pe_pdf() to pe_pdf_grid()

Details

The function pe_pdf() is one of the function design to help the use to interpret the GAMLSS model. Provides the partial effect that one of the continuous terms has on distribution of the response while the rest of the variables in the model are set on specific values or scenarios. Others similar functions are pe_param(), pe_moment() and pe_quantile().

Value

A plot of the conditional distribution given the term

Author(s)

Mikis Stasinopulos, Rober Rigby and Fernanda de Bastiani

References

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/).

See Also

pe_param

Examples

m1 <- gamlss(R~pb(Fl)+pb(A)+loc+H, data=rent, gamily=GA)
pe_pdf(m1, "A")
pe_pdf(m1, "A")
pe_pdf(m1, "A", horizontal=FALSE)
pe_pdf_grid(m1, c("Fl", "A", "H", "loc"))

---

Plotting the profile deviance of one fitted term

Description

Plotting the profile deviance of a fitted term in GAMLSS

Usage

prof_term(model = NULL, criterion = c("GD", "GAIC"), 
      penalty = 2.5,  from = NULL, to = NULL, 
      step = NULL, length = 7, xlabel = NULL, plot = TRUE, 
      perc = 95, start.prev = TRUE, line.col = "darkgreen", 
      dash.line.type = 3, dash.line.size = 0.8, text.size = 5, title)

Arguments

model	a GAMLSS fitted model
criterion	whether Global deviance or GAIC
penalty	the penalty k for GAIC
from	start from
to	finish at
step	using step
length	if the step is left NULL then length is considered for evaluating the grid for the parameter. It has a default value of 11.
xlabel	if a x label is required
plot	whether tto plot the function
perc	what percentage confidence interval is required
start.prev	whether to start from the previous fitted model parameters values or not (default is TRUE)
line.col	the colour of the plotting line
dash.line.type	the type of verical dash line for CI's
dash.line.size	The size of the dash lines
text.size	the size of text
title	the title

Details

This function is the ggplot2 version of the original prof.term() function.

Value

creates a plot

Author(s)

Mikis Stasinopoulos

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.

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/).

See Also

prof.term

Examples

data(aids)
# fitting a linear model
gamlss(y~x+qrt,family=NBI,data=aids)
# testing the linear beta parameter
mod<-quote(gamlss(y ~ offset(this * x) + qrt, data = aids, family = NBI))
prof_term(mod, from = .06, to=0.13)

---

Density of the residuals in a GAMLLSS model

Description

The function resid_density() plots an histogram and a density estimator of the normalised quantile residuals from a fitted GAMLSS model. The function model_density() plots density estimators of the normalised quantile residuals from more than one fitted GAMLSS models.

Usage

resid_density(obj, resid, hist.col = "black", hist.fill = "white", 
              dens.fill = "#FF6666", title)
model_density(obj, ..., title)

Arguments

obj	The function needs a GAMLSS fitted model or
resid	any standarised residual
hist.col	The colour of the border of the histogram
hist.fill	The colout of the hisogram
dens.fill	the colour of the desnsity
title	A title if needed
...	extra GAMLSS models

Details

This function resid_density() is a denity plot (similar to of the four plots produded when the plotting function plot.gamlss() is used within the gamlss package. I uses plotting function from the ggplot2 package.

Value

A density plot of the residuals is produced.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

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/).

See Also

plot.gamlss

Examples

data(abdom)
a<-gamlss(y~pb(x),family=LO,data=abdom)
b<-gamlss(y~pb(x),family=NO,data=abdom)
resid_density(a)
model_density(a,b)

---

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, ...)

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

Value

A ggplot is generated

Author(s)

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/).

See Also

resid_wp

Examples

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))

---

A residual plots

Description

The function resid_index() is plotting the residuals of a GAMLSS fitted model (or any other suitable standardised residual) against the observation number index.

The function resid_mu() plots the residuals against fitted values for mu.

The function resid_median() plots the residuals against fitted median values.

The function resid_param() plots the residuals against any of the GAMLSS fitted parameters, mu, sigma, nu, or tau.

The function resid_quantile() plots the residuals against any fitted quantile.

The function resid_xvar() plots the residuals against an explanatory term.

The function resid_plots() produces a plot similar to the one that the function plot() produce for a GAMLSS model in package gamlss. This is, four plots: a) resid_index()(b) resid_mu(), (c) resid_density() and (d) resid_qqplot().

Residuals above (or below) certain specified value are identified.

Usage

resid_index(obj, resid, plot = TRUE, value = 2, title, annotate = TRUE, 
           no.lines = FALSE)
           
resid_mu(obj, resid, plot = TRUE, value = 2, title, annotate = TRUE)

resid_median(obj, resid, plot = TRUE, value = 3, title, 
            annotate = TRUE)

resid_param(obj, param = c("mu", "sigma", "nu", "tau"), title, 
            line.col = "darkred", point.col = "steelblue4", 
            point.shape = 20)            

resid_quantile(obj, quantile = 0.5, title, newdata, 
            line.col = "darkred", point.col = "steelblue4", 
            point.shape = 20)
            
resid_plots(obj, theme = c("original", "ts", "new", "ecdf"), value = 3)

resid_xvar(obj, xvar, plot = TRUE, value = 2, title, annotate = TRUE)

Arguments

obj	a GAMLSS object
resid	or any other suitable standardised residual vector.
xvar	a continuous explanatory variable
plot	whether to plot the result
param	which GAMLSS parameter mu, sigma, nu, or tau
value	the cut off value for the identification of very large or very small residuals
annotate	whether the threshold annotation should appear or not
line.col	the colour of the line
point.col	the colour of the points
point.shape	the shape of the points
title	a title of the plot if needed
theme	what type of plots should resid_plots() used : "original" is like using plot.gamlss(), "ts" is like using plot.gamlss(,ts="TRUE") (not implemented yet), "new" it uses (a) resid_index(), (b) resid_density(), (c) resid_wp() and (d) resid_dtop().
no.lines	this option allows to hide the horizontal lines so the resulting gg-plot can be used later with say facet_wrap() see example
newdata	whether the evaluation should be in newdata or the old data points
quantile	which quantile? default the median (0.50).

Value

A plot of the residuals is returned.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

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.

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

gamlss, plot.gamlss

Examples

library(ggplot2)
data(rent)
r1<-gamlss(R~pb(Fl)+pb(A)+H+loc,family=GA,data=rent)
resid_index(r1)
resid_mu(r1)
resid_median(r1)
resid_param(r1)
resid_quantile(r1)
resid_xvar(r1, A)
resid_plots(r1)
resid_index(r1, no.lines=TRUE)+facet_wrap(~ cut_number(rent$A, 6))

---

QQ-plot of the residuals of a GAMLSS model

Description

The function resid_qqplot() produces a single QQ-plot of the residuals from a fitted GAMLSS model or any other model with suitable standardised residuals.

The function add_resid_qqplot() takes a QQ-plot created by resid_qqplot() and adds another QQ-plot from a different fitted model.

The function model_resid_qqplots() takes different fitted models and creates QQ-plots for all fitted models.

Usage

resid_qqplot(obj, resid, value = 3, points.col = "steelblue4", 
              line.col = "darkgray", check_overlap = TRUE, title)
              
add_resid_qqplot(gg, obj, value = 3, points.col = "sienna",
             line.col = "darkgray", check_overlap = TRUE, title)  
             
model_qqplot(obj, ..., line.col = "steelblue4", title)

Arguments

obj	A GAMLLS fitted model or
resid	any other residual suitable standardised.
gg	a ggplot
value	A cut off value to identify large or small residuals
points.col	the colout of the points in the plot
line.col	the colout of the line in the plot
check_overlap	if observations are identify this reduvce the cluterring
title	a title if needed it
...	extra GAMLSS models

Details

This is a stanard QQ-plot but with the advadance of able to identify large or samll residuals

Value

A QQ-plotbis created

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

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/).

See Also

plot.gamlss

Examples

data(abdom)
a<-gamlss(y~pb(x),family=LO,data=abdom)
b<-gamlss(y~pb(x),family=NO,data=abdom)
gg <- resid_qqplot(a)
add_resid_qqplot(gg, b)
model_qqplot(a,b)

---

Symmetry plots

Description

The functions resid_symmetry() and y_symmetry() plot symmtry plots for residuals and single variable, respectively.

Usage

resid_symmetry(model, title)

y_symmetry(y, title)

Arguments

model	A model which allows the function resid()
y	a single variable
title	A title for the plot if needed

Details

The function orders the data (or residuals) and takes the median minus the lower half and plot it against the upper half minus the median.

Value

The symmetry plot is produced.

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

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/).

See Also

resid_index

Examples

y <- rBCT(1000, mu=3, sigma=.1, nu=-1, tau=5)
y_hist(y)
gg <- y_symmetry(y)

---

Worm plot using ggplot2

Description

The function produces worm plot of the residuals of a fitted model. A worm plot is a de-trended normal QQ-plot so departure from normality is highlighted.

The function plot_wp() it is similar to the gamlss package function wp() when the argument xvar is not used.

Usage

resid_wp(obj, resid, value = 3, points_col = "steelblue4", 
         poly_col = "darkred", 
         check_overlap = TRUE, title, ylim)

model_wp(obj, ..., title)  

resid_wp_wrap(obj, resid, value = 3, xvar = NULL, n_inter = 4, 
         points_col = "steelblue4", poly_col = "darkred", 
         alpha_bound = 0.1, check_overlap = TRUE, title, ylim)
         
model_wp_wrap(obj, ..., xvar = NULL, value = 3, n_inter = 4, 
         points_col = "steelblue4", alpha_bound = 0.1, 
         check_overlap = TRUE, ylim, title)

Arguments

obj	a GAMLSS fitted object or any other fitted model where the resid() method works (preferably the residuals should be standardised or better normalised quantile residuals. Note for model_wp only gamlss object are accepted.)
resid	if object is missing this argument can be used to specify the residual vector (again it should a normalised quantile residual vector)
value	A cut off point to indicate large residuals, default is value=3
xvar	the x term for which the worm plot will be plotted against
n_inter	the number of intervals for continuous x-term
points_col	the color of the points in the plot
poly_col	the colour of the fitted polynomial in the plot
check_overlap	to check for overlap when plotting the observation numbers
alpha_bound	the transparency parameter for the coinfidence bound
title	required title
ylim	if the y limit should be different from the default max(y)+.1
...	extra GAMLSS models

Value

A worm plot is produced

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

van Buuren and Fredriks M. (2001) Worm plot: simple diagnostic device for modelling growth reference curves. Statistics in Medicine, 20, 1259–1277

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/).

See Also

wp

Examples

data(abdom)
# with data
a<-gamlss(y~pb(x),sigma.fo=~pb(x,1),family=LO,data=abdom)
resid_wp(a)
resid_wp(resid=resid(a))

---

Plotting the response against quantities of the fitted model

Description

All plots are of the response variable against fitted values of interest.

The function resp_mu() is the ‘original’ one plotting the response against the parameter mu. The function reports the Pearson's correlation coefficient and plot a lines (45% degrees) throught the graph.

The function resp_param() plots the response against any fitted parameter mu, sigma, nu or tau. The function also plots a smooth curve going throught the data and gives the Pearson's correlation coefficient.

The function resp_quantile() plots the response against any fitted quantile, with default the median (0.50). The function also plots a smooth curve going throught the data and gives the Pearson's correlation coefficient.

The function quantile_gamlss() is used by the function resp_quantile() to calculate the quantiles of the fitted distribution .

Usage

resp_mu(obj, title, line.col = "darkred", 
           point.col = "steelblue4", 
           point.shape = 20)
           
resp_param(obj, param = c("mu", "sigma", "nu", "tau"), 
           title, line.col = "darkred", point.col = "steelblue4", 
           point.shape = 20)

resp_quantile(obj, quantile = 0.5, title, newdata, 
           line.col = "darkred", point.col = "steelblue4", 
           point.shape = 20)

quantile_gamlss(obj, quantile = 0.5, newdata)

Arguments

obj	a GAMLSS fitted object
param	which parameters? mu, sigma, nu or tau, [only for resp_param()].
quantile	which quantile? default the median (0.50), [only for resp_quantile() and quantile_gamlss()].
title	a tittle if needed it, by default for the function fitted_resp it print the correlation coefficients between the two variable.
line.col	the colour of the line
point.col	the colour of the points
point.shape	the shape of the points
newdata	whether the evaluation should be in newdata or the old data points [only for functions resp_quantile() and quantile_gamlss() ]

Details

This is standard plot in regression where the fitted values are plotted against the response. In GAMLSS model is done by plotting the response against the fitted values of the mu model which is most case is a location parameter.

Value

A plot is returned

Note

Do not use this plot if mu is not a location parameter.

Author(s)

Mikis Stasinopulos, Rober Rigby and Fernanda de Bastiani

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.

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/).

See Also

resid_plots

Examples

m1 <- gamlss(R~pb(Fl)+pb(A)+H+loc, data=rent, family=GA )
resp_mu(m1)
resp_param(m1)
resp_quantile(m1)

---

Histogram and density plot.

Description

The function y_hist() creates a histogram and a density plot for a continuous variable.

The functions y_acf() and y_pacf() plot the autocorrolation and partial autocorrolation functions for y.

The function y_dots() is design for long tail right skewed variables. It is a plot emphasising the right tail of the distribution for such variables.

Usage

y_hist(y, data, with.density = TRUE, hist.col = "black",
         hist.fill = "white", dens.fill = "#FF6666", 
         binwidth = (max(y)-min(y))/20,  from, to, title)
         
y_acf(x, data, title)

y_pacf(x, data, title)

y_dots(y, data, value=3, point.size = 2, point.col = "gray", 
          quantile = c(.10, .50, .90),
          line.col = c("black","red", "black"),
          line.type = c("dotted", "solid",  "dotted"),
          line.size = c(1,1,1), x.axis.col = "black", 
          x.axis.line.type = "solid", seed = 123, from, to, title)

Arguments

y, x	a continuous variable
data	where to find argument y
value	value to identify outliers i.e. for upper tail an outliers is if it is greater than Q_3+value*IQ
with.density	whether a density is required, default is TRUE
hist.col	the colour of lines of the histogram
hist.fill	the colour of the histogram
dens.fill	the color of the density plot
binwidth	the binwidth for the histogram
from	where to start the histogram (you may have to change binwidth)
to	where to finish the histogram (you may have to change binwidth)
point.size	the size of the points in y_dots
point.col	the colour of the points in y_dots
quantile	the quantile values to plot in y_dots, the default is 0.10, .50 and .90
line.col	the color of the vertical lines indicating the 0.10, .50 and .90 quantiles in y_dots
line.type	the type of the verical lines indicationg the 0.10, .50 and .90 quantiles in y_dots
line.size	the size of the verical lines indication the 0.10, .50 and .90 quantiles in y_dots
x.axis.col	the colour of the x-axis
x.axis.line.type	the type of the x-axix
seed	the seed to jitter the y
title	use this for a different title

Value

A ggplot is returned

Author(s)

Mikis Stasinopoulos, Bob Rigby and Fernanda De Bastiani

References

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/).

See Also

plot.ecdf

Examples

library(ggplot2)
y <- rBCT(1000, mu=3, sigma=.1, nu=-1, tau=5)
y_hist(y)
gg <- y_hist(y, with.dens=FALSE)
gg + stat_function(fun = dBCT, args=list(mu=3, sigma=.1,  nu=-1, tau=5), 
                 colour = "black")
gg + stat_function(fun = dBCT, args=list(mu=3, sigma=.1,  nu=-1, tau=5), 
                  geom = "area", alpha=0.5, fill="pink", color="black", n=301)
                  
y_acf(diff(EuStockMarkets[,1]))    

y_dots(rent$R)

---