fitted_cdf {gamlss.ggplots}

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)