gamlss.inf-package {gamlss.inf}

Models for Mixed (Inflated and Adjusted) Response Variables.

Description

This package allows mixed distribution fitting in GAMLSS. A mixed distribution is one containing both continuous and discrete parts, see Chapter 5 of Stasinopoulos et al. (2017). There are some mixed distribution in the GAMLSS implementation in R like the BEINF, BEINF0, BEINF1 for data defined on [0,1] or ZAGA, ZAIG for data defined on a positive real line but the choice is very limited. This package enhance the availability of mixed distribution within the GAMLSS framework.

For historical reasons the authors use the terminology "Inflated" for models on [0,1], "Adjusted" for models on [0,Inf]. We will follow the same terminology here. So this package allows the fit of an inflated GAMLSS model when the response variable is defined in the intervals [0,1), (0,1] and [0,1] and the fit of zero adjusted models when the response variable is defined in the positive real line, (but where there are zeros in the data).

For models with inflated proportion response variables the package provides up to two extra parameters, a mass point at zero and a mass point at one. Adding an extra inflation point at zero (or at one), is equivalent to fit two separate GAMLSS models, a GAMLSS model with a continuous distribution defined at the interval (0,1), and a logit model for zero (or ones). When both zero and one are present, i.e. [0,1], a multinomial model is needed to fit the non-(0,1) part.

For the zero adjusted models with a response defined on the positive real line (but where zeros exist in the data), the actual fitting can be achieved by fitting two separate GAMLSS models one with a distribution on the real positive line and one binomial model for the zeros and non-zeros.

This package uses the two models fitting procedures but the resulting fitted object behaves like a typical GAMLSS object so a lot of standard GAMLSS diagnostics can be used with it. It also allows transformed or truncated gamlss.family distributions to be used for the continuous part of the distribution therefore giving a great flexibility of the type of mixed distribution to be used.

The functions gamlssInf0to1() and gamlssZadj() can fit the Inflated and Adjusted models, respectively, and they are described in the two vignettes available with the package.

Details

Package:	gamlss.inf
Type:	Package
Version:	1.0-1
Date:	2019-03-12
License:	GPL-2 | GPL-3

Author(s)

Marco Enea <[e-mail]>, Mikis Stasinopoulos <[e-mail]>, Bob Rigby and Abu Hossain

Maintainer: Marco Enea <[e-mail]>

References

Hossain, A., Stasinopoulos, M., Rigby, R. and Enea, M. (2015). Centile estimation for a proportion response variable. Statistics in Medicine, doi: 10.1002/sim.6748.

Ospina R. and Ferrari S. L. P. (2010) Inflated beta distributions, Statistical Papers, 23, 111-126.

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.

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, http://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. https://www.crcpress.com/Flexible-Regression-and-Smoothing-Using-GAMLSS-in-R/Stasinopoulos-Rigby-Heller-Voudouris-Bastiani/p/book/9781138197909.

See Also

gamlss

Examples

# An artificial example using simulated data in [0,1)

# Firstly, we use function gen.Family() to create 
# the logit skew student t (logitSST) distribution which is defined in the (0,1) 
# interval. Then we use function gen.Inf0to1() to create the 0-inflated logitSST 
# distribution defined in [0,1).

gen.Family("SST", "logit")
gen.Inf0to1("logitSST","Zero") 

#now we can generate the data and run the model 

set.seed(10)
Y <- rlogitSSTInf0(300,mu=0.5,sigma=0.7,nu=0.5,tau=5,xi0=0.5,log=FALSE)
m1 <- gamlssInf0to1(y=Y,mu.formula=~1,
                    sigma.formula=~1,
                    nu.formula=~1,
                    tau.formula=~1,
                    xi0.formula=~1,
                    family=logitSST,
                    trace = TRUE)
summary(m1)